Journal articles: 'Cosmology Mathematical models'

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Christianto, Victor, and Yunita Umniyati. "Remark on ‘The future of mathematical Cosmology” and “100 years of mathematical cosmology: Models, theories and problems, Part B” by S. Cotsakis and A.P. Yefremov." Journal of Cosmology, Filaments and Astrobiology 2, no. 1 (2022): 38–41. http://dx.doi.org/10.54216/jcfa.020105.

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In this review article, allow us to offer a few remark on “the future of mathematical cosmology” “100 years of mathematical cosmology: Models, theories and problems, Part B” by Cotsakis and Yefremov, which seems to us very interesting piece of review on progress on the last 3 or 4 decades in theoretical cosmology development. In particular, we would emphasize on testability of cosmology models, which seem to us this criterion can only be achieved via correspondence between condensed mattersuperfluiditylow temperature physics and cosmology (cf. for instance, Kibble Pickett, 2008).

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Tzvi Langermann, Y. "Arabic Cosmology." Early Science and Medicine 2, no. 2 (1997): 185–213. http://dx.doi.org/10.1163/157338297x00113.

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AbstractRepresentations of the heavens in various levels of detail can be found in a number of branches of Arabic literature. One particular genre, the hay'a texts, has as its purpose a full though non-mathematical discussion of the arrangement of the celestial orbs; hay'a writers are particularly sensitive to the philosophical requirements which all systems must meet. The pivotal work in this genre, On the Configuration, was written by Ibn al-Haytham. Later writers continued to produce works in the spirit of On the Configuration. In the east, al-Tusi and his followers developed new models; in the west, a group of thinkers tried to rediscover the models which, so they thought, were the ones endorsed by Aristotle himself.

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Elizaga Navascués, Beatriz, Mercedes Martín-Benito, and Guillermo A. Mena Marugán. "Hybrid models in loop quantum cosmology." International Journal of Modern Physics D 25, no. 08 (July 2016): 1642007. http://dx.doi.org/10.1142/s0218271816420074.

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In the framework of Loop Quantum Cosmology (LQC), inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid LQC.

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DEL CAMPO, SERGIO, RAMÓN HERRERA, and JOEL SAAVEDRA. "CLOSED INFLATIONARY UNIVERSE MODELS IN BRANE WORLD COSMOLOGY." International Journal of Modern Physics D 14, no. 05 (May 2005): 861–72. http://dx.doi.org/10.1142/s0218271805007036.

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In this article we study closed inflationary universe models proposed by Linde in a brane world cosmological context. In this scenario we determine and characterize the existence of a closed universe, in presence of one self-interacting scalar field with an inflationary stage. We have found that our model, which takes into account a Brane World Cosmology, is less restrictive than the one that uses standard Einstein's General Relativity cosmology.

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COLEY, A. A. "BRANE-WORLD COSMOLOGY." International Journal of Modern Physics D 11, no. 10 (December 2002): 1609–14. http://dx.doi.org/10.1142/s0218271802002979.

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It is argued that typically the initial singularity is isotropic in brane world cosmological models. Consequently brane cosmology naturally gives rise to a set of initial data that provide the conditions for inflation to subsequently take place, leading to a self-consistent and viable cosmological scenario.

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SAHNI, VARUN, and YURI SHTANOV. "NEW VISTAS IN BRANEWORLD COSMOLOGY." International Journal of Modern Physics D 11, no. 10 (December 2002): 1515–21. http://dx.doi.org/10.1142/s0218271802002827.

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Traditionally, higher-dimensional cosmological models have sought to provide a description of the fundamental forces in terms of a unifying geometrical construction. In this essay we discuss how, in their present incarnation, higher-dimensional "braneworld" models might provide answers to a number of cosmological puzzles including the issue of dark energy and the nature of the big bang singularity.

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MACÍAS, ALFREDO, ECKEHARD W. MIELKE, and JOSÉ SOCORRO. "SUPERSYMMETRIC QUANTUM COSMOLOGY FOR BIANCHI CLASS A MODELS." International Journal of Modern Physics D 07, no. 05 (October 1998): 701–12. http://dx.doi.org/10.1142/s0218271898000462.

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The canonical theory of [Formula: see text] supergravity, with a matrix representation for the gravitino covector–spinor, is applied to the Bianchi class A spatially homogeneous cosmologies. The full Lorentz constraint and its implications for the wave function of the universe are analyzed in detail. We found that in this model no physical states other than the trivial "rest frame" type occur.

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Stornaiolo, Cosimo. "Tomographic analysis of quantum and classical de Sitter cosmological models." International Journal of Modern Physics D 28, no. 16 (October 15, 2019): 2040009. http://dx.doi.org/10.1142/s021827182040009x.

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In this work, we show the importance of introducing the quantum tomography formalism to analyze the properties of wave functions in quantum cosmology. In particular, we examine the initial conditions of the universe proposed by various authors in the context of de Sitter’s cosmology studying their classical limit and comparing it with the classical tomogram obtained from the Hamiltonian constraint in General Relativity. This comparison gives us the opportunity to find under which conditions there is a transition from the quantum universe to the classical one. A relevant result is that in these models the decay of the cosmological constant is a sufficient condition for this transition.

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Jawad, Abdul, Shamaila Rani, Ines G. Salako, and Faiza Gulshan. "Pilgrim dark energy models in fractal universe." International Journal of Modern Physics D 26, no. 06 (November 22, 2016): 1750049. http://dx.doi.org/10.1142/s0218271817500493.

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We discuss the cosmological implications of interacting pilgrim dark energy (PDE) models (with Hubble, Granda–Oliveros and generalized ghost cutoffs) with cold dark matter ([Formula: see text]CDM) in fractal cosmology by assuming the flat universe. We observe that the Hubble parameter lies within observational suggested ranges while deceleration parameter represents the accelerated expansion behavior of the universe. The equation of state (EoS) parameter ([Formula: see text]) corresponds to the quintessence region and phantom region for different cases of [Formula: see text]. Further, we can see that [Formula: see text]–[Formula: see text] (where prime indicates the derivative with respect to natural logarithmic of scale factor) plane describes the freezing and thawing regions and also corresponds to [Formula: see text] limit for some cases of [Formula: see text] (PDE parameter). It is also noted that the [Formula: see text]–[Formula: see text] (state-finder parameters) plane corresponds to [Formula: see text] limit and also shows the Chaplygin as well as phantom/quintessence behavior. It is observed that pilgrim dark energy models in fractal cosmology expressed the consistent behavior with recent observational schemes.

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COTSAKIS, SPIROS. "STRUCTURE OF INFINITY IN COSMOLOGY." International Journal of Modern Physics D 22, no. 03 (March 2013): 1330003. http://dx.doi.org/10.1142/s0218271813300036.

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We discuss recent developments related to certain blow-up methods suitable for the analysis of cosmological singularities and asymptotics. We review results obtained in a variety of currently popular themes and describe ongoing research about universes with various kinds of extreme states, higher-order gravity and certain models of braneworlds.

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VAKILI, BABAK. "COSMOLOGY WITH MINIMAL LENGTH UNCERTAINTY RELATIONS." International Journal of Modern Physics D 18, no. 07 (July 2009): 1059–71. http://dx.doi.org/10.1142/s0218271809014935.

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We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and anti-de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory, its effects in the early universe might be expected. Adopting the existence of such a minimum length results in the generalized uncertainty principle (GUP), which is a deformed Heisenberg algebra between minisuperspace variables and their momenta operators. We extend these deformed commutating relations to the corresponding deformed Poisson algebra in the classical limit. Using the resulting Poisson and Heisenberg relations, we then construct the classical and quantum cosmology of dS and AdS models in a canonical framework. We show that in classical dS cosmology this effect yields an inflationary universe in which the rate of expansion is larger than that of the usual dS universe. Also, for the AdS model it is shown that the GUP might change the oscillatory nature of the corresponding cosmology. We also study the effects of the GUP in quantized models through approximate analytical solutions to the Wheeler–DeWitt (WD) equation, in the limit of a small scale factor for the universe, and compare the results with the ordinary quantum cosmology in each case.

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CAPOZZIELLO, SALVATORE, RUGGIERO DE RITIS, and PAOLO SCUDELLARO. "NÖTHER’S SYMMETRIES IN QUANTUM COSMOLOGY." International Journal of Modern Physics D 03, no. 03 (September 1994): 609–21. http://dx.doi.org/10.1142/s0218271894000745.

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We construct minisuperspace models for a class of theories of gravity nonminimally coupled with a scalar field. We show that when a Nöther symmetry exists, it is always possible to integrate the Wheeler-DeWitt equation and recover the semiclassical regime for the wave function of the universe. In this sense, we can interpret the Nöther symmetries as a selection rule in the philosophy of the so called Hartle criterion: when they exist, it is possible to select classical universes.

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Sadeghi, J., M. Khurshudyan, and H. Farahani. "Interacting ghost dark energy models in the higher dimensional cosmology." International Journal of Modern Physics D 25, no. 14 (December 2016): 1650108. http://dx.doi.org/10.1142/s021827181650108x.

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We investigate interacting ghost dark energy models in higher dimensional cosmology. We attempt to model dark matter within a barotropic fluid with [Formula: see text]. In this work, we consider four different models based on choosing equation of state (EoS) parameter and interaction term. We confirm that our models agree with observational data.

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Brevik, I., and A. V. Timoshkin. "Holographic cosmology with two coupled fluids in the presence of viscosity." International Journal of Geometric Methods in Modern Physics 18, no. 09 (June 11, 2021): 2150149. http://dx.doi.org/10.1142/s0219887821501498.

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We explore the cosmological models of the late-time universe based on the holographic principle, taking into account the properties of the viscosity of the dark fluid. We use the mathematical formalism of generalized infrared cutoff holographic dark energy, as presented by Nojiri and Odintsov [Covariant generalized holographic dark energy and accelerating universe, Eur. Phys. J. C 77 (2017) 528]. We consider the Little Rip, the Pseudo Rip, and a bounce exponential model, with two interacting fluids, namely dark energy and dark matter in a spatially-flat Friedmann–Robertson–Walker universe. Within these models, analytical expressions are obtained for infrared cutoffs in terms of the particle horizons. The law of conservation of energy is presented, from a holographic point of view.

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Akbarieh, Amin Rezaei, Hossein Motavalli, and Elham Nouri. "Non-canonical Chameleon cosmology." International Journal of Modern Physics D 30, no. 08 (May 12, 2021): 2150059. http://dx.doi.org/10.1142/s0218271821500590.

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One of the most important issues in modern cosmology is understanding the origin of the accelerated expansion of the universe, known as “dark energy”. The scalar–tensor model is one of the most interesting candidates for describing dark energy. In this paper, we investigate the non-canonical scalar model, which is written in the framework of Chameleon models. In this model, the scalar field is coupled to a mass density [Formula: see text] under an arbitrary [Formula: see text] coupling function. We study the cosmological aspect of this model according to its Chameleon state and we conclude that for high densities, the mass of the Chameleon field becomes larger, so its effect will not be seen in high-density areas. We also examine the dynamical behavior of this model for different coupling functions and potentials. According to the dynamic behavior of the model, we can conclude that using this model can explain the accelerated expansion of the universe. Finally, we investigate the tensor perturbations in this model and show that the mass of the gravitational waves obtained in the framework of this model can be in good agreement with the observations.

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Khlopov, Maxim Yu. "Removing the conspiracy of BSM physics and BSM cosmology." International Journal of Modern Physics D 28, no. 13 (October 2019): 1941012. http://dx.doi.org/10.1142/s0218271819410128.

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The standard model (SM) of elementary particles finds no contradictions in the experimental data, but appeals to extensions for solutions of its internal problems and physical basis of the modern cosmology. The latter is based on inflationary models with baryosynthesis and dark matter/energy that involves Physics beyond the standard model (BSM) of elementary particles. However, studies of the BSM physical basis of the modern cosmology inevitably reveals additional particle model-dependent cosmological consequences that go beyond the modern standard cosmological model. The mutual relationship of the BSM particle physics basis of the modern cosmology and the nontrivial features of the corresponding cosmological scenario are the subject of this paper.

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Díaz-Barrón, Luis Rey, Abraham Espinoza-García, S. Pérez-Payán, and J. Socorro. "Anisotropic chiral cosmology: Exact solutions." International Journal of Modern Physics D 30, no. 11 (July 8, 2021): 2150080. http://dx.doi.org/10.1142/s0218271821500802.

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In this work, we investigate the anisotropic Bianchi type I cosmological model in the chiral set-up in a twofold manner. Firstly, we consider a quintessence plus a [Formula: see text]-essence-like model, where two scalar fields but only one potential term is considered. Secondly, we look at a model where in addition to the two scalar fields the two potential terms are taken into account as well as the standard kinetic energy and the mixed term. Regarding this second model, it is shown that two possible cases can be studied: a quintom-like case and a quintessence-like case. In each of the models, we were able to find both classical and quantum analytical solutions.

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Jamal, Sameerah. "Multiscalar field models: Interaction potentials, wave functions and cosmological solutions." International Journal of Modern Physics D 29, no. 07 (May 2020): 2050046. http://dx.doi.org/10.1142/s0218271820500467.

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We consider a multiscalar tensor cosmology model described by Friedmann–Robertson–Walker (FRW) spacetime with zero spatial curvature. Three specific scalar interaction potentials that characterize the model are analyzed under a set of coordinate transformations. By implication, we solve for the wave function of the universe, reduce the dimension of the underlying Hamiltonian system and consequently, establish analytical solutions of the multiscalar model’s field equations.

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Banks, Tom, and W. Fischler. "The holographic spacetime model of cosmology." International Journal of Modern Physics D 27, no. 14 (October 2018): 1846005. http://dx.doi.org/10.1142/s0218271818460057.

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This essay outlines the Holographic Spacetime (HST) theory of cosmology and its relation to conventional theories of inflation. The predictions of the theory are compatible with observations, and one must hope for data on primordial gravitational waves or non-Gaussian fluctuations to distinguish it from conventional models. The model predicts an early era of structure formation, prior to the Big Bang. Understanding the fate of those structures requires complicated simulations that have not yet been done. The result of those calculations might falsify the model, or might provide a very economical framework for explaining dark matter and the generation of the baryon asymmetry.

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COULE, D. H. "ENTROPIC ISSUES IN CONTEMPORARY COSMOLOGY." International Journal of Modern Physics D 12, no. 06 (July 2003): 963–76. http://dx.doi.org/10.1142/s0218271803003530.

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Penrose1 has emphasized how the initial big bang singularity requires a special low entropy state. We address how recent brane cosmological schemes address this problem and whether they offer any apparent resolution. Pushing the start time back to t = -∞, or utilizing maximally symmetric AdS spaces, simply exacerbates or transfers the problem. Since the entropy of de Sitter space is S ≤ 1/Λ, using the present acceleration of the universe as a low energy (Λ ~ 10-120) inflationary stage, as in cyclic ekpyrotic models, produces a gravitational heat death after one cycle. Only higher energy driven inflation, together with a suitable, quantum gravity holography style, restriction on ab initio degrees of freedom, gives a suitable low entropy initial state. We question the suggestion that a high energy inflationary stage could be naturally reentered by Poincaré recurrence within a finite causal region of an accelerating universe. We further give a heuristic argument that the so-called eternal inflation is not consistent with the second law of thermodynamics within a causal patch.

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Wang, Deng. "Cosmology with Type II supernovae." International Journal of Modern Physics D 28, no. 08 (June 2019): 1950106. http://dx.doi.org/10.1142/s0218271819501062.

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With the recent progresses on the Type II supernovae, we attempt to investigate whether there does exist new physics beyond the standard cosmological paradigm, i.e. the cosmological constant [Formula: see text] plus cold dark matter ([Formula: see text]CDM). Constraining four alternative cosmological models with a data combination of currently available Type II supernovae calibrated by the standard color method, Type Ia supernovae, baryon acoustic oscillations (BAO), cosmic microwave background (CMB) and cosmic chronometers, at the [Formula: see text] confidence level, we find that (i) a spatially flat universe is supported for the nonflat [Formula: see text]CDM model; (ii) the constrained equation-of-state of dark energy [Formula: see text] is consistent with the [Formula: see text]CDM hypothesis for the [Formula: see text]CDM model, where [Formula: see text] is a free parameter; (iii) for the decaying vacuum model, there is no evidence of interaction between dark matter and dark energy in the dark sector of the universe; (iv) there is also no hint of dynamical dark energy for the dark energy density-parametrization scenario. It is very obvious that a larger Type II supernovae sample is required if we expect to draw definitive conclusions about the formation and evolution of the universe.

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KONSTANTINOV, M. YU, V. N. MELNIKOV, and M. NOVELLO. "NUMERICAL INVESTIGATION OF INTEGRABLE WEYL GEOMETRY IN MULTIDIMENSIONAL COSMOLOGY." International Journal of Modern Physics D 04, no. 03 (June 1995): 339–55. http://dx.doi.org/10.1142/s0218271895000260.

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The evolution of 4-dimensional and (4+D)-dimensional (D=1, 2) cosmological models based on the integrable Weyl geometry are considered numerically both for empty space-time and for scalar field with nonminimal coupling with gravity. In both cases nonsingular solutions exist only for the open exterior space and flat (with torus topology) interior space. It is shown that in the nonsingular case the scenario of dynamical dimension reduction is realized. Some characteristic features of the considered models and their possible generalizations are discussed.

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Ahmed, Nasr, Anirudh Pradhan, and F. Salama. "A new topological perspective of expanding space-times with applications to cosmology." International Journal of Geometric Methods in Modern Physics 18, no. 08 (May 12, 2021): 2150130. http://dx.doi.org/10.1142/s0219887821501309.

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We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension from a circle [Formula: see text] to the whole space [Formula: see text] and the cosmic expansion from a non-zero volume to the whole space-time in non-singular cosmological models. A topological analogy to the cosmic scale factor function has been suggested, the paper refers to the possible applications of the topological extension in mathematical physics.

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KIM, KYONG HEE, and YUN SOO MYUNG. "TEST OF PATCH COSMOLOGY WITH WMAP." International Journal of Modern Physics D 14, no. 10 (October 2005): 1813–29. http://dx.doi.org/10.1142/s0218271805007425.

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We calculate the power spectrum, spectral index, and running spectral index for inflationary patch cosmology arisen from Gauss–Bonnet braneworld scenario using the Mukhanov equation. This patch cosmology consists of Gauss–Bonnet (GB), Randall–Sundrum (RS-II), and four-dimensional (4D) cosmological models. There exist several modifications in higher order calculations. However, taking the power-law inflation by choosing different potentials depending on the model, there exist minor changes up to second order corrections. Since second order corrections are rather small in the slow-roll limit, we could not choose a desired power-law model which explains the WMAP data. Finally we discuss the reliability of high order calculations based on the Mukhanov equation by comparing the perturbed equation including 5D metric perturbations. It turns out that first order corrections are reliable, while second order corrections are not proved to be reliable.

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ANDRIANOV, ALEXANDER A., FRANCESCO CANNATA, ALEXANDER YU KAMENSHCHIK, and DANIELE REGOLI. "PHANTOM COSMOLOGY BASED ON PT SYMMETRY." International Journal of Modern Physics D 19, no. 01 (January 2010): 97–111. http://dx.doi.org/10.1142/s0218271810016269.

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We consider the PT-symmetric flat Friedmann model of two scalar fields with positive kinetic terms. While the potential of one "normal" field is taken real, that of the other field is complex. We study a complex classical solution of the system of the two Klein–Gordon equations together with the Friedmann equation. The solution for the normal field is real, while the solution for the second field is purely imaginary, realizing classically the "phantom" behavior. The energy density and pressure are real and the corresponding geometry is well defined. The Lagrangian for the linear perturbations has the correct potential signs for both the fields so that the problem of stability does not arise. The background dynamics is determined by an effective action including two real fields — one normal and one "phantom." Remarkably, the phantom phase in the cosmological evolution is transient and the Big Rip never occurs. Our model is contrasted with well known quintom models, which also include one normal and one phantom field.

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KARAMI, K., S. ASADZADEH, M. MOUSIVAND, and Z. SAFARI. "QCD MODIFIED GHOST SCALAR FIELD DARK ENERGY MODELS." International Journal of Modern Physics D 22, no. 05 (April 2013): 1350018. http://dx.doi.org/10.1142/s0218271813500181.

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Within the framework of FRW cosmology, we study the QCD modified ghost scalar field models of dark energy (DE) in the presence of both interaction and viscosity. For a spatially nonflat FRW universe containing modified ghost dark energy (MGDE) and dark matter (DM), we obtain the equation of state of MGDE, the deceleration parameter as well as a differential equation governing the MGDE density parameter. We also investigate the growth of structure formation for our model in a linear perturbation regime. Furthermore, we reconstruct both the dynamics and potentials of the quintessence, tachyon, K-essence and dilaton scalar field DE models according to the evolution of the MGDE density.

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Moniz, P. V. "Conserved Currents in Supersymmetric Quantum Cosmology?" International Journal of Modern Physics D 06, no. 05 (October 1997): 625–41. http://dx.doi.org/10.1142/s0218271897000388.

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In this paper we investigate whether conserved currents can be sensibly defined in super-symmetric minisuperspaces. Our analysis deals with k = +1 FRW and Bianchi class-A models. Supermatter in the form of scalar supermultiplets is included in the former. Moreover, we restrict ourselves to the first-order differential equations derived from the Lorentz and supersymmetry constraints. The "square-root" structure of N = 1 super-gravity was our motivation to contemplate this interesting research. We show that conserved currents cannot be adequately established except for some very simple scenarios. Otherwise, equations of the type ∇a Ja = 0 may only be obtained from Wheeler–DeWittlike equations, which are derived from the supersymmetric algebra of constraints. Two appendices are included. In Appendix A we describe some interesting features of quantum FRW cosmologies with complex scalar fields when supersymmetry is present. In particular, we explain how the Hartle–Hawking state can now be satisfactorily identified. In Appendix B we initiate a discussion about the retrieval of classical properties from supersymmetric quantum cosmologies.

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BARCELÓ, CARLOS, STEFANO LIBERATI, and MATT VISSER. "ANALOGUE MODELS FOR FRW COSMOLOGIES." International Journal of Modern Physics D 12, no. 09 (October 2003): 1641–49. http://dx.doi.org/10.1142/s0218271803004092.

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It is by now well known that various condensed matter systems may be used to mimic many of the kinematic aspects of general relativity, and in particular of curved-spacetime quantum field theory. In this essay we will take a look at what would be needed to mimic a cosmological spacetime — to be precise a spatially flat FRW cosmology — in one of these analogue models. In order to do this one needs to build and control suitable time dependent systems. We discuss here two quite different ways to achieve this goal. One might rely on an explosion, physically mimicking the big bang by an outflow of whatever medium is being used to carry the excitations of the analogue model, but this idea appears to encounter dynamical problems in practice. More subtly, one can avoid the need for any actual physical motion (and avoid the dynamical problems) by instead adjusting the propagation speed of the excitations of the analogue model. We shall focus on this more promising route and discuss its practicality.

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GUNZIG, E., and ALBERTO SAA. "QUANTUM EFFECTS AND SUPERQUINTESSENCE IN THE NEW AGE OF PRECISION COSMOLOGY." International Journal of Modern Physics D 13, no. 10 (December 2004): 2255–59. http://dx.doi.org/10.1142/s0218271804006292.

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Recent observations of Type Ia supernova at high redshifts establish that the dark energy component of the universe has (a probably constant) ratio between pressure and energy density [Formula: see text]. The conventional quintessence models for dark energy are restricted to the range -1≤w<0, with the cosmological constant corresponding to w=-1. Conformally coupled quintessence models are the simplest ones compatible with the marginally allowed superaccelerated regime (w<-1). However, they are known to be plagued with anisotropic singularities. We argue here that the extension of the classical approach to the semiclassical one, with the inclusion of quantum counterterms necessary to ensure the renormalization, can eliminate the anisotropic singularities preserving the isotropic behavior of conformally coupled superquintessence models. Hence, besides of having other interesting properties, they are consistent candidates to describe the superaccelerated phases of the universe compatible with the present experimental data.

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Benetti, Micol, Simony Santos da Costa, Salvatore Capozziello, Jailson S. Alcaniz, and Mariafelicia De Laurentis. "Observational constraints on Gauss–Bonnet cosmology." International Journal of Modern Physics D 27, no. 08 (May 30, 2018): 1850084. http://dx.doi.org/10.1142/s0218271818500840.

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We analyze a fully geometric approach to dark energy in the framework of [Formula: see text] theories of gravity, where [Formula: see text] is the Ricci curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant. The latter invariant naturally exhausts, together with [Formula: see text], the whole curvature content related to curvature invariants coming from the Riemann tensor. In particular, we study a class of [Formula: see text] models with power law solutions and find that, depending on the value of the geometrical parameter, a shift in the anisotropy peaks position of the temperature power spectrum is produced, as well as an increasing in the matter power spectrum amplitude. This fact could be extremely relevant to fix the form of the [Formula: see text] model. We also perform an MCMC analysis using both Cosmic Microwave Background data by the Planck (2015) release and the Joint Light-Curve Analysis of the SNLS–SDSS collaborative effort, combined with the current local measurements of the Hubble value, [Formula: see text], and galaxy data from the Sloan Digital Sky Survey (BOSS CMASS DR11). We show that such a model can describe the CMB data with slightly high [Formula: see text] values, and the prediction on the amplitude matter spectrum value is proved to be in accordance with the observed matter distribution of the universe. At the same time, the value constrained for the geometric parameter implies a density evolution of such a component that is growing with time.

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GALIAKHMETOV, A. M. "SPATIALLY FLAT FRW MODELS WITH A NONMINIMALLY COUPLED GHOST SCALAR FIELD AND PERFECT FLUID IN EINSTEIN–CARTAN THEORY." International Journal of Modern Physics D 21, no. 01 (January 2012): 1250001. http://dx.doi.org/10.1142/s0218271812500010.

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Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat Friedmann cosmologies with a nonminimally coupled ghost scalar field and perfect fluid. It is shown that both singular and bouncing models are possible. An analogous problem is investigated in general relativity. Some effects of torsion are elucidated. The role of perfect fluid in the Einstein–Cartan cosmology is discussed.

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ALTSHULER, B. L., A. M. BOYARSKY, and A. YU NERONOV. "THE PROBLEM OF CLASSICAL LIMIT IN QUANTUM COSMOLOGY: THE EFFECTIVE ACTION LANGUAGE." International Journal of Modern Physics D 05, no. 06 (December 1996): 869–84. http://dx.doi.org/10.1142/s0218271896000527.

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The tool of functional averaging over some “large” diffeomorphisms is used to describe quantum systems with constraints, in particular quantum cosmology, in the language of quantum Effective. Action. Simple toy models demonstrate a supposedly general phenomenon: the presence of a constraint results in “quantum repel” from the classical mass shell.

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Mijić, Milan. "Quantum Squeezing and Late Time Classical Behavior of Massive Fields in Expanding Robertson–Walker Universe." International Journal of Modern Physics D 06, no. 04 (August 1997): 505–14. http://dx.doi.org/10.1142/s0218271897000303.

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A Schroedinger picture analysis of time dependent quantum oscillators, in a manner of Guth and Pi, clearly identifies two physical mechanisms for possible decoherence of vacuum fluctuations in the early universe: turning of quantum oscillators upside-down, and rapid squeezing of upside-right oscillators so that certain squeezing factor diverges. In inflationary cosmology the former mechanism explains the stochastic evolution of light inflatons and the classical nature of density perturbations in most of the inflationary models, while the later one is responsible for the classical evolution of relatively heavy fields, with masses in a narrow range above the Hubble parameter: [Formula: see text]. The same method may be applied to the study of the decoherence of quantum fluctuations in any Robertson–Walker cosmology.

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ALLEMANDI, GIANLUCA, and MAURO FRANCAVIGLIA. "THE VARIATIONAL APPROACH TO ALTERNATIVE THEORIES OF GRAVITY." International Journal of Geometric Methods in Modern Physics 04, no. 01 (February 2007): 1–23. http://dx.doi.org/10.1142/s0219887807001965.

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This paper is based on lectures given in Ladek-Zdroj, Poland during the 42nd edition of the Karpac winter school on Theoretical Physics. The aim of these lectures was to give an introduction to a rigorous, mathematically well based, variational approach to alternative theories of Gravity, in view of their very interesting recent applications in the framework of Cosmology. We discuss alternative theories of Gravity both in the metric, purely affine and Palatini formalism, stressing differences and analogies both from a physical and mathematical viewpoint. Moreover we give and introduction to almost all the alternative theories of Gravity, that have been recently studied in view of their physical interest (higher order theories of Gravity, including Lovelock and Chern-Simons Lagrangians). Finally we skip to one of the most striking recent applications of alternative theories of Gravity in the framework of cosmological models: alternative theories of Gravity have been proven to provide a consistent model for accelerating universes.

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El Hanafy, W., and G. G. L. Nashed. "Lorenz gauge fixing of f(T) teleparallel cosmology." International Journal of Modern Physics D 26, no. 14 (December 2017): 1750154. http://dx.doi.org/10.1142/s0218271817501541.

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In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or [Formula: see text]CDM as separate scenarios. We reconstruct the [Formula: see text] gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and Standard Model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular [Formula: see text] gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.

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ALVARENGA, F. G., A. B. BATISTA, and J. C. FABRIS. "DOES QUANTUM COSMOLOGY PREDICT A CONSTANT DILATONIC FIELD?" International Journal of Modern Physics D 14, no. 02 (February 2005): 291–307. http://dx.doi.org/10.1142/s0218271805005955.

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Quantum cosmology may permit to determine the initial conditions of the Universe. In particular, it may select a specific model between many possible classical models. In this work, we study a quantum cosmological model based on the string effective action coupled to matter. The Schutz's formalism is employed in the description of the fluid. A radiation fluid is considered. In this way, a time coordinate may be identified and the Wheeler–DeWitt equation reduces in the minisuperspace to a Schrödinger-like equation. It is shown that, under some quite natural assumptions, the expectation values indicate a null axionic field and a constant dilatonic field. At the same time the scale factor exhibits a bounce revealing a singularity-free cosmological model. In some cases, the mininum value of the scale factor can be related to the value of gravitational coupling.

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Chakraborty, Subenoy, and Arabinda Ghosh. "Brans–Dicke Cosmology—A Generalization in Four and Five Dimensional Space-time Models." Physica Scripta 68, no. 1 (January 1, 2003): 98–100. http://dx.doi.org/10.1238/physica.regular.068a00098.

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Zecca, Antonio. "Models of H-atom in Lemaitre Tolman Bondi cosmology from Dirac equation with `curved' Coulomb potential." Advanced Studies in Theoretical Physics 16, no. 3 (2022): 121–30. http://dx.doi.org/10.12988/astp.2022.91877.

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Rabha, Chayanika, and Sanjeev Kalita. "Cosmic expansion with curved dark energy cosmology: Inevitability of cosmic doomsday." International Journal of Modern Physics D 30, no. 07 (April 8, 2021): 2150048. http://dx.doi.org/10.1142/s0218271821500486.

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In this work, we have constructed deceleration–acceleration and future evolution of cosmic expansion with curved dynamical dark energy models. Closed and open spatial curvatures are calculated by assuming that dark energy density does not exceed 85% of the closure density and by obtaining lower bounds on the ratio of dark energy to matter density, in terms of equation of state of dark energy. The range of transition epoch [Formula: see text] realized for spatial curvature [Formula: see text] is consistent with model independent estimations coming from galactic ages, strong lensing, Type Ia supernovae and recent constraints coming from [Formula: see text] measurements in non-flat dynamical dark energy models. Two novel parametrizations of dark energy equation of state namely the logarithmic and oscillatory, which are singularity free at future point [Formula: see text] are used to study the deceleration parameter q(z). Irrespective of spatial curvature, cosmic doomsday has been found inevitable for both the parametrizations. The time evolution of logarithmic parametrization, being reminiscent of a quintom field (canonical[Formula: see text]phantom), is converted into dynamics of a canonical quintessence and a phantom field for the redshift range ([Formula: see text],[Formula: see text]) and ([Formula: see text], [Formula: see text]). It is found that irrespective of spatial curvature, the quintessence component becomes sub-dominant in future giving it’s way to the phantom component.

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Padilla, Luis E., Luis O. Tellez, Luis A. Escamilla, and Jose Alberto Vazquez. "Cosmological Parameter Inference with Bayesian Statistics." Universe 7, no. 7 (June 28, 2021): 213. http://dx.doi.org/10.3390/universe7070213.

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Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the ΛCDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.

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Desgrange, Célia, Asta Heinesen, and Thomas Buchert. "Dynamical spatial curvature as a fit to Type Ia supernovae." International Journal of Modern Physics D 28, no. 11 (August 2019): 1950143. http://dx.doi.org/10.1142/s0218271819501438.

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Few statements in cosmology can be made without assuming a cosmological model within which to interpret data. Statements about cosmic acceleration are no exception to this rule, and the inferred positive volume acceleration of our universe often quoted in the literature is valid in the context of the standard Friedmann–Lemaître–Robertson–Walker (FLRW) class of spacetimes. Using the Joint Light-curve Analysis (JLA) catalogue of supernovae Type Ia (SNIa), we examine the fit of a class of exact scaling solutions with dynamical spatial curvature formulated in the framework of a scalar averaging scheme for relativistic inhomogeneous spacetimes. In these models, global volume acceleration may emerge as a result of the nonlocal variance between expansion rates of clusters and voids, the latter gaining volume dominance in the late-epoch universe. We find best-fit parameters for a scaling model of backreaction that are reasonably consistent with previously found constraints from SNIa, CMB, and baryon acoustic oscillations data. The quality of fit of the scaling solutions is indistinguishable from that of the ΛCDM model and the timescape cosmology from an Akaike Information Criterion (AIC) perspective. This indicates that a broad class of models can account for the [Formula: see text] expansion history.

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SOURADEEP, TARUN. "COSMOLOGICAL QUESTS IN THE CMB SKY." International Journal of Modern Physics D 15, no. 10 (October 2006): 1725–42. http://dx.doi.org/10.1142/s0218271806009066.

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Observational cosmology has indeed made a very rapid progress in recent years. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation measurements of CMB anisotropy and, more recently, polarization has played a very important role. Besides precise determination of various parameters of the "standard" cosmological model, observations have also established some important basic tenets that underlie models of cosmology and structure formation in the universe — "acausally" correlated initial perturbations in a flat, statistically isotropic universe, adiabatic nature of primordial density perturbations. These are consistent with the expectation of the paradigm of inflation and the generic prediction of the simplest realization of inflationary scenario in the early universe. Further, gravitational instability is the established mechanism for structure formation from these initial perturbations. In the next decade, future experiments promise to strengthen these deductions and uncover the remaining crucial signature of inflation — the primordial gravitational wave background.

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Momeni, Davood, and Ratbay Myrzakulov. "Cosmological reconstruction of f(T, 𝒯) gravity." International Journal of Geometric Methods in Modern Physics 11, no. 08 (September 2014): 1450077. http://dx.doi.org/10.1142/s0219887814500777.

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Motivated by the newly proposal for gravity as the effect of the torsion scalar T and trace of the energy momentum tensor 𝒯, we investigate the cosmological reconstruction of different models of the Universe. Our aim here is to show that how this modified gravity model, f(T, 𝒯) is able to reproduce different epochs of the cosmological history. We explicitly show that f(T, 𝒯) can be reconstructed for ΛCDM as the most popular and consistent model. Also we study the mathematical reconstruction of f(T, 𝒯) for a flat cosmological background filled by two fluids mixture. Such model describes phantom–non-phantom era as well as the purely phantom cosmology. We extend our investigation to more cosmological models like perfect fluid, Chaplygin gas and massless scalar field. In each case we obtain some specific forms of f(T, 𝒯). These families of f(T, 𝒯) contain arbitrary function of torsion and trace of the energy momentum.

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KRASIŃSKI, ANDRZEJ, and KRZYSZTOF BOLEJKO. "EXACT INHOMOGENEOUS MODELS AND THE DRIFT OF LIGHT RAYS INDUCED BY NONSYMMETRIC FLOW OF THE COSMIC MEDIUM." International Journal of Modern Physics D 22, no. 06 (April 28, 2013): 1330013. http://dx.doi.org/10.1142/s0218271813300139.

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After introducing the Szekeres and Lemaître–Tolman cosmological models, the real-time cosmology program is briefly mentioned. Then, a few widespread misconceptions about the cosmological models are pointed out and corrected. Investigation of null geodesic equations in the Szekeres models shows that observers in favorable positions would see galaxies drift across the sky at a rate of up to 10-6 arc s per year. Such a drift would be possible to measure using devices that are under construction; the required time of monitoring would be ≈10 years. This effect is zero in the FLRW models, so it provides a measure of inhomogeneity of the Universe. In the Szekeres models, the condition for zero drift is zero shear. But in the shearfree normal models, the condition for zero drift is that, in the comoving coordinates, the time dependence of the metric completely factors out.

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Schmidt, H. J. "BOOK REVIEW: Modern Mathematical Models of Time and Their Applications to Physics and Cosmology edited by W. Tifft and W. Cocke." General Relativity and Gravitation 33, no. 8 (August 2001): 1425. http://dx.doi.org/10.1023/a:1012017910820.

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Avetisyan, Zhirayr G. "A unified mode decomposition method for physical fields in homogeneous cosmology." Reviews in Mathematical Physics 26, no. 03 (April 2014): 1430001. http://dx.doi.org/10.1142/s0129055x14300015.

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The methods of mode decomposition and Fourier analysis of classical and quantum fields on curved spacetimes previously available mainly for the scalar field on Friedman–Robertson–Walker (FRW) spacetimes are extended to arbitrary vector bundle fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. The limits of applicability and uniqueness of mode decomposition by separation of the time variable in the field equation are found. It is shown how mode decomposition can be naturally extended to weak solutions of the field equation under some analytical assumptions. It is further shown that these assumptions can always be fulfilled if the vector bundle under consideration is analytic. The propagator of the field equation is explicitly mode decomposed. A short survey on the geometry of the models considered in mathematical cosmology is given and it is concluded that practically all of them can be represented by a semidirect homogeneous vector bundle. Abstract harmonic analytical Fourier transform is introduced in semidirect homogeneous spaces and it is explained how it can be related to the spectral Fourier transform. The general form of invariant bi-distributions on semidirect homogeneous spaces is found in the Fourier space which generalizes earlier results for the homogeneous states of the scalar field on FRW spacetimes.

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REN, JIE, and XIN-HE MENG. "TACHYON FIELD-INSPIRED DARK ENERGY AND SUPERNOVAE CONSTRAINTS." International Journal of Modern Physics D 17, no. 12 (November 2008): 2325–35. http://dx.doi.org/10.1142/s0218271808013893.

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The tachyon field in cosmology is studied in this paper by applying the generating function method to obtain exact solutions. The equation of state parameter of the tachyon field is [Formula: see text], which can be expressed as a function in terms of the redshift z. Based on these solutions, we propose some tachyon-inspired dark energy models to explore the properties of the corresponding cosmological evolution. The explicit relations between the Hubble parameter and redshift enable us to test the models with SNe Ia data sets easily. In this paper, we employ the SNe Ia data with the parameter [Formula: see text] measured from the SDSS and the shift parameter [Formula: see text] from WMAP observations to constrain the parameters in our models.

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Burde, Georgy I. "Cosmological models based on relativity with a privileged frame." International Journal of Modern Physics D 29, no. 06 (April 2020): 2050038. http://dx.doi.org/10.1142/s0218271820500388.

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Cosmological models, stemming from the extension of the “special relativity (SR) with a privileged frame” to general relativity (GR), are developed and fitted to the observational data. The framework termed “SR with a privileged frame” incorporates the privileged frame into SR while retaining the fundamental spacetime symmetry which, in the standard SR, manifests itself as Lorentz invariance. The correspondingly modified GR, like the standard GR, is based on the equivalence principle but with the properly modified spacetime local symmetry in which an invariant combination differs from the Minkowski interval of the standard SR. Applying the modified GR to cosmology yields the luminosity distance — redshift relation corrected such that the observed deceleration parameter can be negative as it is obtained from the data for Type Ia supernovae. Thus, the observed negative values of the deceleration parameter can be explained within the matter-dominated Friedman–Robertson–Walker (FRW) cosmological model of the universe without introducing the dark energy. A number of other observations, such as Baryon Acoustic Oscillations and Cosmic Microwave Background, also can be well fit to the cosmological model arising from the GR based on the SR with a privileged frame.

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Chetry, Binod, Jibitesh Dutta, and Wompherdeiki Khyllep. "Thermodynamics of scalar field models with kinetic corrections." International Journal of Modern Physics D 28, no. 15 (November 2019): 1950163. http://dx.doi.org/10.1142/s0218271819501633.

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In this work, we compare the thermodynamical viability of two types of noncanonical scalar field models with kinetic corrections: the square kinetic and square root kinetic corrections. In modern cosmology, the generalized second law of thermodynamics (GSLT) plays an important role in deciding thermodynamical compliance of a model as one cannot consider a model to be viable if it fails to respect GSLT. Hence, for comparing thermodynamical viability, we examine the validity of GSLT for these two models. For this purpose, by employing the Unified first law (UFL), we calculate the total entropy of these two models in apparent and event horizons. The validity of GSLT is then examined from the autonomous systems as the original expressions of total entropy are very complicated. Although, at the background level, both models give interesting cosmological dynamics, however, thermodynamically we found that the square kinetic correction is more realistic as compared to the square root kinetic correction. More precisely, the GSLT holds for the square kinetic correction throughout the evolutionary history except only during the radiation epoch where the scalar field may not represent a true description of the matter content. On the other hand, the square root kinetic model fails to satisfy the GSLT in major cosmological eras.

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Endress, Gerhard. "Averroes' De Caelo Ibn Rushd's Cosmology in his Commentaries on Aristotle's On the Heavens." Arabic Sciences and Philosophy 5, no. 1 (March 1995): 9–49. http://dx.doi.org/10.1017/s0957423900001934.

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Averroes defended philosophy by returning to the true Aristotle. For this purpose, Aristotle's book “On the Heaven,” in which he explained the eternity, uniqueness and movement of the universe, occupied a place of special importance. But the Aristotelian philosopher had a hard time holding his own in the face of contradictions within the book and with respect to Aristotle's later works. In his early Compendium, later Paraphrase, and final Long Commentary of De Caelo, Ibn Rushd continued the efforts of the Hellenistic commentators in order to integrate all the elements of his doctrine into a unified system, to harmonize his early cosmology with his later Metaphysics – the early doctrine of natural movement of the elements, and of the self-moving star-souls (a Platonic element), with the doctrine of potency and actuality and the theory of the First Mover – and to uphold his models of homocentric planetary spheres against the mathematical paradigm of Ptolemaic astronomy. By insisting throughout on demonstrative arguments based on rational principles, he asserted the philosophers' claim to irrefutable truth.

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Journal articles on the topic 'Cosmology Mathematical models'

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