Journal articles: 'Horndeski action'

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Mironov, S., and V. Volkova. "Properties of perturbations in beyond Horndeski theories." International Journal of Modern Physics A 33, no. 27 (September 27, 2018): 1850155. http://dx.doi.org/10.1142/s0217751x18501555.

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We study whether the approach of Deffayet et al. (DPSV) can be adopted for obtaining a derivative part of quadratic action for scalar perturbations in beyond Horndeski theories about homogeneous and isotropic backgrounds. We find that even though the method does remove the second and higher derivatives of metric perturbations from the linearized Galileon equation, in the same manner as in the general Horndeski theory, it gives incorrect result for the quadratic action. We analyze the reasons behind this property and suggest the way of modifying the approach, so that it gives valid results.

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2

Volkova, Victoria. "On perturbations in Horndeski theories." EPJ Web of Conferences 182 (2018): 02127. http://dx.doi.org/10.1051/epjconf/201818202127.

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This research has been carried out in collaboration with R. Kolevatov, S. Mironov, V. Rubakov and N. Sukhov. We study the approach suggested by Deffayet et al. for obtaining a derivative part of the quadratic action for scalar perturbations in the cubic Horndeski theory. We analyse the validity of the approach and generalize it for the complete Horndeski theory. We explicitly check that the generalized method gives the correct result.

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Helpin, Thomas, and Mikhail S. Volkov. "A metric-affine version of the Horndeski theory." International Journal of Modern Physics A 35, no. 02n03 (January 24, 2020): 2040010. http://dx.doi.org/10.1142/s0217751x20400102.

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We study the metric-affine versions of scalar-tensor theories whose connection enters the action only algebraically. We show that the connection can be integrated out, resulting in an equivalent metric theory. Specifically, we consider the metric-affine generalisations of the subset of the Horndeski theory whose action is linear in second derivatives of the scalar field. We determine the connection and find that it can describe a scalar-tensor Weyl geometry without a Riemannian frame. Still, as this connection enters the action algebraically, the theory admits the dynamically equivalent (pseudo)-Riemannian formulation in the form of an effective metric theory with an extra K-essence term. This may have interesting phenomenological applications.

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Hohmann, Manuel. "Disformal Transformations in Scalar–Torsion Gravity." Universe 5, no. 7 (July 7, 2019): 167. http://dx.doi.org/10.3390/universe5070167.

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We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, and which possesses different invariant subclasses. For the most simple of these subclasses we explicitly derive all terms that may appear in the action. We propose to study actions from this class as possible teleparallel analogues of healthy beyond Horndeski theories.

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Bernardo, Reginald Christian, Jackson Levi Said, Maria Caruana, and Stephen Appleby. "Well-tempered Minkowski solutions in teleparallel Horndeski theory." Classical and Quantum Gravity 39, no. 1 (December 8, 2021): 015013. http://dx.doi.org/10.1088/1361-6382/ac36e4.

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Abstract Well-tempering stands among the few classical methods of screening vacuum energy to deliver a late-time, low energy vacuum state. We build on the class of Horndeski models that admit a Minkowski vacuum state despite the presence of an arbitrarily large vacuum energy to obtain a much larger family of models in teleparallel Horndeski theory. We set up the routine for obtaining these models and present a variety of cases, all of which are able to screen a natural particle physics scale vacuum energy using degeneracy in the field equations. We establish that well-tempering is the unique method of utilizing degeneracy in Horndeski scalar-tensor gravity—and its teleparallel generalisation—that can accommodate self-tuned flat Minkowski solutions, when the explicit scalar field dependence in the action is minimal (a tadpole and a conformal coupling to the Ricci scalar). Finally, we study the dynamics of the well-tempered teleparallel Galileon. We generate its phase portraits and assess the attractor nature of the Minkowski vacuum under linear perturbations and through a phase transition of vacuum energy. ‘The effort to understand the Universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy.’-Steven Weinberg

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Vázquez-Báez, V., and C. Ramírez. "Quantum Cosmology of Quadratic f(R) Theories with a FRW Metric." Advances in Mathematical Physics 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/1056514.

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We study the quantum cosmology of a quadratic fR theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.

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Pardede, Kevin F. S., Agus Suroso, and Freddy P. Zen. "Nonlinear matter terms in general scalar–tensor braneworld cosmology." International Journal of Modern Physics D 28, no. 11 (August 2019): 1950138. http://dx.doi.org/10.1142/s0218271819501384.

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A five-dimensional braneworld cosmological model in general scalar–tensor action that is comprised of various Horndeski Lagrangians is considered. The Friedmann equations in the case of strongly and weakly coupled [Formula: see text] Horndeski Lagrangians have been obtained. The strongly coupled [Formula: see text] model produces the Cardassian term [Formula: see text] with [Formula: see text], which can serve as an alternative explanation for the accelerated expansion phase of the universe. Furthermore, the latest combined observational facts from BAO, CMB, SNIa, [Formula: see text] and [Formula: see text] value observation suggest that the [Formula: see text] term lies quite close to the constrained value. On the other hand, the weakly coupled [Formula: see text] case has several new correction terms which are omitted in the braneworld Einstein–Hilbert model, e.g. the cubic [Formula: see text] and the dark radiation–matter interaction term [Formula: see text]. Furthermore, this model provides a cosmological constant constructed from the bulk scalar field, requires no brane tension and supports the big bang nucleosynthesis (BBN) constraint naturally.

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van de Bruck, Carsten, and Chris Longden. "Einstein-Gauss-Bonnet Gravity with Extra Dimensions." Galaxies 7, no. 1 (March 19, 2019): 39. http://dx.doi.org/10.3390/galaxies7010039.

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We consider a theory of modified gravity possessing d extra spatial dimensions with a maximally symmetric metric and a scale factor, whose ( 4 + d ) -dimensional gravitational action contains terms proportional to quadratic curvature scalars. Constructing the 4D effective field theory by dimensional reduction, we find that a special case of our action where the additional terms appear in the well-known Gauss-Bonnet combination is of special interest as it uniquely produces a Horndeski scalar-tensor theory in the 4D effective action. We further consider the possibility of achieving stabilised extra dimensions in this scenario, as a function of the number and curvature of extra dimensions, as well as the strength of the Gauss-Bonnet coupling. Further questions that remain to be answered such as the influence of matter-coupling are briefly discussed.

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Gleyzes, Jérôme, David Langlois, and Filippo Vernizzi. "A unifying description of dark energy." International Journal of Modern Physics D 23, no. 13 (November 2014): 1443010. http://dx.doi.org/10.1142/s021827181443010x.

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We review and extend a novel approach that we recently introduced, to describe general dark energy or scalar-tensor models. Our approach relies on an Arnowitt-Deser-Misner (ADM) formulation based on the hypersurfaces where the underlying scalar field is uniform. The advantage of this approach is that it can describe in the same language and in a minimal way a vast number of existing models, such as quintessence, F(R) theories, scalar tensor theories, their Horndeski extensions and beyond. It also naturally includes Horava–Lifshitz theories. As summarized in this review, our approach provides a unified treatment of the linear cosmological perturbations about a Friedmann-Lemaître-Robertson-Walker (FLRW) universe, obtained by a systematic expansion of our general action up to quadratic order. This shows that the behavior of these linear perturbations is generically characterized by five time-dependent functions. We derive the full equations of motion in the Newtonian gauge. In the Horndeski case, we obtain the equation of state for dark energy perturbations in terms of these functions. Our unifying description thus provides the simplest and most systematic way to confront theoretical models with current and future cosmological observations.

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10

Sebastiani, Lorenzo. "Static spherically symmetric solutions in a subclass of Horndeski theories of gravity." International Journal of Geometric Methods in Modern Physics 15, no. 09 (August 8, 2018): 1850152. http://dx.doi.org/10.1142/s0219887818501529.

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In this paper, we will consider a subclass of models of Horndeski theories of gravity and we will check for several Static Spherically Symmetric solutions. We will find a model which admits an exact black hole (BH) solution and we will study its thermodynamics by using the Euclidean Action. We will see that, in analogy with the case of General Relativity (GR), the integration constant of the solution can be identified with the mass of the BH itself. Other solutions will be discussed, by posing special attention on the possibility of reproducing the observed profiles of the rotation curves of galaxies. a

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11

Kase, Ryotaro, and Shinji Tsujikawa. "Effective field theory approach to modified gravity including Horndeski theory and Hořava–Lifshitz gravity." International Journal of Modern Physics D 23, no. 13 (November 2014): 1443008. http://dx.doi.org/10.1142/s0218271814430081.

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In this paper, we review the effective field theory of modified gravity in which the Lagrangian involves three-dimensional geometric quantities appearing in the 3+1 decomposition of spacetime. On the flat isotropic cosmological background, we expand a general action up to second-order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories — including Horndeski theory/its recent generalizations and the projectable/nonprojectable versions of Hořava–Lifshitz gravity. We derive the equations of motion for linear cosmological perturbations and apply them to the calculations of inflationary power spectra as well as the dark energy dynamics in Galileon theories. We also show that our general results conveniently recover stability conditions of Hořava–Lifshitz gravity already derived in the literature.

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12

Fang, Qiong, Songbai Chen, and Jiliang Jing. "Dynamical evolution of electromagnetic perturbation in the background of a scalar hairy black hole in Horndeski theory." International Journal of Modern Physics D 28, no. 09 (July 2019): 1950112. http://dx.doi.org/10.1142/s0218271819501128.

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We have investigated dynamical evolution of electromagnetic perturbation in a scalar hairy black hole spacetime, which belongs to solutions in Horndeski theory with a logarithmic cubic term. Our results show that the parameter [Formula: see text] affects the existence of event horizon and modifies the asymptotical structure of spacetime at spatial infinity, which imprints on the quasinormal frequency of electromagnetic perturbation. Moreover, we find that the late-time tail of electromagnetic perturbation in this background depends also on the parameter [Formula: see text] due to the existence of solid angle deficit. These imply that the spacetime properties arising from the logarithmic cubic term in the action play important roles in the dynamical evolutions of the electromagnetic perturbation in the background of a scalar hairy black hole.

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13

Domènech, Guillem, Atsushi Naruko, Misao Sasaki, and Christof Wetterich. "Could the black hole singularity be a field singularity?" International Journal of Modern Physics D 29, no. 03 (February 2020): 2050026. http://dx.doi.org/10.1142/s0218271820500261.

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In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

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14

Blanco, Daniel Sobral, and Lucas Lombriser. "Exploring the self-tuning of the cosmological constant from Planck mass variation." Classical and Quantum Gravity 38, no. 23 (November 10, 2021): 235003. http://dx.doi.org/10.1088/1361-6382/ac3148.

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Abstract Recently, the variation of the Planck mass in the general relativistic Einstein–Hilbert action was proposed as a self-tuning mechanism of the cosmological constant, preventing standard model vacuum energy from freely gravitating and enabling an estimation of the magnitude of its observed value. We explore here new aspects of this proposal. We first develop an equivalent Einstein-frame formalism to the current Jordan-frame formulation of the mechanism and use this to highlight similarities and differences of self-tuning to the sequestering mechanism. We then show how with an extension of the local self-tuning action by a coupled Gauss–Bonnet term and a companion four-form field strength, graviton loops can be prevented from incapacitating the degravitation of the standard model vacuum energy. For certain cases, we furthermore find that this extension can be recast as a Horndeski scalar–tensor theory and be embedded in the conventional local self-tuning formalism. We then explore the possibility of a unification of inflation with self-tuning. The resulting equations can alternatively be used to motivate a multiverse interpretation. In this context, we revisit the coincidence problem and provide an estimation for the probability of the emergence of intelligent life in our Universe as a function of cosmic age, inferred from star and terrestrial planet formation processes. We conclude that we live at a very typical epoch, where we should expect the energy densities of the cosmological constant and matter to be of comparable size. For a dimensionless quantity to compare the emergence of life throughout the cosmic history of different universes in an anthropic analysis of the multiverse, we choose the order of magnitude difference of the evolving horizon size of a Universe to the size of its proton as the basic building block of atoms, molecules, and eventually life. For our Universe we find this number to form peak at approximately 42. We leave the question of whether the same number is frequently assumed for the emergence of life across other universes or singles out a special case to future exploration.

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15

Ageeva, Yulia, Pavel Petrov, and Valery Rubakov. "Horndeski genesis: consistency of classical theory." Journal of High Energy Physics 2020, no. 12 (December 2020). http://dx.doi.org/10.1007/jhep12(2020)107.

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Abstract Genesis within the Horndeski theory is one of possible scenarios for the start of the Universe. In this model, the absence of instabilities is obtained at the expense of the property that coefficients, serving as effective Planck masses, vanish in the asymptotics t → −∞, which signalizes the danger of strong coupling and inconsistency of the classical treatment. We investigate this problem in a specific model and extend the analysis of cubic action for perturbations (arXiv:2003.01202) to arbitrary order. Our study is based on power counting and dimensional analysis of the higher order terms. We derive the latter, find characteristic strong coupling energy scales and obtain the conditions for the validity of the classical description. Curiously, we find that the strongest condition is the same as that obtained in already examined cubic case.

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Koyama, Kazuya, Gustavo Niz, and Gianmassimo Tasinato. "Effective theory for the Vainshtein mechanism from the Horndeski action." Physical Review D 88, no. 2 (July 3, 2013). http://dx.doi.org/10.1103/physrevd.88.021502.

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17

Dialektopoulos, Konstantinos F., Jackson Levi Said, and Zinovia Oikonomopoulou. "Classification of teleparallel Horndeski cosmology via Noether symmetries." European Physical Journal C 82, no. 3 (March 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10201-7.

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AbstractTeleparallel Horndeski theory offers an avenue through which to circumvent the speed constraint of gravitational waves in an efficient manner. However, this provides an even larger plethora of models due to the increase in action terms. In this work we explore these models in the context of cosmological systems. Using Noether point symmetries, we classify the dynamical systems that emerge from teleparallel Horndeski cosmologies. This approach is very effective at selecting specific models in the general class of second-order teleparallel scalar–tensor theories, as well as for deriving exact solutions within a cosmological context. By iterating through the Lagrangians selected through the Noether symmetries, we solve for a number of cosmological systems which provides new cosmological systems to be studied.

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Bettoni, Dario, and Stefano Liberati. "Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action." Physical Review D 88, no. 8 (October 14, 2013). http://dx.doi.org/10.1103/physrevd.88.084020.

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Akama, Shingo, and Tsutomu Kobayashi. "General theory of cosmological perturbations in open and closed universes from the Horndeski action." Physical Review D 99, no. 4 (February 19, 2019). http://dx.doi.org/10.1103/physrevd.99.043522.

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Tumurtushaa, Gansukh. "Inflation with derivative self-interaction and coupling to gravity." European Physical Journal C 79, no. 11 (November 2019). http://dx.doi.org/10.1140/epjc/s10052-019-7443-7.

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Abstract We consider a subclass of Horndeski theories for studying cosmic inflation. In particular, we investigate models of inflation in which the derivative self-interaction of the scalar field and the non-minimal derivative coupling to gravity are present in the action and equally important during inflation. In order to control contributions of each term as well as to approach the single-term limit, we introduce a special relation between the derivative interaction and the coupling to gravity. By calculating observable quantities including the power spectra and spectral tilts of scalar and tensor perturbation modes, and the tensor-to-scalar ratio, we found that the tensor-to-scalar ratio is suppressed by a factor of $$(1+1/\gamma )$$(1+1/γ), where $$\gamma $$γ reflects the strength of the derivative self-interaction of the inflaton field with respect to the derivative coupling gravity. We placed observational constraints on the chaotic and natural inflation models and showed that the models are consistent with the current observational data mainly due to the suppressed tensor-to-scalar ratio.

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21

Chatzifotis, Nikos, Christoforos Vlachos, Kyriakos Destounis, and Eleftherios Papantonopoulos. "Stability of black holes with non-minimally coupled scalar hair to the Einstein tensor." General Relativity and Gravitation 54, no. 6 (May 30, 2022). http://dx.doi.org/10.1007/s10714-022-02929-0.

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AbstractGeneral relativity admits a plethora of exact compact object solutions. The augmentation of Einstein’s action with non-minimal coupling terms leads to modified theories with rich structure, which, in turn, provide non-trivial solutions with intriguing phenomenology. Thus, assessing their viability under generic fluctuations is of utmost importance for gravity theories. We consider static and spherically-symmetric solutions of a Horndeski subclass which includes a massless scalar field non-minimally coupled to the Einstein tensor. Such theory possesses second-order field equations and admits an exact black hole solution with scalar hair. Here, we study the stability of such solution under axial gravitational perturbations and find that it is linearly stable. The qualitative features of the ringdown waveform depend solely on the ratio of the two available parameters of spacetime, namely the black hole mass m and the non-minimal coupling strength $$\ell _\eta $$ ℓ η . Finally, we demonstrate the gravitational-wave ringdown transitions between three distinct patterns as the ratio $$m/\ell _\eta $$ m / ℓ η increases; a state which is dominated by photon-sphere excitations and maintains a typical quasinormal ringdown, an intermediate long-lived state which exhibits gravitational-wave echoes and, finally, a state where the ringdown and echoes are depleted rapidly to turn to an exponential tail.

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Journal articles on the topic 'Horndeski action'

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