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Статті в журналах з теми "THEORIES OF GRAVITY"

1

Alani, Ivo, and Osvaldo P. Santillán. "Cosmological singularity theorems forf(R) gravity theories." Journal of Cosmology and Astroparticle Physics 2016, no. 05 (May 10, 2016): 023. http://dx.doi.org/10.1088/1475-7516/2016/05/023.

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2

Souza, Cynelle Olívia de. "Complements to Gravity Theories." International Journal of Innovative Science and Research Technology 5, no. 7 (July 31, 2020): 673–78. http://dx.doi.org/10.38124/ijisrt20jul535.

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Gravity, electricity, magnetism and strong and weak nuclear forces form the fundamental energies and force fields for the organization of matter in the universe. All visible matter emits electromagnetic waves at specific frequencies; dark matter does not emit them. It is assumed, or else, that it can be formed by particles like the neutrino, which subtly interact with electromagnetic waves and with matter. Under the action of strong energy, the neutrino can theoretically reach speeds greater than that of light. Such an effect can occur when this particle becomes detached from electromagnetic interference, which is very difficult to observe. Sound also participates in the transport of matter and energy and can participate as the main means of coupling neutrinos and transmitting their information.
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3

Capozziello, Salvatore, and Mariafelicia De Laurentis. "Extended Theories of Gravity." Physics Reports 509, no. 4-5 (December 2011): 167–321. http://dx.doi.org/10.1016/j.physrep.2011.09.003.

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4

Flanagan, Éanna É. "Higher-order gravity theories and scalar–tensor theories." Classical and Quantum Gravity 21, no. 2 (December 4, 2003): 417–26. http://dx.doi.org/10.1088/0264-9381/21/2/006.

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5

Myrzakulov, Nurgissa, Ratbay Myrzakulov, and Lucrezia Ravera. "Metric-Affine Myrzakulov Gravity Theories." Symmetry 13, no. 10 (October 3, 2021): 1855. http://dx.doi.org/10.3390/sym13101855.

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In this paper, we review the so-called Myrzakulov Gravity models (MG-N, with N = I, II, …, VIII) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lemaître–Robertson–Walker background to study cosmological aspects and applications. Historical motivation for this research is thoroughly reviewed and specific physical motivations are provided for the aforementioned family of alternative theories of gravity.
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6

Heisenberg, Lavinia. "Scalar-vector-tensor gravity theories." Journal of Cosmology and Astroparticle Physics 2018, no. 10 (October 29, 2018): 054. http://dx.doi.org/10.1088/1475-7516/2018/10/054.

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Langlois, David, Michele Mancarella, Karim Noui, and Filippo Vernizzi. "Mimetic gravity as DHOST theories." Journal of Cosmology and Astroparticle Physics 2019, no. 02 (February 15, 2019): 036. http://dx.doi.org/10.1088/1475-7516/2019/02/036.

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8

Day, Charles. "Testing theories of modified gravity." Physics Today 70, no. 3 (March 2017): 21. http://dx.doi.org/10.1063/pt.3.3485.

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9

ISENBERG, JAMES A. "WAVELESS APPROXIMATION THEORIES OF GRAVITY." International Journal of Modern Physics D 17, no. 02 (February 2008): 265–73. http://dx.doi.org/10.1142/s0218271808011997.

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The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.
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Sotiriou, Thomas P., and Valerio Faraoni. "f(R)theories of gravity." Reviews of Modern Physics 82, no. 1 (March 1, 2010): 451–97. http://dx.doi.org/10.1103/revmodphys.82.451.

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Дисертації з теми "THEORIES OF GRAVITY"

1

Sbisa, Fulvio. "Modified theories of gravity." Thesis, University of Portsmouth, 2013. https://researchportal.port.ac.uk/portal/en/theses/modified-theories-of-gravity(3b9310e3-5d97-4e48-aa05-0444d1e89363).html.

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Анотація:
The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. This unexpected conclusion can be explained assuming the presence of a non-vanishing yet extremely fine tuned cosmological constant, or invoking the existence of an exotic source of energy, dark energy, which is not observed in laboratory experiments yet seems to dominate the energy budget of the Universe. On the other hand, it may be that these observations are just signalling the fact that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In order to study if the latter explanation is correct, we have to formulate new theories of the gravitational interaction, and see if they admit cosmological solutions which fit the observational data in a satisfactory way. Quite generally, modifying General Relativity introduces new degrees of freedom, which are responsible for the different large distance behaviour. On one hand, often these new degrees of freedom have negative kinetic energy, which implies that the theory is plagued by ghost instabilities. On the other hand, for a modified gravity theory to be phenomenologically viable it is necessary that the extra degrees of freedom are efficiently screened on terrestrial and astrophysical scales. One of the known mechanisms which can screen the extra degrees of freedom is the Vainshtein mechanism, which involves derivative self-interaction terms for these degrees of freedom. In this thesis, we consider two different models, the Cascading DGP and the dRGT massive gravity, which are candidates for viable models to modify gravity at very large distances. Regarding the Cascading DGP model, we consider the minimal (6D) set-up and we perform a perturbative analysis at first order of the behaviour of the gravitational field and of the branes position around background solutions where pure tension is localized on the 4D brane. We consider a specific realization of this set-up where the 5D brane can be considered thin with respect to the 4D one. We show that the thin limit of the 4D brane inside the (already thin) 5D brane is well defined, at least for the configurations that we consider, and confirm that the gravitational field on the 4D brane is finite for a general choice of the energymomentum tensor. We also confirm that there exists a critical tension which separates background configurations which possess a ghost among the perturbation modes, and background configurations which are ghost-free. We find a value for the critical tension which is different from the value which has been obtained in the literature; we comment on the difference between these two results, and perform a numeric calculation in a particular case where the exact solution is known to support the validity of our analysis. Regarding the dRGT massive gravity, we consider the static and spherically symmetric solutions of these theories, and we investigate the effectiveness of the Vainshtein screening mechanism. We focus on the branch of solutions in which the Vainshtein mechanism can occur, and we truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all non-linearities of the mode which is involved in the screening. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. Moreover, we analyze in detail in which cases the solutions match in an intermediate region. We show that asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while non asymptotically flat solutions can connect both with inner solutions which display the Vainshtein mechanism, or with solutions which display a self-shielding behaviour of the gravitational field. We show furthermore that there are some regions in the parameter space of the theory where global solutions do not exist, and characterize precisely in which regions the Vainshtein mechanism takes place.
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2

Clifton, Timothy. "Alternative theories of gravity." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612712.

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3

Sbisa', F. "MODIFIED THEORIES OF GRAVITY." Doctoral thesis, Università degli Studi di Milano, 2013. http://hdl.handle.net/2434/214951.

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The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. This unexpected conclusion can be explained assuming the presence of a non-vanishing yet extremely fine tuned cosmological constant, or invoking the existence of an exotic source of energy, dark energy, which is not observed in laboratory experiments yet seems to dominate the energy budget of the Universe. On the other hand, it may be that these observations are just signalling the fact that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In order to study if the latter explanation is correct, we have to formulate new theories of the gravitational interaction, and see if they admit cosmological solutions which fit the observational data in a satisfactory way. A necessary condition for the viability of a theory of ``modified gravity'' is that it has to reproduce to high precision the results of General Relativity in experimental setups where the latter is well tested. Quite in general, modifying General Relativity introduces new degrees of freedom, which are responsible for the different large distance behavior. For a modified gravity theory to be phenomenologically viable, it is necessary that the extra degrees of freedom are efficiently screened on terrestrial and astrophysical scales. One of the known mechanisms which can screen the extra degrees of freedom is known as the Vainshtein mechanism, which involves derivative self-interaction terms for these degrees of freedom. In this thesis, we consider a class of nonlinear massive gravity theories known as dGRT Massive Gravity. These theories are candidates as viable models to modify gravity at very large distances, and, apart from the mass, they contain two free parameters. We investigate the effectiveness of the Vainshtein screening mechanism in this class of theories. There are two branches of static and spherically symmetric solutions, and we consider only the branch in which the Vainshtein mechanism can occur. We truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak f\mbox{}ield limit for the gravitational potentials, while keeping all non-linearities of the mode which is involved in the screening. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. We analyze in detail in which cases the solutions match in an intermediate region. Asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while non asymptotically flat solutions can connect both with inner solutions which display the Vainshtein mechanism, or with solutions which display a self-shielding behaviour of the gravitational field. We show furthermore that there are some regions in the parameter space where global solutions do not exist, and characterise precisely in which regions of the phase space the Vainshtein mechanism takes place.
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4

Gullu, Ibrahim. "Massive Higher Derivative Gravity Theories." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613975/index.pdf.

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Анотація:
In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in D dimensional (Anti)-de Sitter and flat spacetimes for the most general quadratic curvature theory augmented with the Pauli-Fierz mass term. From the amplitude expression, the Newtonian potential energies are calculated for various cases. Also, from this amplitude and the propagator structure, a three dimensional unitary theory is identified. In the second part of the thesis, the found three dimensional unitary theory is studied in more detail from a canonical point of view. The general higher order action is written in terms of gauge-invariant functions both in flat and de Sitter backgrounds. The analysis is extended by adding static sources, spinning masses and the gravitational Chern-Simons term separately to the theory in the case of flat spacetime. For all cases the microscopic spectrum and the masses are found. In the discussion of curved spacetime, the masses are found in the relativistic and non-relativistic limits. In the Appendix, some useful calculations that are frequently used in the bulk of the thesis are given.
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5

Bahamonde, Sebastian. "Modified teleparallel theories of gravity." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10055604/.

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Teleparallel gravity is an alternative formulation of gravity which has the same field equations as General Relativity (GR), therefore, it is also known as the Teleparallel equivalent of General Relativity (TEGR). This theory is a gauge theory of the translations with the torsion tensor being non-zero but with a vanishing curvature tensor, hence, the manifold is globally flat. An interesting approach for understanding the late-time accelerating behaviour of the Universe is called modified gravity where GR is extended or modified. In the same spirit, since TEGR is equivalent to GR, one can consider its modifications and study if they can describe the current cosmological observations. This thesis is devoted to studying several modified Teleparallel theories of gravity with emphasis on late-time cosmology. Those Teleparallel theories are in general different to the modified theories based on GR, but one can relate and classify them accordingly. Various Teleparallel theories are presented and studied such as Teleparallel scalar-tensor theories, quintom models, Teleparallel non-local gravity, and f(T,B) gravity and its extensions (coupled with matter, extensions of new GR and Gauss-Bonnet) where T is the scalar torsion and B is the boundary term which is related with the Ricci scalar via R=-T+B.
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6

Michele, Oliosi. "New viable theories of modified gravity : Minimal Theories and Quasidilaton." Kyoto University, 2019. http://hdl.handle.net/2433/244509.

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7

German, Velarde G. "Aspects of gravity and supergravity theories." Thesis, University of Oxford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380006.

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8

Uddin, Kotub. "The viability of modified gravity theories." Thesis, Queen Mary, University of London, 2009. http://qmro.qmul.ac.uk/xmlui/handle/123456789/386.

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This thesis studies the viability of classes of modified gravity (MG) theories based on generalisations of the Einstein-Hilbert action. Particular emphasis is given to f(R) theories in both the metric and Palatini formalisms, scalar-tensor theories and generalised Gauss-Bonnet theories. An urgent task at present is to devise stringent tests in order to reduce the range of candidate models based on these theories. In this thesis a detailed study is made of the viability of these models using constraints from requirement of stability, background cosmological dynamics, local gravity constraints (LGC) and matter density perturbations. In each case the conditions required for stability and viability of the background dynamics are presented. In the case of generalised Gauss-Bonnet theories the circumstances leading to the existence and stability of cosmological scaling solutions are established. In the scalar-tensor theories considered here, which includes metric-f(R) theories as a special case, there is a strong coupling of the scalar field to matter in the Einstein frame which violates all LGC. It is shown that using a chameleon mechanism, models that are compatible with LGC may be constructed. It is found that such models, which are also consistent with background dynamics, are constrained to be close to the CDMmodel during the radiation/matter epochs and can lead to the divergence of the equation of state of dark energy. In contrast, such constraints only impose mild restrictions on Palatini-f(R) models. Still more stringent constraints are provided by studying matter density perturbations. In particular, it is shown that the unconventional evolution of perturbations in the Palatini formalism leads to f(R) models in this case to be practically identical to the CDM model. For each case it is also shown that (for viable models) matter perturbation equations derived under a sub-horizon approximation are reliable even for super-Hubble scales provided the oscillating mode does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism, where the oscillating mode is absent. In summary, the analyses carried out in this thesis suggest that subjectingMG theories to observational constraints confines the viable range of models to be very close to (and in some cases indistinguishable from) the CDM model.
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9

Oreta, Timothy. "Vector-Galileon-Tensor theories of gravity." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20925.

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A detailed study of the cosmological evolution in a particular vector-tensor theory of gravity with a potential and a Galileon-motivated interaction terms is presented. The evolution of vector field self interactions that are relatively related to Galileon fields throughout the expansion history of the universe is considered and a classification of the parameters M (mass term) and H (Hubble parameter) according to the behaviour of the field in each cosmological epoch is carried out. In particular, we obtain conditions for the parameters so that the field grows exponentially or oscillates with decreasing amplitude. We also obtain an autonomous system for the inflationary case. The general features of the phasemaps are given and the critical point is appropriately characterised. It is not possible to obtain an autonomous system for radiation and matter dominated epochs hence, we consider other analytical methods. We obtain eigenvalues and hence, phasemaps. The general features of the phasemaps are given and the point to which the trajectories on the phasemaps converge is appropriately characterised. Therefore, we show that it is possible to obtain a wide variety of behaviours or interesting phenomenologies for the cosmological evolution of vector field self-interactions that are relatively related to Galileon fields by choosing suitable values for the parameters M and H of given conditions.
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10

Hackebill, Aric. "Thermodynamics of Modified Theories of Gravity." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/2143.

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Анотація:
Einstein’s equations are derived by following Jacobson’s thermodynamic method. It is seen that a family of possible field equations exist which satisfy the thermodynamic argument. Modified theories of gravity are addressed as possible candidates for replacing dark matter as an explanation for anomalous cosmological phenomena. Many of the proposed modified theories are not powerful enough to explain the currently observed phenomena and are rejected as viable theories of gravity. A surviving candidate, TeVeS, is further analyzed under the aforementioned thermodynamic argument to check for its consistency with thermodynamics.
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Книги з теми "THEORIES OF GRAVITY"

1

Brane-localized gravity. Singapore: World Scientific, 2004.

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2

Narlikar, Jayant V., and T. Padmanabhan. Gravity, Gauge Theories and Quantum Cosmology. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4508-1.

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3

Vecchiato, Alberto. Variational Approach to Gravity Field Theories. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51211-2.

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4

T, Schucker, ed. Differential geometry, guage theories and gravity. Cambridge: CUP, 1989.

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5

Narlikar, Jayant V. Gravity, Gauge Theories and Quantum Cosmology. Dordrecht: Springer Netherlands, 1986.

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6

1957-, Padmanabhan T., ed. Gravity, gauge theories, and quantum cosmology. Dordrecht, Holland: Reidel, 1986.

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7

T, Schücker, ed. Differential geometry, gauge theories, and gravity. Cambridge, [Cambridgeshire]: Cambridge University Press, 1987.

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8

Gambini, Rodolfo. Loops, knots, gauge theories, and quantum gravity. Cambridge: Cambridge University Press, 1996.

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9

Storey, Charles R. Electricity, magnetism, gravity & the big bang. Parsons, W. Va: McClain Print. Co., 1999.

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10

A, Sevrin, ed. Gauge theories, applied supersymmetry and quantum gravity, II. London: Imperial College Press, 1997.

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Частини книг з теми "THEORIES OF GRAVITY"

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Aldrovandi, Ruben, and José Geraldo Pereira. "Gauge Theories and Gravitation." In Teleparallel Gravity, 25–38. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5143-9_3.

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2

’t Hooft, Gerard. "Quantum Gravity." In Fundamental Theories of Physics, 89–90. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41285-6_6.

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3

Martín-Moruno, Prado. "Horndeski/Galileon Theories." In Modified Gravity and Cosmology, 79–87. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83715-0_6.

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4

Asselmeyer-Maluga, Torsten. "Smooth Quantum Gravity: Exotic Smoothness and Quantum Gravity." In Fundamental Theories of Physics, 247–308. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31299-6_15.

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Anderson, Edward. "Quantum Gravity Programs." In Fundamental Theories of Physics, 157–79. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58848-3_11.

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Baryshev, Yurij, and Pekka Teerikorpi. "Predictions of Gravity Theories." In Fundamental Questions of Practical Cosmology, 111–30. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-2379-5_6.

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Mashhoon, Bahram. "General Relativistic Gravity Gradiometry." In Fundamental Theories of Physics, 143–57. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11500-5_5.

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Gegenberg, J. D. "The Ground State of Stringy Gravity." In Super Field Theories, 489–94. Boston, MA: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4613-0913-0_26.

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Pearson, Jonathan. "Explicit Theories." In Generalized Perturbations in Modified Gravity and Dark Energy, 127–40. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01210-0_5.

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Boulatov, Dimitri. "3D Gravity and Gauge Theories." In Quantum Field Theory and String Theory, 39–57. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-1819-8_4.

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Тези доповідей конференцій з теми "THEORIES OF GRAVITY"

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Sobreiro, Rodrigo Ferreira. "Gauge theories and gravity." In 7th International Conference on Mathematical Methods in Physics. Trieste, Italy: Sissa Medialab, 2013. http://dx.doi.org/10.22323/1.175.0019.

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Rivelles, Victor O. "Noncommutative Theories and Gravity." In Fourth International Winter Conference on Mathematical Methods in Physics. Trieste, Italy: Sissa Medialab, 2004. http://dx.doi.org/10.22323/1.013.0029.

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Krajewski, Thomas. "Group Field Theories." In 3rd Quantum Gravity and Quantum Geometry School. Trieste, Italy: Sissa Medialab, 2013. http://dx.doi.org/10.22323/1.140.0005.

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4

MANN, ROBERT. "A6: ALTERNATIVE THEORIES OF GRAVITY." In Proceedings of the 16th International Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776556_0022.

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WILL, CLIFFORD M. "A6: ALTERNATIVE THEORIES OF GRAVITY." In Proceedings of the 17th International Conference. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701688_0022.

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Olmo, Gonzalo J. "Cosmology in Palatini theories of gravity." In TOWARDS NEW PARADIGMS: PROCEEDING OF THE SPANISH RELATIVITY MEETING 2011. AIP, 2012. http://dx.doi.org/10.1063/1.4734415.

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PERIVOLAROPOULOS, L. "OBSERVATIONAL SIGNATURE OF EXTENDED GRAVITY THEORIES." In Proceedings of the Sixth International Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770288_0084.

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8

Arbuzova, Elena. "Instabilities in modified theories of gravity." In Multifrequency Behaviour of High Energy Cosmic Sources - XIII. Trieste, Italy: Sissa Medialab, 2020. http://dx.doi.org/10.22323/1.362.0026.

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9

Bjerrum-Bohr, Niels Emil Jannik, and Pierre Van Hove. "Amplitudes in Gravity and Yang-Mills Theories." In Workshop on Continuum and Lattice Approaches to Quantum Gravity. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.079.0004.

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10

CLIFTON, T. "ASYMPTOTIC FLATNESS AND BIRKHOFF'S THEOREM IN HIGHER-DERIVATIVE THEORIES OF GRAVITY." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0117.

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Звіти організацій з теми "THEORIES OF GRAVITY"

1

Perelstein, M. Topics in Theories of Quantum Gravity. Office of Scientific and Technical Information (OSTI), April 2005. http://dx.doi.org/10.2172/839827.

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2

Lim, Hyun. Nonlinear Dynamics of Modified Gravity Theories. Office of Scientific and Technical Information (OSTI), December 2020. http://dx.doi.org/10.2172/1727409.

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3

Evenett, Simon, and Wolfgang Keller. On Theories Explaining the Success of the Gravity Equation. Cambridge, MA: National Bureau of Economic Research, April 1998. http://dx.doi.org/10.3386/w6529.

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4

Rizzo, Thomas G. Using Scalars to Probe Theories of Low Scale Quantum Gravity. Office of Scientific and Technical Information (OSTI), March 1999. http://dx.doi.org/10.2172/10016.

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5

Faraggi, A. E., and J. C. Pati. Meeting the constraint of neutrino-Higgsino mixing in gravity unified theories. Office of Scientific and Technical Information (OSTI), February 1997. http://dx.doi.org/10.2172/466855.

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6

Awada, M., and Zongan Qiu. The critical points of the multimatrix model as the theories of 2-d W-gravity. Office of Scientific and Technical Information (OSTI), March 1990. http://dx.doi.org/10.2172/6767420.

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7

Rizzo, Thomas G. Top Quark Production at the Tevatron: Probing Anomalous Chromomagnetic Moments and Theories of Low Scale Gravity. Office of Scientific and Technical Information (OSTI), February 1999. http://dx.doi.org/10.2172/9950.

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