Cosmological solutions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>gravity

Paliathanasis, Andronikos; Barrow, John D.; Leach, P. G. L.

doi:10.1103/physrevd.94.023525

Cited by 179 publications

(131 citation statements)

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“…This analysis was applied to the case of Bianchi I models in ref. [42]. It was found that there exists a family of solutions of the f (T ) arbitrary function with a Kasner-like profile in the vacuum setting.…”

Section: Tegr In Nonlinear F (T )-Gravitymentioning

confidence: 99%

“…T ρ ν = 0, a vacuum solution of GR in which R = 0, also turns out to be a solution of TEGR and thus of f (T ) gravity without cosmological constant, given that there exists a frame such the following conditions are satisfied [42] …”

Section: Tegr In Nonlinear F (T )-Gravitymentioning

confidence: 99%

“…Recently, this work inspired an analogous analysis in f (T ) gravity in ref. [42] where new conditions were found for the current context, i.e. the field equations in Eq.…”

Section: Tegr In Nonlinear F (T )-Gravitymentioning

confidence: 99%

“…Recently anisotropic vacuum solutions of the Kasner type were found in ref. [42]. Specifically, the conditions for the f (T ) function in which a nonlinear f (T ) theory provides a solution of TEGR/GR were determined and consequently the Kasner universe is found to satisfy the field equations in f (T ) gravity.…”

Section: Introductionmentioning

confidence: 99%

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Stability of the Kasner universe in f(T) gravity

2018

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f (T ) gravity theory offers an alternative context in which to consider gravitational interactions where torsion, rather than curvature, is the mechanism by which gravitation is communicated. We investigate the stability of the Kasner solution with several forms of the arbitrary lagrangian function examined within the f (T ) context. This is a Bianchi type-I vacuum solution with anisotropic expansion factors. In the f (T ) gravity setting, the solution must conform to a set of conditions in order to continue to be a vacuum solution of the generalized field equations. With this solution in hand, the perturbed field equations are determined for power-law and exponential forms of the f (T ) function. We find that the point which describes the Kasner solution is a saddle point which means that the singular solution is unstable. However, we find the de Sitter universe is a late-time attractor. In general relativity, the cosmological constant drives the the isotropization of the spacetime while in this setting the extra f (T ) contributions now provide this impetus.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

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Section: Tegr In Nonlinear F (T )-Gravitymentioning

confidence: 99%

Section: Tegr In Nonlinear F (T )-Gravitymentioning

confidence: 99%

“…Recently, this work inspired an analogous analysis in f (T ) gravity in ref. [42] where new conditions were found for the current context, i.e. the field equations in Eq.…”

Section: Tegr In Nonlinear F (T )-Gravitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability of the Kasner universe in f(T) gravity

2018

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“…This strategy has been implemented recently in several papers [24][25][26][27]. The resulting equations of motion appear to be nonpathological.…”

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confidence: 99%

On Kasner solution in Bianchi I f(T) cosmology

Skugoreva

Toporensky

2018

Eur. Phys. J. C

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Recently the cosmological dynamics of an anisotropic Universe in f (T ) gravity became an area of intense investigations. Some earlier papers devoted to this issue contain contradictory claims about the nature and propertied of vacuum solutions in this theory. The goal of the present paper is to clarify this situation. We compare properties of f (T ) and f (R) vacuum solutions and outline differences between them. The Kasner solution appears to be an exact solution for the T = 0 branch, and an asymptotic solution for the T = 0 branch. It is shown that the Kasner solution is a past attractor if T < 0, being a past and future attractor for the T > 0 branch.The Kasner solution, being one of the first known exact solutions in relativistic cosmology [1] continues to be one of the most important exact solutions in general relativity (GR) or its modifications. One of the reasons is that despite this being a vacuum solution, it is a good approximation near a cosmological singularity for almost all matter sources (except for a stiff fluid) in a flat anisotropic Universe. Moreover, a general cosmological singularity is believed to be constructed as an infinite series of consecutive epochs, each of them being a particular Kasner solution with a good accuracy (though a mathematical proof of this scenario is still absent in full details; see, for example, [2])-the famous BelinskiiKhalatnikov-Lifshitz (BKL) scenario [3]. Therefore the Kasner set of solutions provides "building blocks" for the BKL picture.If we assume that GR needs some modifications at UV scale, it is natural to expect that such modifications should change the behavior near a cosmological singularity significantly. That is why the fate of the Kasner solution in modified gravity theories is an area of intense investigations. A lot of efforts have been devoted to Kasner solutions and their modifications in quadratic gravity. We remind the reader that the Kasner solution is a solution for an anisotropically expanda e-mail: masha-sk@mail.ru b e-mail: atopor@rambler.ru ing Universe with scale factors changing as powers of time. These power exponents are subject of two conditions giving us their sum as well as the sum of their squares (both sums are equal to unity). In quadratic gravity, two different situations were identified:• If the equations of motion are of the second order, as in GR (that is, in Gauss-Bonnet gravity), the power-law solution for the scale factor is an asymptotic solution.In the high-curvature regime, these two conditions for power exponents are different from those in the GR Kasner solution [4][5][6], while the GR Kasner solution is an asymptotic solution in the low-curvature regime.• In fourth order gravity (like R + R 2 or a general quadratic gravity) the Kasner solution (with the same conditions for the exponents) is an exact vacuum solution. However, since the phase space has two additional dimensions in comparison with GR, a Kasner solution in quadratic gravity may be in some situations unstable [7,8].Recently a new class of mod...

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New analytic solutions in f(R)‐cosmology from Painlevé analysis

Leon,

Paliathanasis,

Leach

2024

Math Methods in App Sciences

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Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in ‐cosmology. Specifically, for some power‐law ‐theories of particular interest, we apply the ARS algorithm to prove if the field equations possess the Painlevé property. Constraints for the free parameters of the power‐law models are derived, and new analytic solutions are derived, expressed in terms of Laurent expansions.

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Cosmological solutions off(T)gravity

Cited by 179 publications

References 42 publications

Stability of the Kasner universe in f(T) gravity

Stability of the Kasner universe in f(T) gravity

On Kasner solution in Bianchi I f(T) cosmology

New analytic solutions in f(R)‐cosmology from Painlevé analysis

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