Asymptotic solutions in f(R)-gravity

Bukzhalev, E. E.; Ivanov, Mikhail M.; Toporensky, A. V.

doi:10.1088/0264-9381/31/4/045017

Cited by 4 publications

(4 citation statements)

References 85 publications

(152 reference statements)

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“…Since then it has been investigated by many authors [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. It is worth to note that cubic and higher order curvature corrections often lead to Big Rip singularity even in the framework of f (R) theory [32][33][34][35] or at least make important cosmological solutions unstable (for an example beyond the f (R) theory see, for example [36]), so our restriction with only quadratic curvature corrections is justified from phenomenological reasons also. In the context of Kasner like solutions in quadratic gravity, we must mention [37,38].…”

Section: Introductionmentioning

confidence: 99%

On stability of the Kasner solution in quadratic gravity

Toporensky¹,

Müller

2016

Gen Relativ Gravit

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We consider dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described -the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter w is bigger, smaller or equals to 1/3. Initial conditions for numerical integrations have been chosen near General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of coupling constants so that the resulting cosmological singularity is isotropic.

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Section: Introductionmentioning

confidence: 99%

On stability of the Kasner solution in quadratic gravity

Toporensky¹,

Müller

2016

Gen Relativ Gravit

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“…In the latter theory there are two additional degrees of freedom connected with higher derivatives of the scale factor, so they (in contrast to Gauss-Bonnet gravity) are present in the isotropic (3+1) dimension case. They oscillate harmonically in the low-curvature limit (this is the feature of quadratic gravity, for higher order corrections the oscillation are anharmonic, see [51]). and can be expressed in the form of a massive scalar field.…”

Section: Influence Of Mattermentioning

confidence: 98%

Friedmann Dynamics Recovered from Compactified Einstein–Gauss–Bonnet Cosmology

et al. 2017

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In this paper cosmological dynamics in Einstein-Gauss-Bonnet gravity with a perfect fluid source in arbitrary dimension is studied. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely one for the three dimensional space and one for the extra dimensional space, is found that a regime exists where the two scale factors tend to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the (3+1)-dimensional Friedmann model with perfect fluid is recovered. At last, it is worth emphasizing that the present numerical results strongly support a 't Hooft-like interpretation of the parameter 1/D (where D is the number of extra dimensions) as a small expansion parameter in very much the same way as it happens in the large N expansion of gauge theories with 1/N . Indeed, the dependence on D of many of the relevant physical quantities computed here manifests a clear WKB-like pattern, as expected on the basis of large N arguments.

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“…For α = 1 (which includes the Starobinsky model), the scalaron potential is asymptotically flat; for α < 1, it is growing, while for α > 1, it asymptotically declines to zero. Such potentials have been studied in [28][29][30] and other papers.…”

Section: Jcap03(2023)023mentioning

confidence: 99%

Tabletop potentials for inflation from f(R) gravity

Shtanov

Sahni²,

Mishra³

2023

J. Cosmol. Astropart. Phys.

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We show that a large class of modified gravity theories (MOG) with the Jordan-frame Lagrangian f(R) translate into scalar-field (scalaron) models with hilltop potentials in the Einstein frame. (A rare exception to this rule is provided by the Starobinsky model for which the corresponding scalaron potential is plateau-like for ϕ > 0.) We find that MOG models featuring two distinct mass scales lead to scalaron potentials that have a flattened hilltop, or tabletop. Inflationary evolution in tabletop models agrees very well with CMB observations. Tabletop potentials therefore provide a new and compelling class of MOG-based inflationary models. By contrast, MOG models with a single mass scale generally correspond to steep hilltop potentials and fail to reproduce the CMB power spectrum. Inflationary evolution in hilltop/tabletop models can proceed in two alternative directions: towards the stable point at small R describing the observable universe, or towards the asymptotic region at large R. The MOG models which we examine have several new properties including the fact that gravity can become asymptotically vanishing, with G eff → 0, at infinite or large finite values of the scalar curvature R. A universe evolving towards the asymptotically vanishing gravity region at large R will either run into a 'Big-Rip' singularity, or inflate eternally.

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Asymptotic solutions in f(R)-gravity

Cited by 4 publications

References 85 publications

On stability of the Kasner solution in quadratic gravity

On stability of the Kasner solution in quadratic gravity

Friedmann Dynamics Recovered from Compactified Einstein–Gauss–Bonnet Cosmology

Tabletop potentials for inflation from f(R) gravity

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