Higher Dimensional Cosmology: Relations Among the Radii of Two Homogeneous Spaces

Leon, E. A.; Núñez-López, R.; Lipovka, A. A.; Nieto, J. A.

doi:10.1142/s0217732311035316

Cited by 9 publications

(11 citation statements)

References 16 publications

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“…As η 1 is strictly positive The approximations of this appendix, which give rise to the solutions of (A5) and (A9), yield a generalized treatment of the case of dynamical compactification, which has been previously studied elsewhere (see [9][10][11]). There, the higherdimensional scale factor was assumed to dynamically evolve through a relation of the form of (A9), where n was an arbitrary parameter constrained only by the relation n > 0.…”

Section: Discussionmentioning

confidence: 99%

“…Notice that the EoS parameters w and v can in general be time-dependent, in this manuscript they are simply treated as constants. Employing (2.8) and (2.9) to eliminate ρ, p, and p 5 from (2.4) -(2.6) and performing some algebra, we obtain an exact differential equation of the form 10) where we defined the parameter…”

Section: D Anisotropic Frw Cosmologymentioning

confidence: 99%

“…Notice that the higher-dimensional Hubble parameter can change signs with the sign dependent on whether the 4D Hubble parameter or the inverse of the higher-dimensional volume element dominates, assuming γ 0 is positive. By defining an effective EoS parameterw to be of the form 10) the 5D conservation equation, (3.4), reduces to a form that precisely mimics the 4D conservation equation when the integration constant γ 0 is set equal to zero, with w replaced byw. This effective EoS parameter equates to an effective pressure of the formp (3.11) This effective pressure was originally defined in [9] and proves useful in the following sections.…”

Section: D Effective Frw Field Equationsmentioning

confidence: 99%

“…The parameter constraints of (4.9) emerge if one demands that the 3D scale factor is real and we employ (4.2). The approximate solution of (4.8) corresponds to that of a generalized treatment of the case of dynamical compactification of [9][10][11]. In [9], the higher-dimensional scale factor was assumed to dynamically evolve through a relation of the form b(t) ∼ 1 a n (t) (4.10) where n, there, was an arbitrary parameter constrained only by the relation n > 0.…”

Section: General Treatment Of the 4d Effective Field Equationsmentioning

confidence: 99%

“…It was noted in [9] that this effective pressure can be negative for positive values of the density and the pressures and can drive the late-time accelerated expansion of the universe, without the need for dark energy. The work of [9] has been extended and studied in [10,11]. The aforementioned findings of [9] were reached on the assumption of dynamical compactification of an inverse power law form.…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

Middleton

Stanley

2011

Phys. Rev. D

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We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higherdimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations in the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys.Rev.D 65, 104018 (2002)] and the 5D vacuum solution of Detweiler [Phys.Rev.D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.

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Section: Discussionmentioning

confidence: 99%

Section: D Anisotropic Frw Cosmologymentioning

confidence: 99%

Section: D Effective Frw Field Equationsmentioning

confidence: 99%

Section: General Treatment Of the 4d Effective Field Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

Middleton

Stanley

2011

Phys. Rev. D

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Interpenetrating subspaces as a funnel to extra space

Rubin

2016

Physics Letters B

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New solution for two interpenetrating universes is found. Higher derivative gravity acting in 6-dimensional space is the basis of the study that allows to obtain stable solution without introducing matter of any sort. Stability of the solution is maintained by a difference between asymptotic behavior at spacial infinities. For an external observer such a funnel looks similar to a spherical wormhole.Comment: 10 pages, 5 figures, accepted for publication in Phys. Lett. B, revised versio

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Classical evolution of subspaces

2018

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We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties.

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Higher Dimensional Cosmology: Relations Among the Radii of Two Homogeneous Spaces

Cited by 9 publications

References 16 publications

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

Interpenetrating subspaces as a funnel to extra space

Classical evolution of subspaces

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