Accelerating Universe as Window for Extra Dimensions

Abstract

Homogeneous cosmological solutions are obtained in five dimensional space time assuming equations of state p = kρ and p 1 = γρ where p is the isotropic 3 -pressure and p 1 , that for the fifth dimension. Using different values for the constants k and γ many known solutions are rediscovered. Further the current acceleration of the universe has led us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We also extend a recent work of Mohammedi where using a special form of the extra dimensional scale factor a new interpretation of the higher dimensional equations of motion is given and the concept of an effective four dimensional pressure is introduced. Interestingly the 5D matter field remains regular while the effective negative pressure is responsible for the inflation. Relaxing the assumptions of two equations of state we also present a class of solutions which provide early deceleration followed by a late acceleration in a unified manner. Relevant to point out that in this case our cosmology apparently mimics the well known quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter like one takes place. Depending on the relative magnitude of the different constants appearing in our solutions we show that some of the cases are amenable to the desirable property of dimensional reduction.

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

“…Thus, one concludes that if the 3D scale factor is undergoing accelerated expansion in the late universe, when the approximations of this appendix are valid, then the higher-dimensional scale factor can not be dynamically compactifying. A similar result was found in [11].…”

“…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.…”

“…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.…”

“…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.…”

Higher Dimensional Cosmology with Normal Scalar Field and Tachyonic Field

“…In [21] Peng et al extend the direct quantum approach to the FRW cosmology from 4D to 5D and obtained a Hamiltonian formulation for a wave like 5D FRW cosmology. In [22] Panigrahi et al have shown a scenario in homogeneous 5D space time which behave a decelerating expansion in the early epoch along with an accelerating situation at the present line without introducing any external quintessence-like scalar field in the presence of extra dimension.…”