Multidimensional inhomogeneous cosmology in scalar tensor theory

TL;DR

This paper derives exact solutions for a five-dimensional inhomogeneous cosmology with a scalar field, exploring dimensional reduction, matter generation, and a smooth transition from inhomogeneous to homogeneous universe phases.

Contribution

It presents novel exact solutions in scalar-tensor theory with inhomogeneity and analyzes implications for entropy, matter, and dimensional reduction in cosmology.

Findings

Solutions admit indefinite expansion and dimensional reduction.

Scalar field alters expansion behavior for p=-ρ case.

Model suggests a smooth transition from inhomogeneous to homogeneous universe.

Abstract

Exact cosmological solutions are obtained for a five dimensional inhomogeneous fluid distribution along with a Brans-Dicke type of scalar field. The set includes varied forms of matter field including $\rho+p=0$, where p is the 3D isotropic pressure. Depending on the signature of 4-space curvature our solutions admit of indefinite expansion in the usual 3-space and dimensional reduction of the fifth dimension. Due to the presence of the scalar field the case $p=-\rho$ does not yield an exponential expansion of the scale factor, which strikingly differs from our earlier investigations without scalar field.The \emph{effective} four dimensional values of entropy and matter are calculated and possible consequences of entropy and matter generation in the 4D world as a result of dimensional reduction of the extra space are also discussed. Encouraging to point out that aside from the well known big bang singularity our inhomogeneous cosmology is spatially regular everywhere. Further our model seems to suggest an alternative mechanism pointing to a smooth pass over from a primordial, inhomogeneous cosmological phase to a 4D homogeneous one.