A note on cosmology in a brane model

TL;DR

This paper explores cosmological solutions in a five-dimensional brane model with matter, radiation, and a cosmological constant, analyzing how different scale ratios affect the universe's age and primordial element abundance.

Contribution

It provides new solutions to the generalized Friedmann equation in a 5D brane context without explicit brane curvature terms, considering hierarchy between 4D and 5D scales.

Findings

Universe age is comparable to standard cosmology for certain scale ratios but generally smaller.

Primordial helium abundance is about three times higher than in standard cosmology.

Time evolution of temperature differs, affecting nucleosynthesis predictions.

Abstract

We study some aspects of cosmology in a five-dimensional model with matter, radiation and cosmological constant on the four-dimensional brane(s) and without matter in the bulk. The action of the model does not contain explicit curvature terms on the the brane(s). We obtain solution of the generalized Friedman equation as a function of dimensionless ratio of the scales $b^2 = \frac{\mu M^2_{pl}}{M^3}$ ($\mu$ is the scale in the warp factor in the 5D metric which is taken of order $10^{3\div 4}GeV$, $M\geq\mu$ is the $5D$ fundamental scale). We assume that there is a hierarchy between 4D and 5D scales. For $b^2 =O(1)$ the age of the Universe is found comparable, but below the current experimental value, for $b^2\gg 1$ it is obtained much smaller than the experimental bound. Because time dependence of temperature of the Universe in the 5D model is different from that in the standard cosmology, the abundance of ${}^4$He produced in the primordial nucleosynthesis is obtained about three times more than in the standard cosmology.