Variety of $(d+1)$ dimensional Cosmological Evolutions with and without bounce in a class of LQC -- inspired Models

Abstract

The bouncing evolution of an universe in Loop Quantum Cosmolgy can be described very well by a set of effective equations, involving a function $sinx$. Recently, we have generalised these effective equations to $(d+1)$ dimensions and to any function $f(x)$. Depending on $f(x)$ in these models inspired by Loop Quantum Cosmolgy, a variety of cosmological evolutions are possible, singular as well as non singular. In this paper, we study them in detail. Among other things, we find that the scale factor $a(t)\propto t^{\frac{2q}{(2q-1)(1+w)d}}$ for $f(x)=x^q$, and find explicit Kasner--type solutions if $w=2q-1$ also. A result which we find particularly fascinating is that, for $f(x)=\sqrt{x}$, the evolution is non singular and the scale factor $a(t)$ grows exponentially at a rate set, not by a constant density, but by a quantum parameter related to the area quantum.

Version 1. 41 pages. Version 2. 41 pages. Remark (3) rewritten -- a minor change. To appear in General Relativity and Gravitation

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