# Variety of $$(d + 1)$$ ( d + 1 ) dimensional cosmological evolutions with and without bounce in a class of LQC-inspired models

Variety of $$(d + 1)$$ ( d + 1 ) dimensional cosmological evolutions with and without... The bouncing evolution of an universe in Loop Quantum Cosmology can be described very well by a set of effective equations, involving a function sin x. Recently, we have generalised these effective equations to $$(d + 1)$$ ( d + 1 ) dimensions and to any function f(x). Depending on f(x) in these models inspired by Loop Quantum Cosmology, 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 $$a(t) \propto t^{ \frac{2 q}{(2 q - 1) (1 + w) d}}$$ a ( t ) ∝ t 2 q ( 2 q - 1 ) ( 1 + w ) d for $$f(x) = x^q$$ f ( x ) = x q , and find explicit Kasner-type solutions if $$w = 2 q - 1$$ w = 2 q - 1 also. A result which we find particularly fascinating is that, for $$f(x) = \sqrt{x}$$ f ( x ) = 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png General Relativity and Gravitation Springer Journals

# Variety of $$(d + 1)$$ ( d + 1 ) dimensional cosmological evolutions with and without bounce in a class of LQC-inspired models

, Volume 49 (8) – Jul 31, 2017
30 pages

/lp/springer_journal/variety-of-d-1-d-1-dimensional-cosmological-evolutions-with-and-CE7vo25FoE
Publisher
Springer US
Subject
Physics; Theoretical, Mathematical and Computational Physics; Classical and Quantum Gravitation, Relativity Theory; Differential Geometry; Astronomy, Astrophysics and Cosmology; Quantum Physics
ISSN
0001-7701
eISSN
1572-9532
D.O.I.
10.1007/s10714-017-2277-9
Publisher site
See Article on Publisher Site

### Abstract

The bouncing evolution of an universe in Loop Quantum Cosmology can be described very well by a set of effective equations, involving a function sin x. Recently, we have generalised these effective equations to $$(d + 1)$$ ( d + 1 ) dimensions and to any function f(x). Depending on f(x) in these models inspired by Loop Quantum Cosmology, 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 $$a(t) \propto t^{ \frac{2 q}{(2 q - 1) (1 + w) d}}$$ a ( t ) ∝ t 2 q ( 2 q - 1 ) ( 1 + w ) d for $$f(x) = x^q$$ f ( x ) = x q , and find explicit Kasner-type solutions if $$w = 2 q - 1$$ w = 2 q - 1 also. A result which we find particularly fascinating is that, for $$f(x) = \sqrt{x}$$ f ( x ) = 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.

### Journal

General Relativity and GravitationSpringer Journals

Published: Jul 31, 2017

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