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

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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 \((d + 1)\) 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 \(a(t) \propto t^{ \frac{2 q}{(2 q - 1) (1 + w) d}}\) for \(f(x) = x^q\), and find explicit Kasner-type solutions if \(w = 2 q - 1 \) 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.

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Notes

  1. There exists a \((d + 1)\) dimensional LQG formulation, given in [22,23,24]. Our preliminary analysis [25], see [26] also, suggests that one can derive the LQC analogs of the effective equations in \((d + 1)\) dimensions, with \(f(x) = \sin x\).

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Acknowledgements

We thank G. Date for helpful comments.

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  1. Institute of Mathematical Sciences, HBNI, C. I. T. Campus, Tharamani, Chennai, 600 113, India

    S. Kalyana Rama

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Rama, S.K. Variety of \((d + 1)\) dimensional cosmological evolutions with and without bounce in a class of LQC-inspired models. Gen Relativ Gravit 49, 113 (2017). https://doi.org/10.1007/s10714-017-2277-9

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