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arXiv · 2404.18427

Well-defined $f(Q)$ Gravity, Reconstruction of FLRW Spacetime and Unification of Inflation with Dark Energy Epoch

Shin'ichi Nojiri·S. D. Odintsov
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Abstract

We formulate the convenient and mimetic $f(Q)$ gravities in terms of the metric and four scalar fields with the $Q$ being the non-metricity scalar. As a result, it is shown that the obtained field equations are well-defined. By using the field equations, we show how the $f(Q)$ models which realise any given FLRW spacetime may be reconstructed. We construct convenient $f(Q)$ gravity and mimetic $f(Q)$ gravity, which describe the inflation and dark energy epochs and even unify the inflation and dark energy. Moreover, a radiation-dominated epoch and early dark energy may be easily included in the above theories as is explicitly shown. It is shown that the inflationary spectral index $n_s$ and the tensor-to-scalar ratio $r$ are consistent with Planck data for some models of $f(Q)$ gravity. Corresponding asymptotic forms of $f(Q)$ and mimetic $f(Q)$ are given. Finally, some remarks on possible reconstruction for spherically symmetric spacetime are given.

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Shin'ichi Nojiri, S. D. Odintsov. 2024-04-29. Well-defined $f(Q)$ Gravity, Reconstruction of FLRW Spacetime and Unification of Inflation with Dark Energy Epoch. https://arxiv.org/abs/2404.18427

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