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

TL;DR

This paper develops well-defined $f(Q)$ gravity models, reconstructs FLRW spacetime solutions, and unifies inflation with dark energy, showing consistency with observational data and including early universe epochs.

Contribution

It introduces a new formulation of $f(Q)$ gravity with well-defined field equations and demonstrates how to reconstruct cosmological solutions, unifying inflation and dark energy epochs.

Findings

Models are consistent with Planck data for $n_s$ and $r$

Reconstruction of FLRW spacetime is achieved

Early dark energy and radiation epochs are incorporated

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.