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

Understand

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.