Metric-Affine F(T,Q) gravity: cosmological implications and constraints

Abstract

Abstract In this paper, we investigate some exact cosmological models in Metric-Affine $F(T,Q)$ gravity, with observational constraints. The Metric-Affine $F(T,Q)$ gravity is some kind of unification of two known gravity theories, namely, the $F(T)$ gravity and the $F(Q)$ gravity. We obtain the field equations of the Metric-Affine theory by considering the metric tensor and the general affine connection as independent variables. We then focus on the particular case in which the $F(T,Q)$ function characterizing the aforementioned metric-affine models is linear, that is, $F(T,Q)=\lambda T+\mu Q$. We investigate this linear case and consider a Friedmann-Lema\^{i}tre-Robertson-Walker background to study cosmological aspects and applications. We have obtained three exact solutions of the modified field equations in two different cases, $T$ and $Q$, using the Hubble function $H(t)$ and the scale factor $a(t)$. We then placed observational constraints on these solutions using the Hubble $H(z)$ datasets and the MCMC analysis. We have investigated the deceleration parameter $q(z)$ and effective EoS parameters, and a comparative study of all three models with $\Lambda$CDM model has been carried out.