Dynamical reconstruction of the \(\Lambda \)CDM model in the scalar–tensor representation of \(f\left( Q,T\right) \) gravity

Abstract

Motivated by the growing interest in the nonmetricity-matter couplings, we develop the scalar–tensor formulation of recently introduced f(Q, T) gravity, where Q is the nonmetricity and T is the trace of the energy–momentum tensor. The main properties of the scalar–tensor formalism for the Friedmann–Lemaître–Robertson–Walker (FLRW) Universe are discussed, and we introduce an appropriate set of dynamical variables to analyze the cosmic evolution of the scalar–tensor f(Q, T) cosmology as a dynamical system. By considering two distinct cosmic fluids, namely matter and radiation, we have demonstrated that the cosmological phase space exhibits the typical curvature-dominated, radiation-dominated, matter-dominated, and exponentially accelerated fixed points. Furthermore, under an appropriate set of initial conditions compatible with the current observations from the Planck satellite, our analysis shows that the scalar–tensor f(Q, T) successfully yields models indistinguishable from the \(\Lambda \)CDM cosmology and compatible with the weak-field solar system dynamics, without the inclusion of a cosmological constant \(\Lambda \). Thus, the theory introduced herein may be regarded as a suitable candidate to describe the cosmological dynamics of the Universe.