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

TL;DR

This paper develops a scalar-tensor formulation of $f(Q,T)$ gravity, demonstrating it can reproduce $ ext{Lambda}$CDM cosmology and align with observations without a cosmological constant.

Contribution

It introduces a scalar-tensor formalism for $f(Q,T)$ gravity and analyzes its cosmological dynamics, showing compatibility with current observations and standard cosmology.

Findings

The phase space includes curvature, radiation, matter, and accelerated fixed points.

Models can mimic $ ext{Lambda}$CDM without a cosmological constant.

Compatible with Planck data and solar system tests.

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-Lema{\^ i}tre-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.