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-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.

13 pages, 2 figures, 1 table

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• Logarithmic and Strong Coupling Models in Weyl-Type $f(Q,T)$ Gravity
• Lagrangian Identity and Mass Evolution of Particle-like Objects in Nonminimally Coupled Gravity
• Generalized Second Law and Thermodynamical Aspects of $f(Q,\mathcal{T})$ Gravity
• Inflation and primordial fluctuations in $f(Q,T)$ gravity