Reconstruction of $f(Q,T)$ Lagrangian for various cosmological scenario

TL;DR

This paper reconstructs the $f(Q,T)$ gravity Lagrangian for various cosmological scenarios, exploring how different matter sources and solutions like power-law and de-Sitter universes can arise within this modified gravity framework.

Contribution

It introduces a reconstruction method for $f(Q,T)$ gravity, deriving explicit Lagrangians for different matter types and cosmological solutions, expanding the understanding of modified gravity models.

Findings

Several $f(Q,T)$ models admit power-law and de-Sitter solutions.

Explicit forms of $f(Q,T)$ are derived for various matter sources.

Reconstructed models include scalar field cosmologies.

Abstract

The variety of theories that can account for the dark energy phenomenon encourages current research to concentrate on a more in-depth examination of the potential impacts of modified gravity on both local and cosmic scales. We discuss some cosmological reconstruction in $f(Q,T)$ cosmology (where $Q$ is the non-metricity scalar, and $T$ is the trace of the energy-momentum tensor) corresponding to the evolution background in Friedmann-La\^imatre-Robertson-Walker (FLRW) universe. This helps us to determine how any FLRW cosmology can arise from a specific $f(Q,T)$ theory. We use the reconstruction technique to derive explicit forms of $f(Q,T)$ Lagrangian for the different kinds of matter sources and Einstein's static universe. We also formulate the models using several ansatz forms of the $f(Q,T)$ function for $p=\omega \rho$. We demonstrate that several classes of $f(Q,T)$ theories admit the power-law and de-Sitter solutions in some ranges of $\omega$. Additionally, we reconstruct the cosmological model for the scalar field with a specific form of $f(Q,T)$. These new models with cosmological inspiration may impact gravitational phenomena at other cosmological scales.