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

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-Laîmatre-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 = ωρ. We demonstrate that several classes of f (Q , T) theories admit the power-law and de-Sitter solutions in some ranges of ω. 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.