Quintessence phase of the universe in f(Q,T)-gravity with <italic>DESI DR2 BAO</italic> and <italic>Pantheon + SH0ES</italic> samples

This paper investigates the late-time cosmic dynamics using the matter-geometry coupled f(Q,T) gravity model, where Q is the non-metricity scalar and T represents the trace of the energy-momentum tensor. We consider the paradigm power law f(Q,T)-gravity model, f(Q,T) = - αQ−βT2/H02+η0 (where α, β and η0 are constants) to calculate the best-fit values of cosmological parameters Ωm, H0, α, β, rd and M through the Monte Carlo Markov Chain (MCMC) simulations using cosmic chronometers (CC) baryon acoustic oscillation (BAO) taken from Dark Energy Spectroscopy Instrument (DESI) and the SNIa distance moduli measurements from the Pantheon + SH0ES, which consists of 1701 light curves of 1550 distinct supernovae. Some key cosmological parameters: the deceleration parameter q(z), effective equation of state parameters weff(z), Hubble parameter H(z), and distance modulus μ(z) are presented. These dynamical quantities show that the f(Q,T)-gravity model is compatible with transitioning towards a quintessence-like phase in the late-time. In conformity with ΛCDM, we moreover take into account the geometrical interpretations by considering the state-finder parameters r−s and r−q, which are crucial parameters for additional analysis. Additionally, the statistical analysis has been carried out for further investigation of the viability f(Q,T)-gravity model.