Quintessence Universe and cosmic acceleration in <i>f</i> (<i>Q</i>, <i>T</i>) gravity

The problem of cosmic acceleration and dark energy is one of the mysteries presently posed in the scientific society that general relativity has not been able to solve. In this work, we have considered alternative models to explain this late-time acceleration in a flat Friedmann–Lemaitre–Robertson–Walker (FLRW) Universe within the framework of the f (Q,T) modified gravity theory (where Q is the nonmetricity and T is the trace of the energy–momentum tensor) recently proposed by Y. Xu et al. [Eur. Phys. J. C 79 (2019) 708], which is an extension of f (Q) gravity with the addition of the T term. Here, we presume a specific form of [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are free model parameters, and obtained the exact solutions by assuming the cosmic time-redshift relation as [Formula: see text] which produces the Hubble parameter of the form [Formula: see text], where m and n are the nonnegative constants, we find the best values for them using 57 data points of the Hubble parameter H(z). Also, we find the behavior of different cosmological parameters as the deceleration parameter (q), energy density [Formula: see text], pressure (p) and equation of state (EoS) parameter [Formula: see text] and compare them with the observational results. To ensure the validity of the results, we studied the energy conditions along with jerk parameter. Finally, we found that our model behaves similarly to the quintessence Universe.

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