Inflation and primordial fluctuations in $f(Q,T)$ gravity

We investigate slow roll inflation and the creation of primordial density fluctuations in the framework of $f(Q,T)$ gravity. Our focus is on constraining the evolution of both the background and perturbations in this theory, specifically using the form $f(Q,T) = \alpha Q + g(T)$, where $g(T)$ is an arbitrary function of the trace of the stress-energy tensor $T$. We derive the Mukhanov-Sasaki equations for scalar and tensor perturbations, and by solving these equations in the slow-roll regime, we compute the power spectra and spectral index for both modes within the general functional framework of $g(T)$. In particular, we examine power law functional forms of $g(T)$ to establish the observational constraints associated with quadratic potential. By imposing constraints on the model's parameters, we obtain results that align closely with the Planck 2018 data and BAO data for the tensor-to-scalar ratio. Notably, a model that includes $g(T) = \beta T^2$ and a quadratic potential yields the best-fit values consistent with the spectral index and tensor-to-scalar ratio suggested by the Planck and BICEP2 results.