Scalar Field Cosmology with Powerlaw and Hybrid Expansion Law in Symmetric Teleparallel Gravity

Recently, scalar field approaches have been widely considered in cosmological models due to their potential for useful investigation of the cosmological evolution of the Universe. The use of a scalar field as a matter source in a cosmological model within symmetric teleparallel gravity is as interesting as many other modified gravity models sourced by a scalar field. In this paper, we investigate the repercussions of power law and hybrid expansion laws in symmetric teleparallel gravity using an associated scalar field as a total matter source. We find that for both models, a normal scalar field is required to provide a viable description of the Universe's evolution, as opposed to a phantom scalar field, from an ad-hoc introduction of these two expansion laws. To back up this method of implementing these two ad-hoc expansion laws we also examined the evolution of the Hubble parameter by solving the Raychaudhuri equation which yields power law solutions in early radiation and matter dominated epochs and de-Sitter like solution in late Universe. We analysed this evolution in relation to observed Hubble data and found that the dependence of the model parameters in reproducing various epochs of the Universe is non-minimal. Furthermore, to test the stability of our models, we looked into the evolution of the speed of sound squared, which indicates that our models are stable to density perturbations. Finally, we utilize the geometrical method of O m diagnostics to conclude that our model exhibits quintessence like behaviour.