The study of hypersurface-homogeneous space-time in Renyi holographic dark energy

The investigation of this work is carried on the hypersurface-homogeneous space-time in the presence of two fluids, one being the pressureless matter and the other being the Renyi holographic dark energy (RHDE). Eventually, this work solves the cosmological model with Renyi HDE by taking the Hubble horizon as an infrared (IR) cutoff (L = H-1). The geometrical and matter parts of space-time are solved within the Saez-Ballester scalar-tensor theory of gravitation. Interestingly, this study obtains a time-varying deceleration parameter (q) that exhibits a transition from deceleration to acceleration phase. For the configurations of parameter K emerging in space-time, three physically plausible cosmological hypotheses of the cosmos are outlined in this work. The kinematical properties were obtained and discussed for the three values of K. The study of cosmic expansion in the accelerated phase of this work is done through various cosmological parameters like EoS, deceleration parameter, statefinder parameter, etc. The Hubble parameter is derived in terms of cosmic time and redshift both. The present value of this parameter is estimated by taking 25 point data sets of observational Hubble data (OHD). The stability of the model is verified through the analysis of squared speed of sound (v(s)(2)) parameter. In this work, the obtained results match with recent observational data.