https://doi.org/10.1140/epjp/s13360-022-03477-x
Regular Article
The study of accelerating DE models in Saez–Ballester theory of gravitation
Department of Applied Mathematics, Andhra University, 530003, Visakhapatnam, India
Received:
18
February
2022
Accepted:
26
October
2022
Published online:
1
December
2022
The investigation in the present work is carried out on the spatially homogeneous and anisotropic axially symmetric space-time in the presence of two fluids, one being the pressureless matter and other being the different kinds of holographic dark energy (HDE). Eventually, in the present work, cosmological models with Tsallis HDE, Renyi HDE, Sharma–Mittal HDE by taking Hubble radius as infrared (IR) cutoff (
) are obtained. The geometrical and matter parts of space-time are solved within the Saez–Ballester scalar-tensor theory of gravitation. Interestingly, in this study a time varying deceleration parameter (q) which exhibits a transition from deceleration to acceleration phase is obtained without assuming any scale factor. In the present work, the study of cosmic expansion is done through the scalar field (
) and various cosmological parameters like EoS, deceleration, statefinder, etc. The EoS parameter exhibits quintom-like behavior for Tsallis HDE model, the transition from matter-dominated phase to phantom phase for Renyi HDE model, whereas it shows quintessence behavior for Sharma–Mittal HDE. The stability analysis for three models is studied through the squared speed of sound (
). For all redshift (z) values 
, the Sharma–Mittal HDE model is stable throughout the universe’s expansion. In this work, the obtained results match with recent observational data.
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