An insight into holographic inflation under different cosmological settings through rigorous analysis of EoS parameter

The unification of early and late-time universe in the background of holographic fluid is proposed. The study’s first phase examines whether or not the four models based on the scale factor power law, intermediate, logamediate, and emergent, can derive inflationary conditions. In the study’s second phase, the Equation of State parameter is reconstructed, and the behavior of the Equation of State parameter is analyzed. Finally, we have concluded that the four models under consideration are consistent with the inflationary conditions, as they can derive inflation in the presence of a holographic fluid. The study further reveals that in the late-time scenario for power law, intermediate, and emergent cases, the equation of state parameter remains in the phantom era at present, which aligns with observational data. Also, statefinder diagnostics have been discussed for the attainability of $\Lambda$CDM fixed point.