Modified Friedmann equations from DSR-GUP

Abstract

Considering the modified entropy-area relation from doubly special relativity-generalized uncertainity principle (DSR-GUP), we obtain the modified Friedmann equations from the first law of thermodynamics at apparent horizon. Due to the importance of GUP at Planck scale, we investigate the Friedmann equations and show the maximum energy density ρ at Planck scale. Since GUP implies a minimal length, we find a minimum apparent horizon which has a potential to remove the Big Bang singularity. Furthermore, we analyse the effects of DSR-GUP on the deceleration parameter q for the equation of state p=ωρ and the flat case. Finally, we check the validity of the generalized second law (GSL) of thermodynamics and show that it is valid for all eras of the universe for any spatial curvature.