Modified cosmology from quantum deformed entropy

Abstract

Jalalzadeh (2022), established that the thermodynamical entropy of a quantum-deformed black hole with horizon area A can be written as Sq=πsinA8GN/sinπ2N, where N=Lq2/LP2, LP being the Planck length and Lq denoting, generically, the q-deformed cosmic event horizon distance Lq. Motivated by this, we now extend the framework constructed in Jalalzadeh (2022) towards the Friedmann and Raychaudhuri equations describing spatially homogeneous and isotropic universe dynamics. Our procedure in this paper involves a twofold assumption. On the one hand, we take the entropy associated with the apparent horizon of the Robertson–Walker universe in the form of the aforementioned expression. On the other hand, we assume that the unified first law of thermodynamics, dE=TdS+WdV, holds on the apparent horizon. Subsequently, we find a novel modified cosmological scenario characterized by quantum-deformed (q-deformed) Friedmann and Raychaudhuri equations containing additional components that generate an effective dark energy sector. Our results indicate an effective dark energy component, which can explain the Universe’s late-time acceleration. Moreover, the Universe follows the standard thermal history, with a transition redshift from deceleration to acceleration at ztran=0.5. More precisely, according to our model, at a redshift of z=0.377, the effective dark energy dominates with a de Sitter universe in the long run. We include the evolution of luminosity distance, μ, the Hubble parameter, H(z), and the deceleration parameter, q(z), versus redshift. Finally, we have conducted a comparative analysis of our proposed model with others involving non-extensive entropies.