Generalized mass-to-horizon relation: A new global approach to entropic cosmologies and its connection to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>CDM</mml:mi></mml:math>
Hussain Gohar, Vincenzo Salzano
Abstract
In this paper we propose a new generalized mass-to-horizon relation to be used in the context of entropic cosmologies and holographic principle scenarios. We show that a general scaling of the mass with the universe horizon as $M=\ensuremath{\gamma}\frac{{c}^{2}}{G}{L}^{n}$ leads to a new generalized entropy ${S}_{n}=\ensuremath{\gamma}\frac{n}{1+n}\frac{2\ensuremath{\pi}{k}_{B}{c}^{3}}{G\ensuremath{\hbar}}{L}^{n+1}$ from which we can recover many of the recently proposed forms of entropies at cosmological and black hole scales and also establish a thermodynamically consistent relation between each of them and Hawking temperature. We analyze the consequences of introducing this new mass-to-horizon relation on cosmological scales by comparing the corresponding modified Friedmann, acceleration, and continuity equations to cosmological data. We find that when $n=3$, the entropic cosmology model is fully and totally equivalent to the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, thus providing a new fundamental support for the origin and the nature of the cosmological constant. In general, if $\mathrm{log}\text{ }\ensuremath{\gamma}<\ensuremath{-}3$, and irrespective of the value of $n$, we find a very good agreement with the data comparable with $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ from which, in Bayesian terms, our models are indistinguishable.