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In this letter, we propose a new generalized mass-to-horizon relation to beused in the context of entropic cosmologies and holographic principlescenarios. We show that a general scaling of the mass with the Universe horizonas $M=\gamma \frac{c^2}{G}L^n$ leads to a new generalized entropy $S_n = \gamma\frac{n}{1+n}\frac{2 \pi\,k_B\,c^3}{G\,\hbar} L^{n+1}$ from which we canrecover many of the recently proposed forms of entropies at cosmological andblack hole scales and also establish a thermodynamically consistent relationbetween each of them and Hawking temperature. We analyse the consequences ofintroducing this new mass-to-horizon relation on cosmological scales bycomparing the corresponding modified Friedmann, acceleration, and continuityequations to cosmological data. We find that when $n=3$, the entropic cosmologymodel is fully and totally equivalent to the standard $\Lambda$CDM model, thusproviding a new fundamental support for the origin and the nature of thecosmological constant. In general, if $\log \gamma < -3$, and irrespective ofthe value of $n$, we find a very good agreement with the data comparable with$\Lambda$CDM from which, in Bayesian terms, our models are indistinguishable.

A generalized mass-to-horizon relation: a new global approach to entropic cosmologies and its connection to \texorpdfstring{$\Lambda$}{Lambda}CDM