On the Foundations of Entropic Cosmologies: Inconsistencies, Possible Solutions and Dead End Signs

In this letter we explore the foundations of entropic cosmology and highlightsome important flaws which have emerged and adopted in the recent literature.We argue that, when applying entropy and temperature on the cosmologicalhorizon by assuming the holographic principle for all thermodynamic approachesto cosmology and gravity, one must derive the consistent thermodynamicquantities following Clausius relation. One key assumption which is generallyoverlooked, is that in this process one must assume a mass-to-horizon relation,which is generally taken as a linear one. We show that, regardless of the typeof entropy chosen on the cosmological horizon, when a thermodynamicallyconsistent corresponding temperature is considered, all modified entropic forcemodels are equivalent to and indistinguishable from the original entropic forcemodels based on standard Bekenstein entropy and Hawking temperature. As such,they are also plagued by the same problems and inability to describe in asatisfactory qualitative and quantitative way the cosmological dynamics as itemerges from the probes we have. We also show that the standard acceptedparameterization for Hawking temperature (including a γ rescaling) isactually not correctly applied, namely, it is not related to entropy in athermodynamically consistent way. Finally, we clearly state that the explicitform of the entropic force on cosmological horizons is mostly dictated by theassumption on the mass-to-horizon relation. As such, we discuss what should bedone in order to fix all such issues, and what conceptually could be implied byits correct implementation in order to advance in the field.