In this letter we explore the foundations of entropic cosmology and highlight some important flaws which have emerged and adopted in the recent literature. We argue that, when applying entropy and temperature on the cosmological horizon by assuming the holographic principle for all thermodynamic approaches to cosmology and gravity, one must derive the consistent thermodynamic quantities following Clausius relation. One key assumption which is generally overlooked, 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 type of entropy chosen on the cosmological horizon, when a thermodynamically consistent corresponding temperature is considered, all modified entropic force models are equivalent to and indistinguishable from the original entropic force models based on standard Bekenstein entropy and Hawking temperature. As such, they are also plagued by the same problems and inability to describe in a satisfactory qualitative and quantitative way the cosmological dynamics as it emerges from the probes we have. We also show that the standard accepted parameterization for Hawking temperature (including a rescaling) is actually not correctly applied, namely, it is not related to entropy in a thermodynamically consistent way. Finally, we clearly state that the explicit form of the entropic force on cosmological horizons is mostly dictated by the assumption on the mass-to-horizon relation. As such, we discuss what should be done in order to fix all such issues, and what conceptually could be implied by its correct implementation in order to advance in the field.

中文翻译：

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熵宇宙论的基础：不一致、可能的解决方案和死胡同


在这封信中，我们探讨了熵宇宙学的基础，并强调了最近文献中出现和采用的一些重要缺陷。我们认为，当通过假设宇宙学和引力的所有热力学方法的全息原理在宇宙视界上应用熵和温度时，必须导出遵循克劳修斯关系的一致热力学量。一个通常被忽视的关键假设是，在此过程中必须假设质量与地平线的关系，通常将其视为线性关系。我们表明，无论宇宙视界上选择的熵类型如何，当考虑热力学一致的相应温度时，所有修改的熵力模型都与基于标准贝肯斯坦熵和霍金温度的原始熵力模型等效且没有区别。因此，他们也受到同样的问题的困扰，并且无法以令人满意的定性和定量方式描述从我们的探测器中出现的宇宙动力学。我们还表明，霍金温度的标准接受参数化（包括重新调整）实际上没有正确应用，即它与热力学一致的熵不相关。最后，我们明确指出，宇宙视界上熵力的显式形式主要由质量与视界关系的假设决定。因此，我们讨论应该采取什么措施来解决所有这些问题，以及正确实施在概念上可能意味着什么，以便在该领域取得进步。