A No-go Theorem Prohibiting Inflation in the Entropic Force Scenario

TL;DR

The paper demonstrates that implementing inflation within Verlinde's entropic force framework requires negative temperatures, leading to conceptual issues, and shows that avoiding negative temperatures in the derivation of Einstein's equations is impossible.

Contribution

It proves the necessity of negative temperatures for inflation in the entropic force scenario and establishes the impossibility of redefining temperature to circumvent this requirement.

Findings

Negative temperature is required for inflation in the entropic force model.

Avoiding negative temperatures leads to inconsistencies in deriving Einstein's equations.

Theoretical constraints prevent alternative temperature definitions for this purpose.

Abstract

We show that to accommodate inflation in the entropic force scenario of Verlinde, it is necessary to introduce a negative temperature on a holographic screen, this will introduce several puzzles such as energy non-conservation. If one tries to modify the derivation of the Einstein equations to avoid a negative temperature, we prove that it is impossible to find a proper new definition of temperature to derive the Einstein equations.