Inflation and the principle of equivalence

A formal, mathematical statement of the principle of equivalence in general relativity is that one must always be able to find - at each location within a curved spacetime - the local free-falling frame against which one can measure the acceleration-induced time dilation and degree of curvature relative to flat spacetime. In this article, we use this theorem to prove that a de Sitter expansion, required during cosmic inflation, does not satisfy this condition and is therefore inconsistent with the PoE. To emphasize the importance - and reality - of this outcome, we contrast it with the analogous derivation for the Schwarzschild metric, which instead satisfies this requirement completely. We point out that this failure by de Sitter results from its incorrect handling of the Friedmann-Lema & icirc;tre-Robertson-Walker (FLRW) lapse function, g tt {g}_{{\rm{tt}}} . Our conclusion calls into question whether a period of inflated expansion could have even been possible in the context of FLRW cosmologies, and is noteworthy in light of recent, high-precision measurements showing that inflation could not have solved the temperature horizon problem while simultaneously producing the observed primordial power spectrum.