The Arrow of Time Forbids a Positive Cosmological Constant $Λ$

Abstract

Motivated by the mounting evidence for dark energy, here we explore the consequences of a fundamental cosmological constant $Λ$ for our universe. We show that when the gravitational entropy of a pure DeSitter state ultimately wins over matter, then the thermodynamic arrow of time in our universe must reverse in scales of order a Hubble time. We find that due to the dynamics of gravity and nonlocal entanglement, a finite size system such as a DeSitter patch with horizon size $H_0^{-1}$ has a finite lifetime $Δt$. This phenomenon arises from the dynamic gravitational instabilities that develop during a DeSitter epoch and turn catastrophic. A reversed arrow of time is clearly in disagreement with observations. Thus we are led to conclude: Nature forbids a fundamental $Λ$. Or else general relativity must be modified in the IR regime when $Λ$ dominates the expansion of the Universe.