Positive cosmological constant, non-local gravity and horizon entropy

TL;DR

This paper explores a class of gravity theories, including a non-local model, that admit Einstein solutions with arbitrary cosmological constants, showing that positive cosmological constant phases lead to vanishing horizon entropy, impacting the understanding of horizon thermodynamics.

Contribution

It demonstrates that a specific non-local gravity model is ghost-free on Einstein backgrounds and reveals how positive cosmological constant phases affect horizon entropy.

Findings

Non-local gravity model is ghost-free on Einstein spacetimes.

Horizon entropy vanishes in phases with positive cosmological constant.

Horizon entropy is proportional to area when the cosmological constant is zero.

Abstract

We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant $\Lambda>0$ and with zero $\Lambda$. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive $\Lambda$, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.