De Sitter Entropy in Higher Derivative Theories of Gravity

A theorem on higer-order derivative theories of gravity is proved. We find that the de Sitter/anti-de Sitter metric is always a solution of any generally covariant theory of gravity. With this theorem and a general form of entropy function for de Sitter spacetimes, we show how to calculate the entropy of de Sitter spacetime in a generally covariant theory of gravity without knowing the details of the modified metric. As an example, a general formula of dS entropy in Lovelock gravity is obtained.

Automated summary

A theorem on higher-order derivative theories of gravity is proven, showing that the de Sitter/anti-de Sitter metric is always a solution in any generally covariant theory of gravity. Using this theorem and a general form of entropy function for de Sitter spacetimes, the entropy of de Sitter spacetime in a generally covariant theory of gravity can be calculated without knowing the details of the modified metric. As an example, a general formula for dS entropy in Lovelock gravity is obtained.