Towards a no hair theorem for higher order gravity

TL;DR

This paper investigates conditions under which de Sitter space acts as an attractor in higher order gravity models, revealing that non-vanishing R^2 terms are essential for this property across various dimensions.

Contribution

It demonstrates that de Sitter space can be an attractor in higher order gravity theories with arbitrary derivatives, emphasizing the necessity of R^2 terms for this behavior.

Findings

De Sitter space is an attractor for higher order gravity models with non-zero R^2 terms.

Results are dimension-independent, applicable to 1+1 dimensions and Kaluza-Klein cosmology.

Attractor property persists for arbitrarily large order of the field equations.

Abstract

We use gravitational Lagrangians $R \Box \sp k R \sqrt{-g}$ and linear combinations of them; we ask under which circumstances the de Sitter space-time represents an attractor solution in the set of spatially flat Friedman models. Results are: For arbitrary $k$, i.e., for arbitrarily large order of the field equation, on can always find examples where the attractor property takes place. Such examples necessarily need a non-vanishing $R\sp 2$-term. The main formulas do not depend on the dimension, so one gets similar results also for 1+1-dimensional gravity and for Kaluza-Klein cosmology.