Towards a cosmic no hair theorem for higher‐order gravity

We use gravitational Lagrangians R □ k √− g and linear combinations of them motivated from trials how to overcome the non‐ renormalizability of Einstein' s theory. We ask under which circumstances the de Sitter space‐ time represents an attractor solution in the set of spatially flat Friedman models. This property ensures the inflationary model to be a typical solution; nowadays, this property is called cosmic no hair theorem because it is analogous to the no hair theorem for black holes. Results are: for arbitrary k , i.e., for arbitrarily large order 2 k + 4 of the field equation, one can always find examples where the attractor property takes place. Such examples necessarily need a non‐ vanishing R 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.