Towards a no hair theorem for higher order gravity

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.

35 pages, latex, no figures, e-mail [email protected], [email protected] revised version March 1995, subm. to Class. Quant. Grav.

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• Extended Gravity Theories and the Einstein-Hilbert Action
• Eternal inflation and the initial singularity
• Non-Thermal Phase Transitions after Inflation
• The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models
• New no-scalar-hair theorem for black-holes
• The Newtonian limit of fourth and higher order gravity
• Universality and Scaling at the Onset of Quantum Black Hole Formation
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• The de Sitter space-time as attractor solution in higher order gravity
• Stability Properties of the Starobinsky Cosmological Model

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• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach
• Recovering the effective cosmological constant in extended gravity theories
• Cosmography and large scale structure by f(R) gravity: new results
• Cosmological dynamics in six-order gravity
• Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model