Static cosmological solutions in quadratic gravity

Abstract

We consider conditions for existence and stability of a static cosmological solution in quadratic gravity. It appears that such a solution for a Universe filled by only one type of perfect fluid is possible in a wide range of the equation of state parameter $w$ and for both positively and negatively spatially curved Universe. We show that the static solution for the negative curvature is always unstable if we require positive energy density of the matter content. On the other hand, a static solution with positive spatial curvature can be stable under certain restrictions. Stability of this solution with respect to isotropic perturbation requires that the coupling constant with the $R^2$ therm in the Lagrangian of the theory is positive, and the equations of state parameter $w$ is located in a rather narrow interval. Nevertheless, the stability condition does not require violation of the Strong Energy Condition. Taking into account anisotropic perturbations leads to further restrictions on the values of coupling constants and the parameter $w$.

arXiv commentVersion identical to the one published in General Relativity and Gravitation journal

References in corpus (16)

• Planck 2013 results. XXII. Constraints on inflation
• Fourth order gravity: equations, history, and applications to cosmology
• On the Stability of the Einstein Static Universe
• Stability of the Einstein static universe in f(R) gravity
• On the evolution of universes in quadratic theories of gravity
• The stability of the Einstein static state in $f(T)$ gravity
• Einstein Static Universe in Exponential $f(T)$ Gravity
• Dynamics of f(R)-cosmologies containing Einstein static models
• The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
• From stable to unstable anomaly-induced inflation
• Anisotropic cosmological solutions in $R+R^2$ gravity
• Initial conditions for Inflation in an FRW Universe
• Generality of Starobinsky and Higgs inflation in the Jordan frame
• Are $R^2$- and Higgs-inflations really unlikely?
• Bouncing solutions in $f(T)$ gravity
• Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric