Effects of Spatial Curvature on the $f(R)$ Gravity Phase Space: no Inflationary Attractor?

Understand

In this paper we study the effects of spatial curvature of the metric on the phase space of vacuum $f(R)$ gravity.

• Particularly, we appropriately choose the variables of the dynamical system, in order for this to be autonomous, and we study the phase space of the resulting theory, focusing on de Sitter, matter and radiation domination fixed points.
• Our analysis indicates that the effect of spatial curvature on the phase space is radical, since it destabilizes all the stable de Sitter vacua of the flat spacetime vacuum $f(R)$ gravity phase space, making the phase space having non-trivial unstable submanifolds.
• This instability occurs regardless if the spacetime has elliptic or hyperbolic spatial sections, and it is also robust towards the choice of initial conditions.