The Phase Space of $k$-Essence $f(R)$ Gravity Theory

Understand

Among the remaining viable theories that can successfully describe the late-time era is the $k$-Essence theory and in this work we study in detail the phase space of $k$-Essence $f(R)$ gravity in vacuum.

• This theory can describe in a viable way the inflationary era too, so we shall study the phase space in detail, since this investigation may reveal general properties regarding the inflationary attractors.
• By appropriately choosing the dimensionless variables corresponding to the cosmological system, we shall construct an autonomous dynamical system, and we find the fixed points of the system.
• We focus on quasi-de Sitter attractors, but also to radiation and matter domination attractors, and study their stability.