Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models

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In this paper we investigate, from the dynamical systems perspective, the evolution of a Kantowski-Sachs metric in a generic class of $f(R)$ models.

• We present conditions (i.
• e., differentiability conditions, existence of minima, monotony intervals, etc.) for a free input function related to the $f(R)$, that guarantee the asymptotic stability of well-motivated physical solutions, specially, self-accelerated solutions, allowing to describe both inflationary- and late-time acceleration stages of the cosmic evolution.
• We discuss which $f(R)$ theories allows for a cosmic evolution with an acceptable matter era, in correspondence to the modern cosmological paradigm.