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Comprehensive analysis of the compact phase space for Hu-Sawicki <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> dark energy models including spatial curvature
We present a comprehensive dynamical systems analysis of homogeneous and isotropic Friedmann-Lema\^{\i}tre-Robertson-Walker cosmologies in the Hu-Sawicki $f(R)$ dark energy model for the parameter choice ${n,{C}_{1}}={1,1}$. For a generic $f(R)$ theory, we outline the procedures of compactification of the phase space, which in general is four dimensional. We also outline how, …