Generalized scalar field cosmologies

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In this paper, we use both local and global phase-space descriptions and averaging methods to find qualitative features of solutions for the FLRW and Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter.

• We prove new theorems and also retrieve previous results that can be seen as corollaries of the present results.
• We study the stability of the equilibrium points in a phase-space, as well as the dynamics in the regime where the scalar field diverges.
• We obtain equilibrium points that represent some solutions of cosmological interest, such as several types of scaling solutions, a kinetic dominated solution representing a stiff fluid, a solution dominated by an effective energy density of geometric origin, a quintessence scalar field dominated solution, the vacuum de Sitter solution associated to the minimum of the potential, and a non-interacting matter dominated solution.