Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lema\^itre-Robertson-Walker models

Understand

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $\gamma$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric are investigated.

• Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics.
• Therefore, simple time-averaged systems determine the future asymptotic behavior.
• Depending on values of barotropic index $\gamma$ late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution.