Vítor Bessa
Faculdade de Ciências da Universidade do Porto
CMAT, Universidade do Minho
CAMGSD, Instituto Superior Técnico
Motivated by cosmological models of the early universe we analyze the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $V(\phi)\sim \phi^{2n}$, $n\in\mathbb{N}$, interacting with a perfect fluid with linear equation of state in flat Robertson-Walker spacetimes. The interaction is a friction-like term of the form $\Gamma(\phi)\sim \phi^{2p}$, $p\in\mathbb{N}_0$.
We perform a global dynamical analysis of the model and provide a detailed description of the future and past asymptotics. The analysis relies on the introduction of a new regular dynamical systems formulation of the Einstein equations on a compact state space and the use of dynamical systems tools such as averaging methods involving a time-dependent perturbation parameter.