# Global dynamics of interacting monomial scalar field potentials and perfect fluids

### Online | 2021-12-14 | 15:00

Vítor Bessa

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.