Emergence of cosmological scaling behavior in asymptotic regime

Understand

In this paper we consider a scalar field system with a class of potentials given by the expression, $V(\phi)\propto \phi^m {\rm exp}({-\lambda \phi^n/{M^n_{Pl}}})$; $m\geqslant 0, n>1$ for which $\Gamma=V_{\phi \phi}V/V^2_{\phi}\to 1 $ as $|\phi|\to \infty$.

• We carry out dynamical analysis for the underlying system choosing a suitable set of autonomous variables and find all the fixed points.
• In particular, we show that the scaling solution is an attractor of the system in the asymptotic regime.
• We indicate the application of the solution to models of quintessential inflation.