Inflation and Quintessence: Theoretical Approach of Cosmological Reconstruction

Understand

In the first part of this paper, we outline the construction of an inflationary cosmology in the framework where inflation is described by a universally evolving scalar field, with the Lagrangian ${\cal L}_\phi=-{1/2}(\partial\phi)^2 -V(\phi)$.

• By considering a generic situation that inflaton attains a nearly constant velocity, during inflation, $m_P^{-1} (d\phi/dN)\equiv \alpha$ (where $N\equiv \ln a$ is the e-folding time), we find the conditions that have to satisfied by the (reconstructed) scalar potential to be consistent with the WMAP inflationary data.
• In the second part of this paper, we introduce a novel approach of constructing dark energy within the context of the standard scalar-tensor gravity.
• The assumption that a scalar field might roll with a nearly constant velocity, during inflation, can also be applied to {\it quintessence} or dark energy models.