Inflation and Quintessence: Theoretical Approach of Cosmological Reconstruction

Abstract

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 ${\cal L}_ϕ=-{1/2}(\partialϕ)^2 -V(ϕ)$. By considering a generic situation that inflaton attains a nearly constant velocity, during inflation, $m_P^{-1} (dϕ/dN)\equiv α$ (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. For the minimally coupled quintessence, $α_Q\equiv dA(Q)/d(κQ)=0$ (where $A(Q)$ is the standard matter-quintessence coupling), the dark energy equation of state in the range $-1\le w_{DE} < -0.82$ can be obtained for $0\le α< 0.63$. For $α<0.1$, the model allows for only modest evolution of dark energy density with redshift. The effect of the matter-quintessence coupling can be significant only if $|α_Q| \gtrsim 0.1$, while a small coupling $|α_Q|< 0.1$ will have almost no effect on cosmological parameters. The best fit value of $α_Q$ in our model is found to be $α_Q \simeq 0.06$, but it may contain significant numerical errors, viz $α_Q=0.06\pm 0.35$, which thereby implies the consistency of our model with general relativity (for which $α_Q=0$) at $1σ$ level.