Reconstructing a model of quintessential inflation

We present an explicit cosmological model where inflation and dark energy both could arise from the dynamics of the same scalar field. We present our discussion in the framework where the inflaton field phi attains a nearly constant velocity m(p)(-1)vertical bar d phi/dN vertical bar alpha + beta exp(beta N) (where N ln a is the e-folding time) during inflation. We show that the model with vertical bar alpha vertical bar < 0.25 and beta < 0 can easily satisfy inflationary constraints, including the spectral index of scalar fluctuations (n(s) = 0.96 +/- 0.013), tensor-to-scalar ratio ( r < 0.28) and also the bound imposed on Omega(phi) during the nucleosynthesis epoch (Omega(phi)(1 similar to MeV) < 0.1). In our construction, the scalar field potential always scales proportionally to the square of the Hubble expansion rate. One may thereby account for the two vastly different energy scales associated with the Hubble parameters at early and late epochs. The inflaton energy could also produce an observationally significant effective dark energy at a late epoch without violating local gravity tests.