Reconstructing a model of quintessential inflation

TL;DR

This paper proposes a unified cosmological model where a single scalar field drives both inflation and dark energy, satisfying observational constraints and explaining different energy scales in the universe's evolution.

Contribution

It introduces a scalar field model with a specific velocity profile that accounts for both inflation and late-time dark energy within a consistent framework.

Findings

Model satisfies inflationary constraints including spectral index and tensor-to-scalar ratio.

Scalar field potential scales with the square of the Hubble rate, linking early and late universe energy scales.

Inflaton energy can produce significant dark energy effects without violating local gravity tests.

Abstract

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 $m_P^{-1} |d\phi/dN|\equiv \alpha+\beta \exp(\beta N)$ (where $N\equiv \ln a$ is the e-folding time) during inflation. We show that the model with $|\alpha|<0.25$ and $\beta<0$ can easily satisfy inflationary constraints, including the spectral index of scalar fluctuations ($n_s=0.96\pm 0.013$), tensor-to-scalar ratio ($r<0.28$) and also the bound imposed on $\Omega_\phi$ during the nucleosynthesis epoch ($\Omega_\phi (1 {\rm MeV})<0.1$). 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.