We propose an idea to build a bridge between reheating and late-time observations in quintessential inflation by backtracking the evolution of the inflaton field from the present time to the end of reheating. This idea is implemented first in the freezing case when the potential gradient is negligible compared to the Hubble friction, rendering the inflaton field frozen, till the present time. We find a simple analytic relation between the reheating temperature and the current values of observational parameters for dark energy and numerically confirm its validity for explicit models. This relation implies that any quintessential inflation model with a successful reheating with the reheating temperature $1\mathrm{MeV}\lesssim T_{\mathrm{re}}\lesssim {10}^9\mathrm{GeV}$ predicts the current value of the equation of state of dark energy to be within an extremely narrow range very close to $-1$, i.e., $-1+{10}^{-48}\lesssim w_0\lesssim -1+{10}^{-24}$. All of the results are universal and can apply to all quintessential inflation models with any reheating mechanism, unless the inflaton field unfreezes before the present time. Motivated by the results that the imprint of reheating on $w_0$ is not observationally measurable in the freezing case, we extend the analysis to the unfreezing case in which the inflaton field unfreezes before the present time. In particular, we derive the general conditions to have the measurable imprint of reheating on $w_0$ and determine the parameter ranges to be compatible with these conditions for the typical models of quintessential inflation.

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• Cosmology