Non-minimally coupled quintessential inflation

We present a unified framework that simultaneously addresses the dynamics of early-time cosmic inflation and late-time cosmic acceleration within the context of a single scalar field non-minimally coupled to gravity. By employing an exponential coupling function and a scalar potential with dual asymptotic plateaus, our model naturally transitions from inflationary dynamics at small field values to a quintessence-like behavior at large field values. We derive the inflationary predictions for the spectral index ($n_s$) and tensor-to-scalar ratio ($r$) in agreement with current observational constraints. For late-time acceleration, the model produces a viable dark energy component with an equation of state $w_\phi$ approaching $-1$ but retaining a measurable deviation that could serve as an observational signature. This work demonstrates that a single theoretical framework can reconcile both early inflation and the late-time accelerated expansion of the Universe.