Swampland bound on quintessential inflation in IDM

Abstract

We study a quintessential inflation scenario based on the Inert Doublet Model (IDM) coupled to a quintessence field via an exponential potential $V_0e^{-\beta\phi/M_p}$. Using a conformal transformation from the Jordan frame to the Einstein frame, we derive an effective Starobinsky-type potential modulated by an exponential factor that naturally unifies the inflationary epoch with the late-time accelerated expansion of the Universe. We analyze the resulting two-field dynamics, compute the slow-roll parameters, the primordial perturbation spectrum, as well as the inflationary observables $n_s$ and $r$, and then confront the predictions with the latest $Planck$ and $BICEP/Keck$ data. We find amongst others that the quintessence inflaton coupling must remain extremely weak, in the order of $\beta \lesssim 4\times10^{-3}$, to satisfy current $CMB$ data, whereas swampland dS conjecture favors a step potential with $\beta\sim\mathcal{O}(1)$, signaling a significant tension between quantum gravity consistency and cosmological viability. We conclude by discussing possible extensions and stabilization mechanisms that could help reconcile the inflationary predictions with swampland constraints.