Quintessential Inflation in Light of ACT DR6

TL;DR

Can a single canonical scalar field drive both early inflation and late-time acceleration? The paper conducts a precise numerical study of smooth quintessential inflation with a runaway exponential potential, solving the full background and perturbation dynamics and incorporating the post-inflation stiff (kination) phase. It finds that for $N=60$ the model yields $n_s = 0.964241$ and $r = 7.48\times 10^{-5}$, with a narrowly confined field excursion $\Delta\phi \approx 0.03\,M_{\rm Pl}$ and a small negative running $\alpha_s \approx -5.94\times 10^{-4}$; the kinetic-dominated epoch simultaneously predicts a blue-tilted stochastic gravitational-wave background that could be detected by future interferometers. The scenario remains consistent with current Planck+ACT+DESI constraints and provides falsifiable predictions across frequencies from PTA to space-based detectors, linking the inflationary exit and reheating history to the late-time dark-energy behavior in a minimal, testable framework.

Abstract

We perform a precision investigation of smooth quintessential inflation in which a single canonical scalar field unifies the two known phases of cosmic acceleration. Using a CMB-normalized runaway exponential potential, we obtain sharply predictive inflationary observables: a red-tilted spectrum with $n_s = 0.964241$ and an exceptionally suppressed tensor-to-scalar ratio $r = 7.48 \times 10^{-5}$ at $N=60$, lying near the optimal region of current Planck+ACT constraints. Remarkably, all observable scales exit the horizon within an extremely narrow field interval $Δφ\simeq 0.03\,M_{\rm Pl}$, tightly linking early and late-time dynamics and reducing theoretical ambiguities. While inflationary tensors remain invisible to CMB B-mode surveys, the subsequent stiff epoch-an intrinsic hallmark of quintessential cosmology-imprints a blue-tilted stochastic gravitational-wave background within the discovery reach of future interferometers such as LISA, DECIGO, ALIA, and BBO. Our results demonstrate that this minimal, featureless model not only survives current bounds, but provides concrete, falsifiable predictions across gravitational-wave frequencies spanning over twenty orders of magnitude.

Figures (5)

• Figure 1: Runaway inflationary potential $V(\phi)$ for Eq. \ref{['eq:V_runaway_refined']}. The slow-roll plateau gives way to a steep descent that induces a kinetic-dominated epoch.
• Figure 2: Potential slow-roll parameters $\epsilon_V$ and $|\eta_V|$ versus inflaton field value. The end of inflation occurs when $\epsilon_V=1$, driven by curvature variations in the potential.
• Figure 3: E-fold dependence on the inflaton field. The CMB pivot scales probe a limited portion of the potential, enhancing model predictivity and connecting early-time observables to late-time cosmic acceleration.
• Figure 4: Model predictions in the $(n_s,\alpha_s)$ plane compared with present and forecast CMB constraints. The theoretical trajectory traces a narrow curve consistent with the observed degeneracy direction.
• Figure 5: Predictions in the $(n_s,r)$ plane are fully consistent with current bounds. Despite the suppressed tensor amplitude at CMB scales, high-frequency gravitational waves provide an essential observational window into the post-inflationary stiff epoch.