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Non-minimally coupled quintessential inflation

Seong Chan Park

TL;DR

This work develops a unified framework in which a single scalar field non-minimally coupled to gravity drives both early-universe inflation and late-time cosmic acceleration. By employing an exponential non-minimal coupling and a two-plateau potential, the model yields an inflationary epoch with $n_s\approx0.965$ and $r\approx0.003$ for $N_e\approx60$, while at late times it behaves as quintessence with $w_\phi$ approaching $-1$ and possible measurable deviations for finite $f$. The approach remains compatible with current observations (e.g., Planck, DESI BAO+CMB+PantheonPlus) for suitable parameter choices (e.g., $f\gtrsim 7M_P$) and offers a pathway to address the cosmological constant problem within a single scalar-field framework. Overall, it provides a minimal, testable connection between early inflation and late-time acceleration, with distinctive signatures in the dark-energy equation of state and a constrained inflationary parameter space.

Abstract

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 $w_φ$ 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.

Non-minimally coupled quintessential inflation

TL;DR

This work develops a unified framework in which a single scalar field non-minimally coupled to gravity drives both early-universe inflation and late-time cosmic acceleration. By employing an exponential non-minimal coupling and a two-plateau potential, the model yields an inflationary epoch with and for , while at late times it behaves as quintessence with approaching and possible measurable deviations for finite . The approach remains compatible with current observations (e.g., Planck, DESI BAO+CMB+PantheonPlus) for suitable parameter choices (e.g., ) and offers a pathway to address the cosmological constant problem within a single scalar-field framework. Overall, it provides a minimal, testable connection between early inflation and late-time acceleration, with distinctive signatures in the dark-energy equation of state and a constrained inflationary parameter space.

Abstract

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 () and tensor-to-scalar ratio () in agreement with current observational constraints. For late-time acceleration, the model produces a viable dark energy component with an equation of state approaching 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.

Paper Structure

This paper contains 7 sections, 24 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model
  3. General case
  4. Exponential non-minimal coupling
  5. Early time inflation
  6. Late time Dark energy
  7. Summary and conclusions

Figures (3)

  • Figure 1: The potential in Einstein frame in terms of $\phi$. We set $\xi=40,100,200$ and $f=1 M_P$ for illustration purpose.
  • Figure 2: Potential and the slow-roll parameters
  • Figure 3: The equation of state $w_\phi$ is analyzed for $f \in (1, 10)M_P$. To fully account for the dark energy component in the current Universe, we set $\Omega_\phi = 0.7$. The DESI BAO+CMB+PantheonPlus region DESI:2024mwx is shaded.