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Swampland bound on quintessential inflation in IDM

S. Saoud, M. A. Rbah, R. Sammani, E. H. Saidi, R. Ahl Laamara

TL;DR

This work analyzes a quintessential inflation scenario where the Inert Doublet Model (IDM) is coupled to a quintessence field via $V_Q(\phi)=V_0 e^{-\beta \phi/M_p}$. By transforming from the Jordan to the Einstein frame, the authors derive a Starobinsky-like inflationary potential modulated by the exponential coupling and study the resulting two-field dynamics and inflationary observables $(n_s,r)$, confronting them with Planck and BK data. They find that to fit the CMB data, the coupling must be extremely small, $\beta \lesssim 4\times 10^{-3}$, which is in tension with the de Sitter Swampland bound $\beta \sim \mathcal{O}(1)$, signaling a fundamental clash between quantum gravity constraints and cosmological viability in this minimal setup. The paper concludes that reconciling these requirements likely requires extensions or stabilization mechanisms beyond the simplest Quintessential IDM, and it highlights interesting directions for reheating and isocurvature phenomenology in future work.

Abstract

We study a quintessential inflation scenario based on the Inert Doublet Model (IDM) coupled to a quintessence field via an exponential potential $V_0e^{-βφ/M_p}$. 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 $β\lesssim 4\times10^{-3}$, to satisfy current $CMB$ data, whereas swampland dS conjecture favors a step potential with $β\sim\mathcal{O}(1)$, 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.

Swampland bound on quintessential inflation in IDM

TL;DR

This work analyzes a quintessential inflation scenario where the Inert Doublet Model (IDM) is coupled to a quintessence field via . By transforming from the Jordan to the Einstein frame, the authors derive a Starobinsky-like inflationary potential modulated by the exponential coupling and study the resulting two-field dynamics and inflationary observables , confronting them with Planck and BK data. They find that to fit the CMB data, the coupling must be extremely small, , which is in tension with the de Sitter Swampland bound , signaling a fundamental clash between quantum gravity constraints and cosmological viability in this minimal setup. The paper concludes that reconciling these requirements likely requires extensions or stabilization mechanisms beyond the simplest Quintessential IDM, and it highlights interesting directions for reheating and isocurvature phenomenology in future work.

Abstract

We study a quintessential inflation scenario based on the Inert Doublet Model (IDM) coupled to a quintessence field via an exponential potential . 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 and , and then confront the predictions with the latest and data. We find amongst others that the quintessence inflaton coupling must remain extremely weak, in the order of , to satisfy current data, whereas swampland dS conjecture favors a step potential with , 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.

Paper Structure

This paper contains 12 sections, 44 equations, 4 figures.

Table of Contents

  1. Introduction
  2. dS conjecture and the IDM with quintessence
  3. The IDM Higgs sector coupled to quintessence
  4. de Sitter constraints on the coupling potential
  5. Quintessential IDM in the Early Universe
  6. Recasting in the Jordan frame
  7. The effective potential
  8. Inflationary slow-roll observables
  9. Slow--roll parameters
  10. Number of e-folds and the scalar power spectrum
  11. $CMB$ bounds on quintessential IDM
  12. Conclusion

Figures (4)

  • Figure 1: The figure shows the scalar power spectrum $P_s$ as a function of ${ \if@compatibility \mathchar"010C {} \mathchar"010C }$, for a reference value ${ \if@compatibility \mathchar"011E {} \mathchar"011E } / M_{\mathrm{p}} = 1 \, \text{ and a normalization } \, P_s ({ \if@compatibility \mathchar"010C {} \mathchar"010C } = 0) \simeq 2.1 \times 10^{-9}$ade2016planck.
  • Figure 2: a and b shows the dependence of $n_s$ and r to ${ \if@compatibility \mathchar"010C {} \mathchar"010C }$ for the present model
  • Figure 3: The slowly rolling inflationary potential ${ \if@compatibility \mathchar"010C {} \mathchar"010C }=1$
  • Figure 4: The slowly rolling inflationary potential ${ \if@compatibility \mathchar"010C {} \mathchar"010C }=4\times10^{-3}$