Chaotic Inflation RIDES Again

TL;DR

The paper reexamines chaotic inflation with a complex scalar subject to radiative corrections, yielding a Mexican-hat potential that supports inflation from the radial mode and a PNGB quintessence from the angular mode (the RIDE scenario). It demonstrates that the original RIDE model is disfavored by Planck alone, but becomes compatible when including a non-minimal gravity coupling, and can further fit ACT data by incorporating a small quartic term with ξ around unity. This framework effectively unifies inflation and dark energy within a single field, predicting a reduced tensor-to-scalar ratio and an evolution of the dark-energy component similar to ΛCDM today but with distinct late-time behavior. The approach provides a concrete, testable route to reconcile simple inflationary models with current CMB observations, while offering characteristic signatures in r and n_s and a PNGB-driven dark energy sector.

Abstract

Following the recent Atacama Cosmology Telescope (ACT) results, we revisit chaotic inflation based on a single complex scalar field with mass term $M^2 |Φ|^2$, which usually predicts a spectra index $n_s\approx 0.96$ but a too-large tensor to scalar ratio $r\approx 0.16$. With radiative corrections, the potential $M^2 |Φ|^2 \ln \left( |Φ|^2/Λ^2 \right)$ induces spontaneous symmetry breaking near the scale $Λ$, yielding a Pseudo Nambu-Goldstone boson which can play the role of a quintessence field, hence radiative inflation and dark energy (RIDE). Including a non-minimal coupling to gravity $ξ|Φ|^2 R^2$ reduces $r$, allowing a good fit of the RIDE model to Planck data. Allowing a small additional quartic coupling correction $λ|Φ|^4$ increases both $n_s$ and $r$, with a good fit to ACT data sets achieved for $ξ\approx 1$.

Figures (7)

• Figure 1: The schematic shape of the (scaled) inflationary potential ${V(\sigma)}/{(M^2 M_\mathrm{pl}^2)}$ (left panel) and the (scaled) quintessence potential $V(\varphi)/m^4$ (right panel) for the value of $\Lambda=M_\mathrm{pl}$.
• Figure 2: The inflationary potential at different values of $\Lambda$. Note that its minimum occurs near the value of $\Lambda$ in each case.
• Figure 3: The predictions of the original RIDE model (square points) and the RIDE model with a non-minimal coupling to gravity (circle points) for the spectral index $n_s$ and tensor to scalar ratio $r$ as compared to the WMAP 7-year, Planck 2018 and ACT-BK18 data (the lighter and darker shades refer to the $95\%$ and $68\%$ confidence level regions, respectively). The red (black) points are for $\Lambda=M_\mathrm{pl}$ ($\Lambda=0.01\, M_\mathrm{pl}$) for values of $N_e=46$-$60$.
• Figure 4: The time evolution of the quintessence field $\varphi(t)$, scale factor $a(t)$, equation of state $w(t)$ and energy densities scaled by the critical density $\Omega_i(t)$, in the original RIDE model. The time $t=1$ corresponds to the present day.
• Figure 5: The $n_s$-$r$ plot for various $\xi$ values as compared to Planck 2018 data (with the zoomed in view only showing the most constraining Planck 2018 data near the bottom). Two values of $\Lambda=M_\mathrm{pl}$ (red points) and $\Lambda = 0.01 M_\mathrm{pl}$ (black points) are considered.