ACT DR6+Planck impact on inflation with non-zero vacuum expectation value and the post-inflationary behavior

TL;DR

The paper reexamines the Witten-O'Raifeartaigh inflationary model with the WR potential $V(\phi)=\Lambda^4\ln^2\left(\frac{\phi}{M}\right)$ in light of Planck+ACT-DR6+BK18+DESI data, finding that sub-Planckian $M$ is viable and yields $n_s\approx0.9785$ and $r\approx0.02$. It then uses lattice simulations to show that tachyonic amplification after inflation can fragment the inflaton into localized oscillons, which act as a source for gravitational waves, though the resulting GHz-frequency signals lie beyond near-future detector ranges. The work also explores perturbative reheating with a $y\phi\sigma^2$ coupling, deriving constraints such that $10^{-18} \lesssim y \lesssim \mathcal{O}(1)$ for certain $M$, and discusses how future CMB observations could tighten these bounds. Overall, the study demonstrates a coherent link between updated CMB constraints and rich post-inflationary physics, including oscillon dynamics and high-frequency gravitational waves, underscoring the potential for precision cosmology to illuminate microphysical processes in the early Universe.

Abstract

The impact of the most recent cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT) is studied for a model of cosmic inflation which predicts a non-zero vacuum expectation value (VEV) $M$ for a large-field regime. Since lower values of $M$ are compatible with the higher spectral index $n_s$ provided by the ACT+Planck joint analysis, we establish new limits on this parameter while also considering further CMB data from the latest BICEP/Keck Array release for CMB polarization modes. We find $\log_{10}M/M_{Pl}=-2.5^{+1.1}_{-1.3}$ at 68\% confidence level, compatible with $M/M_{Pl}\simeq 0.003$, which is interesting for post-inflationary processes, such as preheating. We conduct a lattice simulation for the inflaton field for the first few e-folds, as the model is compatible with the production of relics such as oscillons, which are possible candidates as sources of gravitational waves and primordial black holes. We find that the model indeed produces localized, quasi-spherical structures compatible with oscillons, which might lead to signatures detectable by future experiments. However, in agreement with recent works, we find that although the abundance of gravitational waves that could be generated in this regime has an amplitude well within the sensitivities of these detectors, the frequency range is on the GHz limit, away from the expected frequencies. Finally, we estimate the impact of a coupling of the type $yφσ^2$ to the inflaton, in the realization of perturbative reheating, directly impacting the predictions of the model, as lower values of $M$ are consistent with both the entire allowed temperature range, and the limits imposed by BICEP/Keck Array+Planck+ACT.

Figures (9)

• Figure 1: Scalar spectral index $n_s$ as a function of the mass scale $M$ (blue curve). The upper axis shows the corresponding values for the tensor-to-scalar ratio $r$, for which the Planck+BK18 limit is shown as the black vertical line, while the green and gray horizontal bands correspond to the $95\%$ confidence level (C.L.) limits on $n_s$ given by Planck and Planck+ACT, respectively.
• Figure 2: 68% and 95% confidence level constraints on the WR model, for a Planck+ACT+BK18+DESI analysis.
• Figure 3: Two-dimensional confidence contours for the $n_s$ and $r$ parameters, as derived for the WR model, at 68% and 95% confidence levels.
• Figure 4: The evolution of the background field $\chi$ for the WR model, as a function of the redefined time $\tau$, for three distinct values of the normalized mass scale $m=0.1$ (blue), $m=0.05$ (red), and $m=0.01$ (purple).
• Figure 5: The background field evolution of the WR model (blue), compared with the lattice solution (black), for $m=0.01$. The dashed and solid lines denote the tachyonic region limit and the minimum of the potential, respectively.