Inflationary attractors and radiative corrections in light of ACT data

TL;DR

ACT data shift the viable region of inflationary observables in the $(n_s,r)$ plane, challenging traditional single-field models. The authors use a UV-agnostic, loop-inspired approach to implement radiative corrections with a dominant parameter $\delta$, showing that both $\xi$- and $\alpha$-attractors can be steered toward ACT-preferred regions, though the corrections affect them differently due to frame effects. Percent-level corrections strongly impact $\xi$-attractors, while sub-percent corrections can notably affect small-$\alpha$ attractors; a simple toy model with a heavy spectator field illustrates plausible UV origins and indicates a potential toward linear inflation at larger $\delta$. These results imply that inflationary predictions may be less discriminating than previously thought unless UV completions are specified, underscoring the need for theory-guided approaches to interpreting cosmological data. Overall, radiative corrections emerge as a natural mechanism to reconcile attractor models with current observations, while challenging the precision with which single-field predictions can be pinned down.

Abstract

In light of the recent results from the Atacama Cosmology Telescope (ACT), which have provided a notable shift in the constraints on $(n_s, r)$ and placed several otherwise viable models of inflation in tension with the latest data, we investigate the possible effects that radiative corrections can have on $ξ$-attractor and $α$-attractor models of inflation. These models, which share much in common with Starobinsky inflation, have likewise been put under pressure by these results. We find that percent (and even sub-percent) level radiative corrections can easily shift both of these classes of inflation models comfortably into the regions of parameter space favoured by the most recent constraints. However, the flexibility under such corrections calls into question to what extent it is possible to precisely pin down model-specific predictions for important cosmological observables.

Figures (6)

• Figure 1: Higgs-like (with $\xi =10$) potential (solid blue line) compared with loop corrected effective potentials for the Higgs-like potential (dashed green line) and E-model $\alpha$-attractor (with $\alpha = 1$) potential (dashed yellow line). While the Higgs-like potential and E-model potential at the chosen values for $\xi$ and $\alpha$ will coincide with the Starobinsky potential at to a very high degree of approximation at tree level, the radiatively corrected versions of these potentials differ more notably because in the Higgs-like case one must performs the conformal transformation after finding the effective potential whereas with the E-models one does not perform a conformal transformation.
• Figure 2: Comparison of $n_s$ and $r$ predictions for $\xi$-attractors (top left) and $\alpha$-attractor T and E-models (top right). Here we see that percent level quantum corrections can move the $\xi$-attractors off of their strong coupling attractor and comfortably within the latest ACT posteriors for the central $N=55$ number of e-foldings where we have considered values of the non-minimal coupling parameter $\log_{10} \xi \in [-8,\ 3.5]$. Additionally, we see that sub-percent level quantum corrections can induce fairly substantial shifts in the predictions for $\alpha$-attractors at small $\alpha$, where we have included the predictions spanning $N \in [50, 60]$ for both T and E-models considering values of $\alpha \in [.02, 4.0]$.
• Figure 3: The results for $\alpha_s$ and $n_s$ (bottom) for $\xi$-attractors and $\alpha$-attractors for representative models from these classes of models ($\xi = 10$ and $\alpha = 0.1$) with a percent level correction spanning $N \in [50, 60]$. We see $n_s$ shift as expected, but the radiative corrections do not induce a notable change in $\alpha_s$.
• Figure 4: As the loop correction term $\delta$ is made larger, the entire family of $\xi$-attractors approaches a new attractor given by linear inflation. See also Artymowski:2016dlz.
• Figure 5: At small $\alpha$ the shift in $\chi_{\mathrm{cmb}}$ induced by the loop corrections occurs where $\eta$ is rapidly changing due to the steepness of the potential. In contrast, for larger $\alpha$, $\chi_{\mathrm{cmb}}$ occurs in a region of field space where $\eta$ is more slowly evolving, which results in a much smaller shift in the observables.