arXiv : Constraints on Attractor Models of Inflation and Reheating from Planck, BICEP/Keck, ACT DR6, and SPT-3G Data

Ellis, John; Olive, Keith A.; Verner, Sarunas; Garcia, Marcos A.G.

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Preprint
Report number	UMN-TH-4512/25 ; FTPI-MINN-25/14 ; KCL-PH-TH/2025-42 ; CERN-TH-2025-199 ; arXiv:2510.18656
Title	Constraints on Attractor Models of Inflation and Reheating from Planck, BICEP/Keck, ACT DR6, and SPT-3G Data
Author(s)	Ellis, John (King's Coll. London (main) ; CERN) ; Garcia, Marcos A.G. (UNAM, Mexico) ; Olive, Keith A. (U. Minnesota, Minneapolis (main)) ; Verner, Sarunas (U. Chicago (main))
Document contact	Contact: arXiv
Imprint	2025-10-21
Number of pages	25
Note	9 figures, 25 pages
Subject category	astro-ph.CO ; Astrophysics and Astronomy ; hep-ph ; Particle Physics - Phenomenology
Abstract	We analyze the latest cosmic microwave background (CMB) constraints on the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from Planck 2018, BICEP/Keck 2018, the Atacama Cosmology Telescope Data Release 6 (ACT DR6), and the South Pole Telescope (SPT-3G) data, focusing on their implications for attractor models of inflation. We compare systematically observational bounds with theoretical predictions for both E-model ($α$-Starobinsky) and T-model potentials. The observational constraints accommodate E-models with $α\lesssim 25$, with the canonical Starobinsky model ($α= 1$) predicting $n_s = 0.958-0.963$ for reheating temperatures between $100 - 10^{10}$ GeV, in good agreement with Planck 2018 data and within the 95% CL region determined by the Planck-ACT-SPT combination, but below the 95% confidence region of the Planck-ACT-DESI combination. Higher reheating temperatures from near-instantaneous reheating improve the compatibility. T-models predict slightly lower $n_s$ values (0.956-0.961), in some tension with Planck 2018 data, and we find an upper limit of $α\lesssim 11$ in these models. We extend our analysis to generalized $α$-attractors with monomial potentials $V(φ) \propto φ^k$ near the minimum, demonstrating that models with $k \geq 6$ naturally predict $n_s \simeq 0.965 - 0.968$ for typical number of $e$-folds, in better agreement with the ACT DR6 data. We also consider deformed E- and T-models, which allow significantly higher values of $n_s$ for low values of $α\simeq 1$.
Other source	Inspire
Copyright/License	preprint: (License: CC BY 4.0)

$Deformed attractor potentials with $\alpha = 1$ and $k = 2$. Left panel: Deformed Starobinsky (E-model) potential for $\kappa = 1$, $0.9999$, $0.9998$, and $0.9997$. Right panel: Deformed T-model potential for the same $\kappa$ values. The deviations from $\kappa = 1$ introduce observable modifications to the inflationary plateau, and become substantial for $\varphi/M_P \gtrsim 6$.$ $The relation between $N_*$ (defined for a pivot scale of $0.05$~Mpc$^{-1}$) and the reheating temperature in the E-model (upper panels) and the T-model (lower panels), for $\alpha = 1$ (left panels) and $\alpha = 10$ (right panels). The horizontal shadings corresponds to the 95\% CL bounds from {\it Planck} 2018, CMB-SPA, and P-ACT-LB. The vertical shadings show the constraints of $T_{\rm RH}$ from Big Bang Nucleosynthesis (BBN) and gravitino production in supersymmetric models. Note that the limits on $n_s$ (right vertical axis) depend on $\alpha$, as the calculated value of $r$ depends on $\alpha$ as seen in Eq~(\ref{eq:gentmodr}).$ $Constraints on $\alpha$-attractor models showing the 68\% and 95\% CL contours from {\it Planck}/BICEP/Keck \cite{BICEP2021} (blue shadings), the P-ACT-LB combination \cite{ACT:2025tim} (purple contours) and the CMB-SPA dataset \cite{SPT-3G:2025bzu} (brown rectangles). Note that the latter provides only an $r$-independent limit on $n_s$. All pivot scales are taken as $k_*=0.05$ Mpc$^{-1}$ except for the {\em Planck} pivot scale for $r$, conventionally chosen to be $k_*=0.002$ Mpc$^{-1}$. Left panel: $\alpha$-Starobinsky (E-model) predictions in the $(n_s, r)$ plane. Solid lines indicate reheating temperatures from $T_{\rm BBN}$ (4 MeV), $T_{\rm EW}$ (100 GeV), $10^{10}$~GeV (the gravitino bound), and $ 2 \times 10^{15}$~GeV (instantaneous reheating with $\Gamma_\varphi = H$). The dashed line shows $N_* = 50$ for reference. Right panel: As in the left panel for the T-model predictions.$ Show more plots

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Record created 2025-10-23, last modified 2025-10-25

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