Higgs-like inflation in scalar-torsion $f(T,φ)$ gravity in light of ACT-SPT-DESI constraints

Abstract

We study Higgs-like inflation in the framework of scalar-torsion gravity, focusing on the general class of $f(T,φ)$ theories in which gravitation is mediated by torsion rather than curvature. Motivated by the increasing precision of cosmic microwave background and large-scale-structure observations, we examine whether Higgs-like inflation remains compatible with current data in this extended gravitational setting. Working within the slow-roll approximation, we analyze the inflationary dynamics both analytically and numerically. In the dominant-coupling regime we derive closed-form expressions for the scalar spectral index and the tensor-to-scalar ratio as functions of the number of e-folds, and we subsequently relax this assumption by numerically solving the slow-roll equations. Confrontation with the latest constraints from Planck 2018, ACT DR6, DESI DR1, and BICEP/Keck shows that Higgs-like inflation in $f(T,φ)$ gravity is fully consistent with current bounds, naturally accommodating the preferred shift in the scalar spectral index and leading to distinctive tensor-sector signatures.

Figures (7)

• Figure 1: Contour plots of the scalar spectral index $n_s$ v/s tensor-to-scalar ratio $r$ at pivot scale $k=0.05Mpc^{-1}$. (a) Predictions for $c \in [0.1100, 0.3857]$ and fixed $s = 0.5110$. (b) Predictions for varying $s \in [0.5005,0.5435]$ and fixed $c = 0.2479$. Endpoints of the bars indicate values at N = 50 (small circle) and N = 60 (large circle).The light-shaded region denotes the $95\%$ CL from Planck 2018, and the dark-shaded region shows the $68\%$ CL from the joint Planck 2018 Planck:2018jri, ACT-2025AtacamaCosmologyTelescope:2025blo, and BICEP/Keck 2021 BICEPKeck:2021gln analysis.
• Figure 2: Constraints on the spectral index $n_s$ and its running $\alpha_s$ pivot scale $k=0.05Mpc^{-1}$ in 68% and 95% confidence levels. The blue contours show results from Planck 2018 data with post lensing+BAO, while the blue contours represent the joint constraints from Planck 2018, ACT DR6, and DESI BAO data. The colored trajectories illustrate theoretical predictions for $N \in [50, 60]$ with varying parameter $c \in [0.1100, 0.3857]$ at a fixed $s = 0.5110$ and $s \in [0.5030, 0.5495]$ at a fixed $s = 0.2479$, respectively in fig.(a) and fig.(b). The small and big circle mark the $N=50$ and $N=60$ endpoints respectively.
• Figure 3: Behavior of the analytically solved background inflationary quantities in our Higgs-like inflation model with $f(T,\phi)$ gravity. The panels display the evolution of the Hubble parameter $H(N_{*})/M_{Pl}$, the inflationary energy scale $E_{\mathrm{inf}}/M_{Pl}$, the non-minimal coupling $\xi(N_{*})/M_{Pl}^{4-c-2s}$, the effective self-coupling $\lambda(N_{*})$, all evaluated at horizon crossing for $N_{*}=60$ for $s \in [0.5030, 0.5495]$ and the slow-roll parameters $\epsilon(N)$ & $\eta_{R}(N)$ calculated at $s=0.515$ throught the inflation for number of e-folds N=0 to 60. Each curve corresponds to a distinct choice of $c \in [0.1100,\,0.3875]$, showing how variations in the torsion-Higgs coupling modify the inflationary predictions across the allowed range of the parameter $s$.
• Figure 4: Constraints in the $n_s$--$r$ plane comparing theoretical predictions with current CMB observations at pivot scale $k=0.05Mpc^{-1}$. The shaded contours represent observational confidence regions: the light-shaded region corresponds to the $95\%$ confidence level from Planck 2018, while the dark-shaded region shows the $68\%$ confidence level from the joint Planck 2018 + ACT-2025 + BICEP/Keck 2021 analysisPlanck:2018jriBICEPKeck:2021glnAtacamaCosmologyTelescope:2025blo. (a) Predictions for $s=0.5121$ and $\gamma=10^{-10}$, with the parameter $c$ varied in the range $c \in [0.2150,\,0.4499]$. (b) Predictions for fixed $c=0.3099$ and $\gamma=10^{-10}$, with $s$ varied in the range $s \in [0.5001,\,0.5480]$. (c) Predictions for fixed $c=0.3099$ and $s=0.5121$, with $\gamma$ varied over the indicated values. In all panels, the endpoints of each theoretical trajectory correspond to the number of e-folds $N = 50$ (small markers) and $N = 60$ (large markers).
• Figure 5: Constraints in the $n_s$--$\alpha_s$ plane comparing theoretical predictions with current CMB observations at pivot scale $k=0.05Mpc^{-1}$. The shaded contours denote observational confidence regions: the light-shaded region corresponds to the $95\%$ confidence level from Planck 2018, while the dark-shaded region represents the $68\%$ confidence level from the joint Planck 2018 + ACT-2025 + BICEP/Keck 2021 analysis. (a) Predictions for $s=0.5121$ and $\gamma=10^{-10}$, with the parameter $c$ varied in the range $c \in [0.2150,\,0.4499]$. (b) Predictions for fixed $c=0.3099$ and $\gamma=10^{-10}$, with $s$ varied in the range $s \in [0.5001,\,0.5480]$. (c) Predictions for fixed $c=0.3099$ and $s=0.5121$, with $\gamma$ varied over the indicated values. In all panels, the endpoints of each theoretical trajectory correspond to the number of e-folds $N = 50$ (small markers) and $N = 60$ (large markers).