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  • Open Access

ACT observations, reheating, and Starobinsky and Higgs inflation

D. S. Zharov1,*, O. O. Sobol2,1,†, and S. I. Vilchinskii3,1

  • *Contact author: dmitriy.zharov.02@knu.ua
  • †Contact author: oleksandr.sobol@knu.ua
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Phys. Rev. D 112, 023544 – Published 23 July, 2025

DOI: https://doi.org/10.1103/km3q-rm34

Abstract

In the recent sixth data release (DR6) of the Atacama Cosmology Telescope (ACT) collaboration, the value of ns=0.9743±0.0034 for the scalar spectral index is reported, which excludes the Starobinsky and Higgs inflationary models at 2σ level. In this paper, we perform a Bayesian inference of the parameters of the Starobinsky or Higgs inflationary model with noninstantaneous reheating using the Markov chain Monte Carlo method. For the analysis, we use observational data on the cosmic microwave background collected by the Planck and ACT collaborations and on baryonic acoustic oscillations from the Dark Energy Spectroscopic Instrument (DESI) collaboration. The reheating stage is modeled by a single parameter Rreh, which contains a combination of the reheating temperature Treh and the effective equation of state parameter during reheating ω¯reh. Using the modified Boltzmann code class and the cobaya software with the getdist package, we perform a direct inference of the model parameter space and obtain their posterior distributions. Using the Kullback-Leibler divergence, we estimate the information gain obtained from the observed data: In the proposed parametrization, we get 8.48 bits of information about the amplitude of the inflaton potential and 2.37 bits of information about the reheating parameter. Inclusion of the ACT DR6 data provides 63% more information about the reheating stage compared to analysis without ACT data. In addition, we draw constraints on the reheating temperature and the average equation of state. While the former can vary within 12 orders of magnitude, values in the 95% credible interval indicate a sufficiently low reheating temperature; for the latter there is a clear preference for values greater than 0.5, which means that the conventional equations of state for dust ω=0 and relativistic matter ω=1/3 are excluded with more than 2σ level of significance. Nevertheless, there is still a big part of parameter space where Starobinsky and Higgs inflationary models exhibit a high degree of consistency with the latest observational data, particularly from ACT DR6. Therefore, it is premature to reject these models.

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Phys. Rev. D 112, 023544– Published 23 July, 2025
  • Received 12 May 2025
  • Accepted 6 June 2025
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