ACT observations, reheating, and Starobinsky and Higgs inflation

In the recent sixth data release (DR6) of the Atacama Cosmology Telescope (ACT) collaboration, the value of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>n</a:mi><a:mi mathvariant="normal">s</a:mi></a:msub><a:mo>=</a:mo><a:mn>0.9743</a:mn><a:mo>±</a:mo><a:mn>0.0034</a:mn></a:math> for the scalar spectral index is reported, which excludes the Starobinsky and Higgs inflationary models at <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mn>2</d:mn><d:mi>σ</d:mi></d:math> 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>R</f:mi><f:mi>reh</f:mi></f:msub></f:math>, which contains a combination of the reheating temperature <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>T</h:mi><h:mi>reh</h:mi></h:msub></h:math> and the effective equation of state parameter during reheating <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mover accent="true"><j:mi>ω</j:mi><j:mo stretchy="false">¯</j:mo></j:mover><j:mi>reh</j:mi></j:msub></j:math>. Using the modified Boltzmann code and the software with the etist 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 <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>ω</n:mi><n:mo>=</n:mo><n:mn>0</n:mn></n:math> and relativistic matter <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>ω</p:mi><p:mo>=</p:mo><p:mn>1</p:mn><p:mo>/</p:mo><p:mn>3</p:mn></p:math> are excluded with more than <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mn>2</r:mn><r:mi>σ</r:mi></r:math> 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.