Improved predictions on Higgs-Starobinsky inflation and reheating with ACT DR6 and primordial gravitational waves

In this letter, we investigate the implications of recent CMB observations for Higgs-Starobinsky inflationary models and their associated reheating dynamics, utilising data from ACT DR6, Planck 2018, BICEP/Keck 2018, and DESI, collectively referred to as P-ACT-LB-BK18. In addition to direct CMB constraints, we incorporate indirect bounds arising from the potential overproduction of primordial gravitational waves (PGWs), particularly through limits on the effective number of relativistic species, $\Delta N_{eff}$, during Big Bang Nucleosynthesis (BBN). These constraints become especially relevant in scenarios featuring a stiff post-inflationary equation of state $w_{RH}\ge 0.58$. Our analysis shows that, when both P-ACT-LB-BK18 data and $\Delta N_{eff}$ bounds are considered, the viable number of inflationary e-folds is restricted to the range 57.9-62.2 at the $2\sigma$ confidence level (C.L.). Correspondingly, 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 $w_{RH}>0.41$. However, no parameter space remains viable at the $1\sigma$ C.L. once $\Delta N_{eff}$ constraints from PGWs are included, rendering the Higgs-Starobinsky model highly restricted.