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, Δ N e f f , during Big Bang Nucleosynthesis (BBN). These constraints become especially relevant in scenarios featuring a stiff post-inflationary equation of state w R H ≥ 0.58 . Our analysis shows that, when both P-ACT-LB-BK18 data and Δ N e f f bounds are considered, the viable number of inflationary e-folds is restricted to the range 57.9–62.2 at the 2 σ 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 R H > 0.41 . However, no parameter space remains viable at the 1 σ C.L. once Δ N e f f constraints from PGWs are included, rendering the Higgs–Starobinsky model highly restricted.