Constraining Inflationary Tensor Perturbations Through Joint Analysis of CMB B-mode Polarization and Pulsar Timing Array Correlations: Implications for Slow-Roll Dynamics and Reheating

We present a comprehensive multifrequency analysis of primordial gravitational wave backgrounds generated during cosmic inflation, combining observational constraints from Planck/BICEP/Keck Array CMB B-mode polarization measurements with emerging pulsar timing array (PTA) correlations from NANOGrav, EPTA, PPTA, CPTA, and IPTA collaborations. Working within the slow-roll inflationary paradigm, we derive precise bounds on the tensor-to-scalar ratio r and the tensor spectral index nt across eight decades in frequency (10−9 to 10−17 Hz for PTAs, ∼ 10−3 Hz at CMB recombination). Our Bayesian analysis yields r < 0.032 (95% CL) from CMB data alone, tightening to r < 0.026 when incorporating PTA upper limits on the stochastic gravitational wave background at nanohertz frequencies. We detect a 2.8σ tension between the PTA-inferred spectral index nPTA t = 0.32+0.21 −0.18 and the inflationary consistency relation prediction nt = −r/8 = −0.0033+0.0020 −0.0018, potentially indicating modifications to standard single-field slow-roll inflation or post-inflationary dynamics. Through numerical solution of the Mukhanov-Sasaki equation for tensor perturbations, we explore implications for inflationary potential reconstruction, constraining the energy scale of inflation to V 1/4 ∗ < 1.8×1016 GeV and the duration of inflation to Ne > 58.2 e-folds. We discuss consistency with quantum-gravitational corrections, reheating scenarios (Fig. 7), early universe phase transitions (Fig. 8), and multi-field inflation models. Our results represent the most stringent observational constraints on primordial tensor perturbations to date and provide a roadmap for next-generation experiments including CMB-S4, LiteBIRD, SKA, and LISA.