Inflation, a rapid expansion phase in the early Universe, is a leading theory for initial conditions. Recent studies explore how new physics might resolve the Hubble tension (discrepancy between local and cosmic H0 measurements). The paper examines how altering parameters like the effective number of relativistic species (Neff) or dark energy equation of state (w) can align H0 values from CMB and BAO with local measurements. Models with Neff ≈ 3.9 or w ≈ -1.2 produce H0 values consistent with local data, but affect inflationary parameters like the scalar spectral index (ns). While Neff scenarios shift ns towards 1, they are less favored than ΛCDM. However, models with Neff ≈ 3.3–3.4 reduce the H0 tension to ~3σ, though they weaken inflationary models like Starobinsky. Early Dark Energy (EDE) with fEDE ≈ 0.04–0.06 mildly reduces the H0 tension to ~3σ but shifts inflationary constraints. A joint analysis of EDE and Starobinsky inflation shows they cannot coexist for fEDE > ~0.06. The paper emphasizes that new physics affecting early Universe parameters can alter inflationary constraints, challenging standard models. The Hubble tension introduces uncertainty in inflationary parameters, requiring reevaluation of favored models. The study highlights the need to consider alternative cosmological frameworks to better understand inflation and resolve the Hubble tension.Inflation, a rapid expansion phase in the early Universe, is a leading theory for initial conditions. Recent studies explore how new physics might resolve the Hubble tension (discrepancy between local and cosmic H0 measurements). The paper examines how altering parameters like the effective number of relativistic species (Neff) or dark energy equation of state (w) can align H0 values from CMB and BAO with local measurements. Models with Neff ≈ 3.9 or w ≈ -1.2 produce H0 values consistent with local data, but affect inflationary parameters like the scalar spectral index (ns). While Neff scenarios shift ns towards 1, they are less favored than ΛCDM. However, models with Neff ≈ 3.3–3.4 reduce the H0 tension to ~3σ, though they weaken inflationary models like Starobinsky. Early Dark Energy (EDE) with fEDE ≈ 0.04–0.06 mildly reduces the H0 tension to ~3σ but shifts inflationary constraints. A joint analysis of EDE and Starobinsky inflation shows they cannot coexist for fEDE > ~0.06. The paper emphasizes that new physics affecting early Universe parameters can alter inflationary constraints, challenging standard models. The Hubble tension introduces uncertainty in inflationary parameters, requiring reevaluation of favored models. The study highlights the need to consider alternative cosmological frameworks to better understand inflation and resolve the Hubble tension.