Precision timing of relativistic binary pulsars generally shows orbital period decay in excellent agreement with general relativity’s quadrupole gravitational-wave emission formula, but a few systems show small residuals, environmental dependencies, or room for additional effects once kinematic and galactic accelerations are modeled out (Weisberg & Huang 2016; Freire & Wex 2010). In ΛCDM this leaves little space for cosmology to play any role in local orbital decay, so attempts to connect tiny excesses or deficits to dark energy, local expansion, or modified gravity sit uneasily alongside the tight GR confirmations, creating a tension between “pure GR in isolation” and hints of broader cosmic influence (Damour & Esposito-Farèse 1998; Ishak 2019).