Recent measurements from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) have placed the strictest constraints on the primordial scalar perturbation spectrum, reporting a spectral index of $n_s\sim 0.967–0.98$ at 95% confidence level. This result indicates a stronger scale invariance of the scalar perturbation than earlier estimates, posing challenges for numerous inflation models. In this work, we propose a novel inflationary scenario based on Weyl scale-invariant gravity, where the quadratic curvature establishes the scale invariance of the scalar spectrum, while the higher-order extensions imprint the observed slight deviation. Specifically, the exponential curvature extensions are introduced to suppress the mass divergence of the inflaton. We find such a scenario naturally yields leading-order predictions of $n_s\simeq 1–3/(2N)\sim 0.97-0.975$ or $n_s\simeq 1–5/(3N)\sim 0.967-0.972$ for various models, in excellent agreement with the ACT/SPT constraints. This result builds a concrete bridge between theoretical and observational scale invariance, implying an enduring cosmic echo of the primordial symmetry.

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• Alternative gravity theories
• Cosmic microwave background
• Inflation
• Conformal symmetry