Positive scalar curvature meets Ricci limit spaces

We investigate the influence of uniformly positive scalar curvature on the size of a non-collapsed Ricci limit space coming from a sequence of n-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. We prove that such a limit space splits at most \(n-2\) $n-2$ lines or \(\mathbb {R}\) $\mathbb{R}$ -factors. When this maximal splitting occurs, we obtain a uniform upper bound on the diameter of the non-splitting factor. Moreover, we obtain a volume gap estimate and a volume growth order estimate of geodesic balls on such manifolds.