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In this paper we prove new classification results for nonnegatively curvedgradient expanding and steady Ricci solitons in dimension three and above,under suitable integral assumptions on the scalar curvature of the underlyingRiemannian manifold. In particular we show that the only complete expandingsolitons with nonnegative sectional curvature and integrable scalar curvatureare quotients of the Gaussian soliton, while in the steady case we proverigidity results under sharp integral scalar curvature decay. As a corollary,we obtain that the only three dimensional steady solitons with less thanquadratic volume growth are quotients of $\mathbb{R}\times\Sigma^{2}$, where$\Sigma^{2}$ is Hamilton's cigar.

Classification of expanding and steady Ricci solitons with integral curvature decay