abstract: For expanding gradient Ricci solitons, we show that
1. when the average scalar curvature \( \frac{1}{Vol(B_r)}\int_{B_r} R \) is larger than \( - C r^{-\varepsilon} \), there exists a lower bound estimate of asymptotic volume ratio
2. when \( \lim \) |Sect| \( r^2=0 \), there is a uniform volume estimate of all geodesic balls.