https://people.math.ethz.ch/~afigalli/papers-pdf/A-quantitative-analysis-of-metrics-on-Rn-with-almost-constant-positive-scalar-curvature-with-applications-to-fast-diffusion-flows.pdf

I am in trouble in understanding one step of theorem 1.1 in the above mentioned paper. Namely in equation \eqref{1}, it is written: "Since $u=\sigma+\rho$, a the Talyor expansion yields $$ \int_{\mathbb{R}^n}u^p\rho=\int_{\mathbb{R}^n}\sigma^p\rho+p\int_{\mathbb{R}^n}\sigma^{p-1}\rho^2+O\left(\int_{\mathbb{R}^n}|\nabla\rho|^2\right)^{1+\gamma}\label{1}\tag{2.8}$$ where $\gamma=\min(\frac{1}{2},\frac{2}{n-2})$."
The problem is the big O term since I do not get it: how this is coming with power $1+\gamma$? Any help is very much appreciated.