Summary: Based on \(X \sim N_d(\theta, \sigma_X^2I_d)\), we study the efficiency of predictive densities under \(\alpha\)-divergence loss \(L_{\alpha}\) for estimating the density of \(Y \sim N_d(\theta, \sigma_Y^2I_d)\). We identify a large number of cases where improvement on a plug-in density are obtainable by expanding the variance, thus extending earlier findings applicable to Kullback-Leibler loss. The results and proofs are unified with respect to the dimension \(d\), the variances \(\sigma_X^2\) and \(\sigma_Y^2\), the choice of loss \(L_{\alpha}\); \(\alpha\in (-1,1)\). The findings also apply to a large number of plug-in densities, as well as for restricted parameter spaces with \(\theta\in\Theta\subset\mathbb{R}^d\). The theoretical findings are accompanied by various observations, illustrations, and implications dealing for instance with robustness with respect to the model variances and simultaneous dominance with respect to the loss.