  In this paper, we have proved a weighted Laplacian comparison of distance
function for manifolds with Bakry-\'Emery curvature bounded from below. Next,
we have shown that a gradient $\rho$-Einstein soliton with a bounded integral
condition on Ricci curvature splits off a line isometrically. Moreover, using
this result, we have established some boundedness conditions on scalar
curvature of gradient $\rho$-Einstein soliton.
