log(det(A+Y)/det(Y)) constraint?

I am trying to maximize a concave objective function subject to the following constraint
log(det(A+Y)/det(Y)), where A is a known positive definite matrix and Y is an n by n diagonal matrix with positive elements (Y is the optimization variable). The cvx does not accept this form of constraints and I have no clue how to overcome this obstacle. Any help is appreciated. Thanks.