Non-geometrical perturbation on homogeneous stealth dust

In this work, we study a non-geometrical perturbation to the stealth field, which means the background remains invariant. The stealh is homogeneous in a universe whose source is dust and demand that perturbation unchanged density. As a regular procedure, we introduce a parameter $\lambda$ to perturb the scalar field equation and get an intriguing expression of the equation, similar to a series expansion in $\lambda$. From this procedure, we distinguish and approach to discriminate solutions, and the numerical solutions show that the most significant contribution to the solution comes from the linear term of $\lambda$.