Solution
= Solution
Writing $r=a(q+\psi)$ to first order gives $x''+\mathcal Hx'\simeq\psi''+\mathcal H\psi'=-\nabla_q\varphi$. The perturbation of Poisson's equation is $\nabla_q^2\varphi=(4\pi G/c^2)a^2\bar\rho_M\delta_M$.
= Solution
Writing $r=a(q+\psi)$ to first order gives $x''+\mathcal Hx'\simeq\psi''+\mathcal H\psi'=-\nabla_q\varphi$. The perturbation of Poisson's equation is $\nabla_q^2\varphi=(4\pi G/c^2)a^2\bar\rho_M\delta_M$.