Evolution Equation for Non-linear Cosmological Perturbations

Understand

We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations.

• Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential.
• We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations.
• First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions.