Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism

Understand

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime.

• The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time.
• Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter.
• For the physically relevant case of cold dark matter in an Einstein--de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion.