The Energy Minimization Principle for Dark Matter Haloes

Abstract: Inferring abundance, position and size of cosmic structures from the initial conditions is a long standing effort in theoretical cosmology. It allows (semi-)analytical predictions of mass function, bias and correlation functions of dark matter haloes, and an intuitive understanding of the formation of the cosmic web, a complementary tool to numerical simulations. Standard methods assume that dark matter haloes originates from critically high peaks of the initial matter density field, which act as seeds for the structure formation process. Although simpe and intuitive, this approach suffers from numerical and conceptual inconsistencies. I will review the standard analytical methods, highlighting their advantages and shortcomings. I will then show how many difficulties can be overcome by focusing on the initial energy of the protohalo patch, rather than its mean density. This approach improves substantially the results of protohalo abundance and mass, and provides a first-principles prediction for protohalo shapes.