Sommaire:

The beta-function formalism was introduced to identify universality among the wide zoology of inflationary models. It relies on a formal analogy between the equation describing the evolution of a scalar field in an expanding background and the renormalization group equation in quantum field theory. In this framework, near-scale invariance experienced by the Universe during inflation is interpreted as a departure of the newly defined cosmological beta-function from a fixed point corresponding to an exact de Sitter spacetime. A single parametrization of the beta-function, close to the fixed point, defines a universality class of models that share a single asymptotic behavior. In this talk, I will illustrate the general ideas of the approach by considering the simplest realization of inflation, then introduce the analytical gains of the method on more sophisticated scenarios, such as warm inflation, and I will conclude with phenomenological considerations in view of the next generation of cosmological experiments.

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