Non-perturbative Effects Via Stochastic Quantum Inflation Based on a Single Canonical Scalar Field: The Linear and Quartic Self-Interaction Potential Case | Chapter 11 | Current Research Progress in Physical Science Vol. 7

Cosmological inflation solves the short-comings of the standard hot big-bang cosmology, while at the same time it generates the primordial fluctuations, and so it provides us with a mechanism that explains the CMB temperature anisotropies as well as the large scale structure of the Universe. The linear inflaton potential, despite its simplicity, has become relevant as it is still in agreement with the latest Planck data, and also because it can be obtained in the context of well-defined quantum field theory from a Coleman-Weinberg potential, provided that a non minimal coupling to gravity is also present. During inflation infrared logarithms of the inflationary scale factor arise in the expectation values of operators of quantum field theories. As those logarithms continuously grow with time, eventually they overcome the small coupling constants, and so perturbation theory breaks down. Starobinsky’s technique of stochastic quantum inflation recovers the leading infrared logarithms at each order, and the series of those leading effects may be resummed to give non-perturbative predictions. The approach is named after Alexei Starobinsky, a prominent physicist who developed key ideas and techniques in this area. Starobinsky inflation, one of the earliest and most successful models of cosmological inflation, leads to a graceful exit from inflation and is compatible with current observational constraints from the Cosmic Microwave Background (CMB). Starobinsky’s formalism has been extended to include other modifications of gravity (e.g. f(R) theories) and interactions with additional fields. This manuscript presents the main developments that apply Starobinsky’s stochastic quantum inflation to the case of a minimally coupled scalar field with quartic and linear self-interaction potential. In the case of the quartic potential a series in the coupling constant is obtained, while in the case of the linear potential we solve the corresponding Fokker-Planck equation exactly, and obtain analytical expressions for the stochastic expectation values.

 

Author (s) Details

 

Grigoris Panotopoulos
Departamento de Ciencias Fisicas, Universidad de la Frontera, Casilla 54-D, 4811186 Temuco, Chile.

 

Please see the book here:-  https://doi.org/10.9734/bpi/crpps/v7/4037