Non perturbative Effects Via Stochastic Quantum Inflation Based on a Single Canonical Scalar Field T
0Non-perturbative Effects Via Stochastic Quantum Inflation Based on a Single Canonical Scalar Field: The Linear and Quartic Self-Interaction Potential Case
Layman Abstract : Cosmological inflation is a theory that explains some key problems with the traditional Big Bang model. It also helps us understand the small variations in temperature we see in the Cosmic Microwave Background (CMB) and how the large-scale structure of the universe formed.
A simple version of inflation, based on a linear potential, is still consistent with the latest observations and can be explained using quantum field theory when certain conditions involving gravity are met. However, during inflation, certain mathematical terms (infrared logarithms) keep growing over time, making standard calculations unreliable.
To handle this, physicist Alexei Starobinsky developed a method called stochastic quantum inflation, which helps make sense of these growing terms and provides more accurate predictions. His work also led to one of the most successful models of inflation, which fits well with current observations.
This study applies Starobinsky’s method to a specific type of field in two cases: one with a quartic (power of four) potential and another with a linear potential. For the quartic case, a series expansion is used, while for the linear case, the calculations can be solved exactly, providing precise results for certain predictions.
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Original Abstract : 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.
View Book: https://doi.org/10.9734/bpi/crpps/v7/4037
#Stochastic_quantum #inflation #canonical_scalar_field #cosmological_inflation #big_bang_cosmology