We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The exact solutions of these equations are free of secular terms and approach a finite limit at late times. This technique is illustrated for the well-known problem of secular growth of correlation functions of a massless scalar field with a quartic self-interaction in de Sitter space. For the expectation value of the product of two fields at coinciding space-time points, we obtain a finite late-time result that is very close to the one following from Starobinsky’s stochastic approach.

Renormalization group inspired autonomous equations for secular effects in de Sitter space / A. Kamenchtchik, T. Vardanyan. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - STAMPA. - 102:6(2020), pp. 065010.1-065010.21. [10.1103/PhysRevD.102.065010]

Renormalization group inspired autonomous equations for secular effects in de Sitter space

A. Kamenchtchik;T. Vardanyan
2020

Abstract

We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The exact solutions of these equations are free of secular terms and approach a finite limit at late times. This technique is illustrated for the well-known problem of secular growth of correlation functions of a massless scalar field with a quartic self-interaction in de Sitter space. For the expectation value of the product of two fields at coinciding space-time points, we obtain a finite late-time result that is very close to the one following from Starobinsky’s stochastic approach.
2020
Renormalization group inspired autonomous equations for secular effects in de Sitter space / A. Kamenchtchik, T. Vardanyan. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - STAMPA. - 102:6(2020), pp. 065010.1-065010.21. [10.1103/PhysRevD.102.065010]
A. Kamenchtchik, T. Vardanyan
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/776599
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