Abstract
We propose a $1/N$ expansion of Starobinsky and Yokoyama's effective stochastic approach for light quantum fields on superhorizon scales in de Sitter spacetime. We explicitly compute the spectrum and the eigenfunctions of the Fokker-Planck operator for a O($N$)-symmetric theory with quartic selfinteraction at leading and next-to-leading orders in this expansion. We obtain simple analytical expressions valid in various nonperturbative regimes in terms of the interaction coupling constant.
Highlights
The stochastic formalism is a powerful way to access the infrared physics of light quantum fields in slow-roll inflationary backgrounds [1]
II, we briefly review the stochastic approach for the OðNÞ theory and its formulation in terms of an eigenvalue problem for the associated Fokker-Planck operator
Let us quickly mention that the general results of the previous section reproduce the findings of Refs. [3,19], where the eigenvalues Λ1;1, Λ2;0, and Λ3;1 had been obtained by other means at leading and next-to-leading—for Λ1;1—orders
Summary
The stochastic formalism is a powerful way to access the infrared physics of light quantum fields in slow-roll inflationary backgrounds [1]. In the case of a quartic potential, we obtain simple analytical expressions of all eigenvalues and eigenfunctions, both at leading and next-to-leading orders, which reproduce and encompass the results mentioned above These provide benchmark results, valid for arbitrary values of the coupling (within the validity of the stochastic approach, i.e., for light fields), for various quantities of physical interest, such as correlation lengths and times, relaxation and decoherence timescales, or various spectral indices, relevant for phenomenological applications [2,27,28,29]. We present some comparison with numerical results in Appendix B
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
