One-loop corrections to the primordial tensor spectrum from massless isocurvature fields
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Springer
Received: October Revised: August Accepted: September Published: October
30, 12, 24, 28,
2019 2020 2020 2020
Hai Siong Tan Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore Physics Division, National Center for Theoretical Sciences, 101 Kuang-Fu Road Section 2, Hsinchu, 30013 Taiwan
E-mail: [email protected] Abstract: We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. Using the Schwinger-Keldysh formalism in cosmological perturbation theory, we employ dimensional regularization and cutoff regularization to study the finite quantum corrections at one-loop arising from isocurvature fields of the massless scalar, fermion and abelian gauge field which are freely propagating on the FRW spacetime. For all cases, we find a logarithH C H4 mic running of the form q3 M 4 log µ where C is a negative constant related to the beta p function, H is the Hubble parameter at horizon exit and µ is the renormalization scale. Keywords: Classical Theories of Gravity, Cosmology of Theories beyond the SM, Models of Quantum Gravity ArXiv ePrint: 1907.07706
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)186
JHEP10(2020)186
One-loop corrections to the primordial tensor spectrum from massless isocurvature fields
Contents 1 Introduction
1 3 3 5 6 8 8 10
3 One-loop logarithmic corrections due to massless spectator fields 3.1 Dirac fermions 3.2 Minimally coupled scalars 3.3 The abelian gauge field
12 13 15 17
4 On seagull diagrams
19
5 Discussion
22
1
Introduction
The Schwinger-Keldysh formalism has been the underlying quantum field theoretic framework for computing correlation functions in cosmological perturbation theory, many crucial aspects of which were presented in the seminal paper by Weinberg in [1]. Essential cosmological observables such as the primordial spectra and bispectra are derived within the validity of this formalism which carries with it the prescription to compute loop effects for these correlation functions. In this paper, we will employ this formalism in the context of inflation to compute quantum corrections at one-loop to the primordial tensor spectrum which at tree-level reads, in momentum space and up to slow-roll corrections, H(τk ) 2 2 2 , (1.1) ∆t (k) = 2 3 π k Mp with H(τk ) = k/a(τk ) is the Hubble scale at horizon crossing. The loop corrections that we study in this paper pertain to those arising from massless spectator/isocurvature fields of spin < 2 freely propagating on the cosmological spacetime, and we compute the various corrections to (1.1) with the slow-roll approximation being invoked in our expressions for the graviton mode and scalar wavefunctions in the comoving gauge. In the context of primordial inflation, loop corrections to the inflaton two-point function have been considered in several works after
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