Matching and running sensitivity in non-renormalizable inflationary models
- PDF / 1,346,489 Bytes
- 34 Pages / 595.276 x 841.89 pts (A4) Page_size
- 65 Downloads / 152 Views
Springer
Received: May 28, 2020 Accepted: August 9, 2020 Published: September 17, 2020
Jacopo Fumagalli,a Marieke Postmab and Melvin van den Boutb a
Institut d’Astrophysique de Paris, GReCO, UMR 7095 du CNRS et de Sorbonne Universit´e, 98bis boulevard Arago, Paris 75014, France b Nikhef, Science Park 105, Amsterdam 1098 XG, The Netherlands
E-mail: [email protected], [email protected], [email protected] Abstract: Most of the inflationary models that are in agreement with the Planck data rely on the presence of non-renormalizable operators. If the connection to low energy particle physics is made, the renormalization group (RG) introduces a sensitivity to ultraviolet (UV) physics that can be crucial in determining the inflationary predictions. We analyse this effect for the Standard Model (SM) augmented with non-minimal derivative couplings to gravity. Our set-up reduces to the SM for small values of the Higgs field, and allows for inflation in the opposite large field regime. The one-loop beta functions in the inflationary region are calculated using a covariant approach that properly accounts for the non-trivial structure of the field space manifold. We run the SM parameters from the electroweak to the inflationary scale, matching the couplings of the different effective field theories at the boundary between the two regimes, where we also include threshold corrections that parametrize effects from UV physics. We then compute the spectral index and tensor-toscalar ratio and find that RG flow corrections can be determinant: a scenario that is ruled out at tree level can be resurrected and vice versa. Keywords: Cosmology of Theories beyond the SM, Higgs Physics, Renormalization Group, Effective Field Theories ArXiv ePrint: 2005.05905
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)114
JHEP09(2020)114
Matching and running sensitivity in non-renormalizable inflationary models
Contents 1
2 The model: Standard Model with non-minimal derivative couplings 2.1 Standard Model with non-trivial kinetic sector 2.2 Tree level analysis and different regimes
4 6 7
3 Covariant formalism 3.1 Large field regime and counterterms 3.2 Covariant fields
7 8 9
4 Renormalization group flow 4.1 Renormalization group equations 4.1.1 Case A 4.1.2 Case B 4.1.3 Case C and D 4.2 Beta-functions summary
10 11 12 13 14 14
5 Predictions for inflation 5.1 Renormalization group dependence: analytical estimate 5.2 Matching and running: numerical results for case A 5.2.1 Boundary conditions at the electroweak scale 5.2.2 Threshold corrections 5.3 Matching and running: other cases
15 15 16 18 19 20
6 Conclusions
23
A Calculation of the self-energies A.1 Renormalized action A.2 Feynman rules A.3 Coupling strengths A.4 Two-point functions in the Abelian-Higgs model A.5 Two-point functions in the SM
24 24 25 26 27 27
1
Introduction
One of the main lessons learned from the Planck constraints on inflation [1] is that quadratic and quartic inflation, arguably the simplest approaches, are
Data Loading...
