Abelian Higgs model in power-law inflation: the propagators in the unitary gauge
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Springer
Received: May 20, 2020 Accepted: July 7, 2020 Published: September 25, 2020
Abelian Higgs model in power-law inflation: the propagators in the unitary gauge
a
Centre for Cosmology, Particle Physics and Phenomenology (CP3), Universit´e catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium b Division of Theoretical Physics, Rudjer Boˇskovi´c Institute, Bijeniˇcka cesta 54, HR-10 000 Zagreb, Croatia c Amsterdam, The Netherlands d Institute for Theoretical Physics (ITF), Spinoza Institute & EMMEΦ, Faculty of Science, Utrecht University, Postbus 80195, 3508 TD Utrecht, The Netherlands e Department of Physics, McGill University, 3600 Rue University, Montr´eal, QC H3A 2T8, Canada
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We consider the Abelian Higgs model in the broken phase as a spectator in cosmological spaces of general D space-time dimensions, and allow for the condensate to be time-dependent. We fix the unitary gauge using Dirac’s formalism for constrained systems, and then quantize the gauge-fixed system. Vector and scalar perturbations develop timedependent masses. We work out their propagators assuming the cosmological background is that of power-law inflation, characterized by a constant principal slow-roll parameter, and that the scalar condensate is in the attractor regime, scaling as the Hubble rate. Our propagators correctly reduce to known results in the Minkowski and de Sitter space limits. We use the vector propagator to compute the equal-time correlators of electric and magnetic fields and find that at super-Hubble separations the former is enhanced, while the latter is suppressed compared to the vacuum fluctuations of the massless vector field. These correlators satisfy the hierarchy governed by Faraday’s law. Keywords: Cosmology of Theories beyond the SM, Spontaneous Symmetry Breaking, Gauge Symmetry, Higgs Physics ArXiv ePrint: 2005.05435
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)165
JHEP09(2020)165
Draˇ zen Glavan,a,b Anja Marunovi´ c,c Tomislav Prokopecd and Zahra Zahraeee
Contents 1 Introduction
2
2 FLRW and power-law inflation
9 12 13 17 19
4 Condensate dynamics
19
5 Scalar perturbations
20
6 Dynamics of vector perturbations 6.1 Scalar-vector decomposition 6.2 Fourier decomposition 6.3 Dynamics of the transverse sector 6.4 Dynamics of the longitudinal sector
21 22 24 25 26
7 Vector field two-point functions 7.1 Equations of motion for two-point functions 7.2 Choice of the state 7.3 Two-point functions as mode sums 7.4 Covariantizing two-point functions 7.5 Various limits 7.5.1 De Sitter limit 7.5.2 Flat space limit 7.5.3 Coincidence limit 7.6 Comparison with previous results
27 27 30 31 33 36 37 37 39 40
8 Field strength correlator 8.1 Equal time E&M correlators 8.1.1 Sub-Hubble limit 8.1.2 Super-Hubble limit
43 45 47 47
9 Discussion
50
A Scalar mode functions in power-law inflation
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B Rescaled propagator function F
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