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-Rubble 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.
Highlights
Quantum effects in primordial inflation are strong for light fields nonconformally coupled to the expanding space-time
The non-vanishing scalar condensate is responsible for the spontaneous symmetry breaking mechanism, as it induces a mass-like term for the vector field, which is more properly seen as an effective non-minimal coupling of the vector field to the Ricci curvature scalar, on the account of its time-dependence tracing the evolution of the Hubble rate, Φ∗Φ gμνAμAν ∝ H2gμνAμAν ∝ R gμνAμAν
We assume that the vector and the scalar masses are generated by a timedependent condensate of the complex scalar field φ(t)
Summary
Quantum effects in primordial inflation are strong for light fields nonconformally coupled to the expanding space-time. The non-vanishing scalar condensate is responsible for the spontaneous symmetry breaking mechanism, as it induces a mass-like term for the vector field, which is more properly seen as an effective non-minimal coupling of the vector field to the Ricci curvature scalar, on the account of its time-dependence tracing the evolution of the Hubble rate, Φ∗Φ gμνAμAν ∝ H2gμνAμAν ∝ R gμνAμAν This is how the conformal coupling of the vector to gravity is broken in the symmetrybreaking attractor solution in power-law inflation, and how the vector becomes sensitive to the expansion of space-time at tree-level.
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