Production and Backreaction of Spin-2 Particles of $SU(2)$ Gauge Field during Inflation

Abstract

Primordial SU(2) gauge fields with an isotropic background lead to the production of spin-2 particles during inflation. We provide a unified formalism to compute this effect in all of the inflation models with isotropic SU(2) gauge fields such as Gauge-flation and Chromo-Natural inflation with and without spectator axion fields or the mass of the gauge field from the Higgs mechanism. First, we calculate the number and energy densities of the spin-2 particles. We then obtain exact analytical formulae for their backreaction on the background equations of motion of SU(2) and axion fields in (quasi) de Sitter expansion, which were calculated only numerically for one particular model in the literature. We show that the backreaction is directly related to the number density of the spin-2 field. Second, we relate the number density of the spin-2 particles to the power spectrum and the energy density of the gravitational waves sourced by them. Finally, we use the size of the backreaction to constrain the parameter space of the models. We find that the tensor-to-scalar ratio of the sourced gravitational waves can at most be on the order of that of the vacuum contribution to avoid a large backreaction on slow-roll dynamics of the gauge and axion fields in quasi-de Sitter expansion.

46 pages, 16 figures. v2: Section 6.1 is added

References in corpus (10)

• Primordial Gravitational Waves from Axion-Gauge Fields Dynamics
• Schwinger Effect in 4D de Sitter Space and Constraints on Magnetogenesis in the Early Universe
• Higgsed Chromo-Natural Inflation
• Gauge-flation trajectories in Chromo-Natural Inflation
• Schwinger Effect by an $SU(2)$ Gauge Field during Inflation
• Non-Gaussianity from Axion-Gauge Fields Interactions during Inflation
• Emerging chromo-natural inflation
• Nonlinear perturbations from the coupling of the inflaton to a non-Abelian gauge field, with a focus on Chromo-Natural Inflation
• Observable Chiral Gravitational Waves from Inflation in String Theory
• Chromo-Natural inflation in Supergravity

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