Abstract
We study the explosive production of gauge fields during axion inflation in a novel gradient expansion formalism that describes the time evolution of a set of bilinear electromagnetic functions in position space. Based on this formalism, we are able to simultaneously account for two important effects that have thus far been mostly treated in isolation: (i) the backreaction of the produced gauge fields on the evolution of the inflaton field and (ii) the Schwinger pair production of charged particles in the strong gauge-field background. This allows us to show that the suppression of the gauge-field production due to the Schwinger effect can prevent the backreaction in scenarios in which it would otherwise be relevant. Moreover, we point out that the induced current, $\boldsymbol{J} = \sigma \boldsymbol{E}$, also dampens the Bunch-Davies vacuum fluctuations deep inside the Hubble horizon. We describe this suppression by a new parameter $\Delta$ that is related to the time integral over the conductivity $\sigma$ which hence renders the description of the entire system inherently nonlocal in time. Finally, we demonstrate how our formalism can be used to construct highly accurate solutions for the mode functions of the gauge field in Fourier space, which serves as a starting point for a wealth of further phenomenological applications, including the phenomenology of primordial perturbations and baryogenesis.
Highlights
Gamma-ray observations from distant blazars provide indirect evidence for the presence of magnetic fields in voids of our Universe [1,2,3,4,5,6,7,8,9,10]
The full system of equations describing the generation of gauge fields during axion inflation in the gradient expansion formalism consists of the Friedmann equation (9) for the scale factor, the Klein-Gordon equation (12) for the inflaton, the system of equations (20)–(22) for bilinear electromagnetic quantities, which must be truncated at some order nmax, and the equation for the energy density of charged particles produced by the Schwinger effect (32)
Its theoretical description becomes challenging in the presence of nonlinear effects such as (i) the backreaction of the produced gauge fields on the evolution of the inflaton field and (ii) the Schwinger pair production of charged particles in the strong gauge-field background
Summary
Gamma-ray observations from distant blazars provide indirect evidence for the presence of magnetic fields in voids of our Universe [1,2,3,4,5,6,7,8,9,10] (for a recent review, see Ref. [11]). To handle the complicated dynamics of the inflaton and gauge fields, taking into account the Schwinger effect and the backreaction of the generated gauge fields and primordial plasma on the cosmological evolution, a novel gradient expansion formalism was developed by three of us in Ref. We will study the problem of generating helical magnetic fields in a model with an axial coupling of the gauge field to the inflaton. An important outcome of our analysis is the fact that the state of the system at any given moment in time t does depend on the choice of parameter values in the Lagrangian and quantities such as the instantaneous velocity of the inflaton field; it depends on the entire prehistory leading up to this moment in time, which controls to what extent the vacuum fluctuations of modes inside the horizon have already been damped in the course of inflation at times t0 ≤ t. We assume that the Universe is described on cosmological scales by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) metric in terms of the cosmic time, gμν 1⁄4 diagf1; −a2ðtÞ; −a2ðtÞ; −a2ðtÞg
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