When Does The Schwinger Preheating Occur? (Quantum Physics / Cosmology)

What will be your answer if i ask you, when does the Schwinger Preheating occur? Yeah, its a tough question. Many of you have not even heard of the term, ‘Schwinger Preheating’ and those who have, will hardly know the answer. But now, Okano and Fujita, in order to answer this question, numerically studied two models, the Starobinsky inflation model with the kinetic coupling and the anisotropic inflation model. Their study recently appeared in Arxiv.

So, what is Schwinger preheating? When the inflaton couples to photons and amplifies electric fields, charged particles produced via the Schwinger effect¹ can dominate the universe after inflation, which is called as the Schwinger preheating. (If you don’t know about Schwinger effect, please refer note below). When the Schwinger preheating occurs, the energy density of the electric fields become comparable to the total energy density at the end of the inflation, and the spacetime anisotropy may not be negligible. Thus, the generalities of the Schwinger preheating as well as the electric field oscillation are still unclear.

Okano and Fujita in their recent paper, applied the kinetic hydrodynamic approach to study the Schwinger effect in the Starobinsky inflation model with the Ratra coupling and the anisotropic inflation model.

In 2019, Gorbar and colleagues analyzed the Starobinsky inflation model with the Ratra coupling and they concluded that the Schwinger preheating occurred when the coefficient of the Ratra coupling satisfies the strong coupling constant, β ≥ 8 without any analytical discussion. Okano and Fujita now confirmed the results of their work and have shown that the Schwinger preheating does not occur in the anisotropic inflation model, but occurs for a sufficiently large inflaton-photon coupling in the Starobinsky model.

They also analytically discussed the condition for the Schwinger preheating. The Schwinger preheating occurs when the energy density of the charged particles dominates the universe and the energy density of the charged particle is supplied from electric fields. Thus, the necessary conditions for the Schwinger preheating is ρE/ρtot ∼ 1/2, (where, ρE is the energy density of the electric field & ρtot is the total energy density of the electric field ρE, the charged fermions ρψ and the inflaton ρφ) which leads to the significant backreaction from the electric fields on the inflaton.

“Fortunately, this system is expected to have an attractor solution of the electric field for the following reason. The electric fields are amplified by the inflaton, because kinetic energy is transferred by the inflaton to the electric fields through the kinetic function. The amplification might be weaker than the dilution effect of the spacetime expansion in the early stage of the inflationary phase. Towards the end of inflation, however, the inflaton velocity φ˙ is accelerated by the potential force, the amplification effect is enhanced and eventually overcomes the dilution effect, and the electric fields begin to grow. When the electric fields are sufficiently amplified and its backreaction on the inflaton becomes significant, the growth stops and energy density of electric field is stabilized. This is because, if the electric fields are further amplified, the inflaton is slowed down by the backreaction, its kinetic energy pumped to the electric fields is reduced, and they decay. If the electric fields are smaller than the stabilized value, the inflaton is accelerated and gives more energy to the electric fields. Therefore, the inflaton and the electric fields constitute a negative feedback system and they should have an attractor solution.”

— wrote authors of the study

In addition, they have derived a general attractor solution of the energy density of the electric fields (ρE) by using the slow-roll approximation, and investigated the stability of the attractor solutions. Their result is consistent with the conventional analysis of the anisotropic inflation model. Using the attractor solution, they evaluated the electric field energy density at the inflaton end. In the Starobinsky model with the Ratra coupling, the analytic evaluation apparently indicated that energy density of the electric fields always dominates the universe at the end of inflation, independent of coupling constant, β. However, they found that energy density of electric fields does not reach the attractor, and hence it remains much smaller than energy density of inflaton (ρφ) in the case of a small β. In particular, the occurrence of the Schwinger preheating in the Starobinsky model is determined by whether the electric fields enter the attractor solution during inflation or not.

Finally, they take into account the anisotropy of the spacetime and estimate its impact on the dynamics. They showed that, the anisotropy hastens the preheating in Starobinsky and Ratra model but delays it in anisotropic inflation. They concluded that the origin of these difference is beyond the scope of this paper.

Featured image: The numerical result in case of the Starobinsky model VS and the Ratra coupling fR with the coupling constant β = 10. They showed, the time evolution of the energy densities of the electric field ρE (red solid), the charged fermions ρψ (blue dashed), the inflaton ρφ (orange solid) and their total ρtot (green dot-dashed). The calculation starts at µt = 0 corresponding to N ≃ 60 and inflation ends at µt = 136 (vertical black dashed line) where H ≡ −α¨/α˙² = 1. The produced fermions dominate the universe after inflation, ρψ > ρφ, ρE, which is called the Schwinger preheating © Okano and Fujita


1) The Schwinger effect is a predicted physical phenomenon whereby matter is created by a strong electric field.

Reference: So Okano, Tomohiro Fujita, “When does the Schwinger Preheating Occur?”, Arxiv, pp. 1-22, 2021. https://arxiv.org/abs/2105.13180

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