Stochastic Inflationary Scalar Electrodynamics

TL;DR

The paper develops a nonperturbative framework to sum leading infrared logarithms in inflationary scalar QED on de Sitter space using Starobinskiı̆'s stochastic formalism. By integrating out the photon (a passive field) and formulating an effective potential for the active scalar, it derives a stochastic description that yields explicit late-time predictions for key observables. It finds that super-horizon photons acquire a mass with $M^2_{\gamma} \simeq 3.2991\,H^2$ while the scalar remains perturbatively light; the induced change in the vacuum energy is negative, and the backreaction on expansion is modest. The work clarifies the roles of ultraviolet effects and the distinction between the effective potential governing scalar evolution and the stress-energy potential governing gravity, providing a controlled, nonperturbative handle on inflationary infrared dynamics in gauge theories.

Abstract

We stochastically formulate the theory of scalar quantum electrodynamics on a de Sitter background. This reproduces the leading infrared logarithms at each loop order. It also allows one to sum the series of leading infrared logarithms to obtain explicit, nonperturbative results about the late time behavior of the system. One consequence is confirmation of the conjecture by Davis, Dimopoulos, Prokopec and Tornkvist that super-horizon photons acquire mass during inflation. We compute a photon mass-suqared of about 3.2991 H^2. The scalar stays perturbatively light with a mass-squared of about 0.8961 3 e^2 H^2/8pi^2. Interestingly, the induced change in the cosmological constant is negative, of about -0.6551 3 G H^4/pi.

Figures (7)

• Figure 1: Two loop contribution to $\langle \Omega \vert F_{\mu\nu}(x) F_{\rho\sigma}(x)\vert \Omega \rangle$.
• Figure 2: Effective $(\varphi^* \varphi)^2$ coupling in SQED.
• Figure 3: Effective $\varphi^* \varphi$ coupling in SQED.
• Figure 4: $V_{\rm eff} = \frac{3 H^4}{8 \pi^2} f(\frac{e^2 \varphi^* \varphi}{ H^2})$ (solid line) and its asymptotic form (crosses).
• Figure 5: Expanded small field behavior of $V_{\rm eff} = \frac{3 H^4}{8 \pi^2} f(\frac{e^2 \varphi^* \varphi}{H^2})$ (solid line) and its asymptotic form (crosses).