[Paper Review] Imprints of Schwinger Effect on Primordial Spectra

Wan Zhen Chua, Qianhang Ding+2 more|arXiv (Cornell University)|Oct 23, 2018

Cosmology and Gravitation Theories94 references4 citations

TL;DR

This paper investigates the imprint of the Schwinger effect—quantum pair production in strong electric fields—on primordial cosmological spectra during inflation. Using a model with a constant electric field in de Sitter space, it derives a unique angular dependence in the primordial power spectrum and bispectrum due to charged scalar particle production, distinguishing it from other anisotropic mechanisms. The key result is a non-trivial $Σ$-dependent bispectrum shape sensitive to electric field strength and particle mass.

ABSTRACT

We study the Schwinger effect during inflation and its imprints on the primordial power spectrum and bispectrum. The produced charged particles by Schwinger effect during inflation can leave a unique angular dependence on the primordial spectra.

Motivation & Objective

• To explore observational signatures of the Schwinger effect in primordial inflationary spectra.
• To model a constant electric field during inflation that resists dilution due to cosmic expansion.
• To derive the primordial power spectrum and bispectrum with angular dependence from charged particle production.
• To distinguish this angular imprint from other anisotropic mechanisms like anisotropic inflation or higher-curvature terms.

Proposed method

• Formulate a QED-like model coupled to a charged scalar field in de Sitter space with a constant electric field via a dilatonic coupling $ f(\phi)^2 F_{\mu\nu}F^{\mu\nu} $.
• Solve the geodesic equation for charged scalar particles in the presence of the electric field.
• Compute the primordial power spectrum using the in-in formalism and the Bunch-Davies vacuum state.
• Derive the bispectrum in the squeezed limit using propagators $ D_{++}, D_{+-}, D_{-+}, D_{--} $, focusing on non-local terms involving $ \alpha\beta^* $ and $ \alpha^*\beta $.
• Simplify the Whittaker functions in the $ k_{1}/k_{3} \ll 1 $ expansion to obtain analytical expressions.
• Extract the shape function $ S(k_1,k_2,k_3) $ and identify its angular dependence through $ \cos\theta $-like behavior in the momentum configuration.

Experimental results

Research questions

• RQ1 Can the Schwinger effect leave a detectable imprint on the primordial power spectrum during inflation?
• RQ2 How does a constant electric field during inflation affect the angular structure of the primordial bispectrum?
• RQ3 What distinguishes the angular dependence from the Schwinger effect from that of anisotropic inflation or Galileon models?
• RQ4 How does the number of produced charged particles influence the amplitude of non-Gaussianities?
• RQ5 What is the analytical form of the bispectrum in the squeezed limit for a charged scalar field under a constant electric field?

Key findings

• The primordial power spectrum acquires a unique angular dependence due to the Schwinger effect, arising from the directional preference of particle production along the electric field.
• The bispectrum exhibits a non-trivial angular modulation proportional to $ \left(\frac{k_1 + k_2}{k_3}\right)^{-\mu} $, with $ \mu $ dependent on the effective mass $ m^2/H^2 + e_0^2 E^2/H^4 $.
• The shape function $ S(k_1,k_2,k_3) $ contains a complex prefactor $ f(\mu,\kappa) $ involving gamma functions and phase factors, encoding the quantum field-theoretic dynamics.
• The angular dependence is distinct from $ \cos^2\theta $ or $ P_1(\cos\theta) $ patterns seen in anisotropic inflation or higher-derivative models.
• The magnitude of non-Gaussianities scales with the number of produced particles, which increases with electric field strength and effective mass.
• The loop-corrected bispectrum retains the same angular structure, confirming the robustness of the signal in the leading-order approximation.