[Paper Review] On the electric charge of the observable Universe

Cody Goolsby-Cole, Lorenzo Sorbo|arXiv (Cornell University)|Nov 23, 2015

Cosmology and Gravitation Theories3 citations

TL;DR

This paper demonstrates that during inflation, quantum fluctuations of electrically charged particles—especially very light charged scalars—can generate a net electric charge in the observable Universe, even if the total Universe is neutral. Despite exact conservation of electric charge, large-scale fluctuations during de Sitter expansion lead to a non-zero variance in charge density, with massive fermions yielding negligible charge and ultra-light scalars potentially exceeding observational bounds by several orders of magnitude.

ABSTRACT

Light fields get large scale fluctuations during inflation. If some of them are electrically charged, then large scale fluctuations of the electric charge will be generated. As a consequence, any finite portion of the Universe, including our observable one, will carry a net electric charge. This fact does not require any form of breaking of the gauge symmetry at any time. We discuss under which conditions such a charge is maintained until the end of inflation, and we estimate its expected magnitude both in the case of charged fermions and of charged scalars. While one charged fermion species yields a charge density that is several orders of magnitude below the observational constraints, extremely light charged scalars can exceed those constraints.

Motivation & Objective

• To investigate whether the observable Universe can acquire a net electric charge due to quantum fluctuations during inflation, even with exact global charge conservation.
• To determine under what conditions such a charge survives until the end of inflation and does not get screened or canceled by pair production.
• To estimate the magnitude of the expected charge density for both charged fermions and charged scalars in the context of inflationary cosmology.
• To resolve discrepancies in prior works by properly accounting for normal-ordering of quantum operators, which avoids divergences and yields finite, physically meaningful results.
• To assess the viability of light charged scalar fields in light of observational constraints on cosmic charge density.

Proposed method

• Computes the charge density variance in a spherical volume of radius R using the power spectrum of the charge density operator, derived from the Fourier transform of the charge density.
• Uses normal-ordered quantum field operators in a time-dependent de Sitter background to avoid ultraviolet divergences, ensuring finite and physically consistent results.
• Applies Bogolyubov transformation techniques to compute particle production during inflation and the subsequent radiation-dominated era, matching exact solutions to adiabatic approximations.
• Evaluates the mode functions of charged fermions and complex scalar fields in a Friedmann-Robertson-Walker (FRW) spacetime with a time-varying scale factor, focusing on superhorizon and non-relativistic modes.
• Derives the Bogolyubov coefficients for scalar fields in the radiation epoch using parabolic cylinder functions, enabling calculation of particle creation rates.
• Estimates the charge density variance in the large-R limit by integrating over the power spectrum weighted by a Gaussian window function, focusing on infrared (k→0) modes.

Experimental results

Research questions

• RQ1 Can a finite portion of the Universe, such as the observable Universe, develop a net electric charge due to quantum fluctuations during inflation, even if the total Universe is neutral?
• RQ2 What is the magnitude of the expected charge density for massive charged fermions and light charged scalars in the observable Universe after inflation?
• RQ3 How do Schwinger pair production and electric field back-reaction affect the stability of the generated charge during inflation?
• RQ4 Why do previous studies that neglect normal-ordering of quantum operators yield divergent or inconsistent results, and how does proper normal-ordering resolve this?
• RQ5 To what extent can light charged scalar fields violate observational bounds on cosmic charge density, and under what conditions?

Key findings

• The variance in the average charge density within a volume of radius R is non-zero due to large-scale quantum fluctuations of charged fields during inflation, even with exact global charge conservation.
• For massive charged fermions with mass m ≈ H, the resulting charge density is estimated at ∼10⁻³³ n_B, which is several orders of magnitude below the observational bound of ∼10⁻²⁶ n_B.
• Charged scalar fields with mass m ≈ H produce a charge density about two to three orders of magnitude larger than fermions, but still below observational limits.
• Extremely light charged scalar fields (m ≪ H) can generate a charge density that exceeds the observational bound by several orders of magnitude, especially in the massless limit.
• The Schwinger effect does not significantly suppress the charge accumulation in most cases, though it may play a role in specific parameter regimes.
• The paper resolves inconsistencies in prior works by properly applying normal-ordering of quantum operators, which yields finite, unambiguous results—contrary to earlier studies that reported divergent or unphysical values.