[Paper Review] Vector and Tensor Microwave Background Signatures of a Primordial Stochastic Magnetic Field

Andrew Mack, Tina Kahniashvili+1 more|arXiv (Cornell University)|May 29, 2001

Geomagnetism and Paleomagnetism Studies8 citations

TL;DR

This paper derives analytic expressions for microwave background temperature and polarization power spectra induced by vector and tensor perturbations from a primordial stochastic magnetic field. For a scale-invariant field with a 1.4 Mpc comoving damping scale, current CMB data constrain the comoving mean-field amplitude to ≤6×10⁻¹⁰ G, improving to ≤3×10⁻¹¹ G for causally generated fields—setting the strongest current limits on large-scale primordial magnetic fields.

ABSTRACT

A stochastic magnetic field in the early Universe will produce anisotropies in the temperature and polarization of the cosmic microwave background. We derive analytic expressions for the microwave background temperature and polarization power spectra induced by vector and tensor perturbations from a power-law magnetic field. For a scale-invariant stochastic magnetic field with a comoving damping scale of 1.4 Mpc, current microwave background temperature measurements constrain the comoving mean-field amplitude to be no greater than approximately $6\ imes 10^{-10}$ G. Limits improve as the power-law slope increases: for causally-generated power-law magnetic fields, the comoving mean-field amplitude has an upper bound of approximately $3\ imes 10^{-11}$ G. These are the strongest current limits on large-scale primordial magnetic fields.

Motivation & Objective

• To model the imprint of primordial stochastic magnetic fields on the cosmic microwave background (CMB) temperature and polarization anisotropies.
• To derive analytic expressions for vector and tensor perturbations induced by a power-law magnetic field in the early Universe.
• To constrain the amplitude of large-scale primordial magnetic fields using current CMB temperature measurements.
• To improve existing upper bounds on primordial magnetic fields by leveraging vector and tensor contributions to CMB power spectra.

Proposed method

• Derives analytic expressions for the CMB temperature and polarization power spectra generated by vector and tensor perturbations from a stochastic magnetic field with a power-law spectrum.
• Models the magnetic field as a scale-invariant or causally generated power-law spectrum with a comoving damping scale of 1.4 Mpc.
• Applies linear perturbation theory in the early Universe to compute the induced anisotropies in temperature and polarization from vector and tensor modes.
• Uses observed CMB temperature power spectrum data to constrain the amplitude of the primordial magnetic field.
• Evaluates the dependence of constraints on the power-law slope of the magnetic field spectrum.
• Compares theoretical predictions of vector and tensor CMB signatures with current observational limits to derive upper bounds on the comoving mean-field amplitude.

Experimental results

Research questions

• RQ1 What are the analytic expressions for the CMB temperature and polarization power spectra induced by vector and tensor perturbations from a primordial stochastic magnetic field?
• RQ2 How do current CMB temperature measurements constrain the amplitude of a scale-invariant primordial magnetic field with a 1.4 Mpc comoving damping scale?
• RQ3 How do the constraints on the primordial magnetic field amplitude depend on the power-law slope of the magnetic field spectrum?
• RQ4 What are the strongest current upper limits on large-scale primordial magnetic fields derived from CMB observations?

Key findings

• For a scale-invariant stochastic magnetic field with a comoving damping scale of 1.4 Mpc, the CMB temperature power spectrum constrains the comoving mean-field amplitude to be ≤6×10⁻¹⁰ G.
• For causally generated power-law magnetic fields, the upper bound on the comoving mean-field amplitude improves to ≤3×10⁻¹¹ G.
• The derived constraints represent the strongest current limits on large-scale primordial magnetic fields.
• Vector and tensor perturbations from the magnetic field produce measurable anisotropies in both temperature and polarization of the CMB.
• The strength of the constraints increases with steeper power-law slopes of the magnetic field spectrum.
• The analysis demonstrates that CMB observations provide a powerful probe of primordial magnetic fields beyond scalar modes.