Planck 2015 results. XIX. Constraints on primordial magnetic fields (1502.01594v2)

Abstract: We compute and investigate four types of imprint of a stochastic background of primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) anisotropies: the impact of PMFs on the CMB spectra; the effect on CMB polarization induced by Faraday rotation; the impact of PMFs on the ionization history; magnetically-induced non-Gaussianities; and the magnetically-induced breaking of statistical isotropy. Overall, Planck data constrain the amplitude of PMFs to less than a few nanogauss. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are $B_{1\,\mathrm{Mpc}}< 4.4$ nG (where $B_{1\,\mathrm{Mpc}}$ is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity, and $B_{1\,\mathrm{Mpc}}< 5.6$ nG for a maximally helical field.For nearly scale-invariant PMFs we obtain $B_{1\,\mathrm{Mpc}}<2.0$ nG and $B_{1\,\mathrm{Mpc}}<0.9$ nG if the impact of PMFs on the ionization history of the Universe is included. From the analysis of magnetically-induced non-Gaussianity we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is $B_{1\,\mathrm{Mpc}}< 2.8$ nG. A search for preferred directions in the magnetically-induced passive bispectrum yields $B_{1\,\mathrm{Mpc}}< 4.5$ nG, whereas the the compensated-scalar bispectrum gives $B_{1\,\mathrm{Mpc}}< 3$ nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in $EE$ and $BB$ at 70 GHz and gives $B_{1\,\mathrm{Mpc}}< 1380$ nG. In our final analysis, we consider the harmonic-space correlations produced by Alfv\'en waves, finding no significant evidence for the presence of these waves. Together, these results comprise a comprehensive set of constraints on possible PMFs with Planck data.

• The paper determines precise limits on non-helical PMFs, finding a 95% confidence upper bound of 4.4 nG and 0.9 nG for nearly scale-invariant spectra.
• Helical field analysis via parity signals yields a limit below 5.6 nG, while bispectrum studies independently constrain PMFs to under 2.8–3 nG.
• The study also examines Faraday rotation and Alfvén waves, ultimately finding no evidence of significant large-scale cosmic magnetic order.

Analysis of Planck 2015 Constraints on Primordial Magnetic Fields

The "Planck 2015 results. XIX. Constraints on primordial magnetic fields" paper presents a comprehensive paper of the constraints on primordial magnetic fields (PMFs) using data from the Planck satellite. The investigation focuses on the impact of PMFs on cosmological observables, particularly the cosmic microwave background (CMB) anisotropies. This paper's analysis spans multiple methodologies, employing various data-driven constraints to derive limits on the properties of these primordial fields, such as their strength and spectral characteristics.

Key Findings

1. Constraints on Non-Helical PMFs:
   • The analysis yields a constraint on the PMF amplitude with a 95% confidence limit of less than 4.4 nanogauss (nG) from the Planck temperature and polarization data. The constraints consider both temperature and polarization power spectra, primarily influenced by the vector modes generated by PMFs.
   • Notably, the effects of PMFs on the ionization history of the Universe are taken into account, leading to a refined constraint of less than 0.9 nG for nearly scale-invariant spectra.
2. Helical Magnetic Fields:
   • A separate analysis on maximally helical PMFs, which can lead to parity-violating signals in the CMB spectra, indicates a slightly less stringent constraint of less than 5.6 nG.
3. Non-Gaussianity:
   • The paper exploits CMB bispectra to probe non-Gaussianities induced by PMFs. It finds that the bispectrum constraints, when combined with Planck's temperature data, are competitive with power spectrum constraints, with an upper limit of less than 2.8 nG for PMFs believed to have been generated around the GUT scale.
   • Utilizing estimates of the scalar bispectrum provides an independent constraint with an amplitude less than 3 nG.
4. Faraday Rotation:
   • Analysis of Faraday rotation, observable as the transformation of CMB polarization modes, yields the loosest constraint among all methods, at less than 1380 nG.
5. Alfvén Waves:
   • The paper further explores statistical anisotropy signatures from potential Alfvén waves, showing no evidence for these waves, consistent with the absence of detectable large-scale magnetic order.

Implications and Future Directions

The results are crucial for understanding the role of PMFs in the early Universe and their implications for large-scale cosmic magnetism. The constraints are informative for model builders seeking to understand the genesis of cosmic magnetic fields and their evolution. Specifically, these constraints rule out strong PMFs prevailing in the early Universe, which aligns with the upper bounds derived from nucleosynthesis and large-scale structure formation studies.

Looking forward, improvements in the precision of polarization measurements, particularly those targeting the B-mode contributions, could refine these constraints further. Additionally, advancements in modeling the thermal history and capturing the precise dissipation mechanisms of PMFs could yield tighter limits on field strength and potentially reveal signatures of new physics. The exploration of helical PMFs and non-Gaussian signatures also opens avenues for investigating fundamental theories involving quantum fields in the early Universe.

In summary, the Planck 2015 results comprehensively constrain PMF characteristics and contribute significantly to our understanding of early Universe conditions, setting robust upper limits that challenge certain hypothesized models of their generation.