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Planck 2015 results. XIX. Constraints on primordial magnetic fields

Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, E. Battaner, K. Benabed, A. Benoît, A. Benoit-Lévy, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, A. Bonaldi, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, A. Catalano, A. Chamballu, H. C. Chiang, J. Chluba, P. R. Christensen, S. Church, D. L. Clements, S. Colombi, L. P. L. Colombo, C. Combet, F. Couchot, A. Coulais, B. P. Crill, A. Curto, F. Cuttaia, L. Danese, R. D. Davies, R. J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, F. -X. Désert, J. M. Diego, K. Dolag, H. Dole, S. Donzelli, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, J. Fergusson, F. Finelli, E. Florido, O. Forni, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frejsel, S. Galeotta, S. Galli, K. Ganga, M. Giard, Y. Giraud-Héraud, E. Gjerløw, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gregorio, A. Gruppuso, J. E. Gudmundsson, F. K. Hansen, D. Hanson, D. L. Harrison, G. Helou, S. Henrot-Versillé, C. Hernández-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, M. Hobson, W. A. Holmes, A. Hornstrup, W. Hovest, K. M. Huffenberger, G. Hurier, A. H. Jaffe, T. R. Jaffe, W. C. Jones, M. Juvela, E. Keihänen, R. Keskitalo, J. Kim, T. S. Kisner, J. Knoche, M. Kunz, H. Kurki-Suonio, G. Lagache, A. Lähteenmäki, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, J. P. Leahy, R. Leonardi, J. Lesgourgues, F. Levrier, M. Liguori, P. B. Lilje, M. Linden-Vørnle, M. López-Caniego, P. M. Lubin, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, M. Maris, P. G. Martin, E. Martínez-González, S. Masi, S. Matarrese, P. McGehee, P. R. Meinhold, A. Melchiorri, L. Mendes, A. Mennella, M. Migliaccio, S. Mitra, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, D. Mortlock, A. Moss, D. Munshi, J. A. Murphy, P. Naselsky, F. Nati, P. Natoli, C. B. Netterfield, H. U. Nørgaard-Nielsen, F. Noviello, D. Novikov, I. Novikov, N. Oppermann, C. A. Oxborrow, F. Paci, L. Pagano, F. Pajot, D. Paoletti, F. Pasian, G. Patanchon, O. Perdereau, L. Perotto, F. Perrotta, V. Pettorino, F. Piacentini, M. Piat, E. Pierpaoli, D. Pietrobon, S. Plaszczynski, E. Pointecouteau, G. Polenta, L. Popa, G. W. Pratt, G. Prézeau, S. Prunet, J. -L. Puget, J. P. Rachen, R. Rebolo, M. Reinecke, M. Remazeilles, C. Renault, A. Renzi, I. Ristorcelli, G. Rocha, C. Rosset, M. Rossetti, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, B. Rusholme, M. Sandri, D. Santos, M. Savelainen, G. Savini, D. Scott, M. D. Seiffert, E. P. S. Shellard, M. Shiraishi, L. D. Spencer, V. Stolyarov, R. Stompor, R. Sudiwala, R. Sunyaev, D. Sutton, A. -S. Suur-Uski, J. -F. Sygnet, J. A. Tauber, L. Terenzi, L. Toffolatti, M. Tomasi, M. Tristram, M. Tucci, J. Tuovinen, G. Umana, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, L. A. Wade, B. D. Wandelt, I. K. Wehus, D. Yvon, A. Zacchei, A. Zonca

TL;DR

This Planck 2015 analysis provides a comprehensive set of constraints on primordial magnetic fields (PMFs) by exploiting multiple CMB signatures: magnetically induced power spectra, Faraday rotation, ionization-history heating, non-Gaussianities, and harmonic-space anisotropies from Alfvén waves. PMFs are modeled as a stochastic background with an amplitude $B_{1\mathrm{Mpc}}$ and a spectral index $n_B$, including both compensated and passive modes, and, in helicity-enabled scenarios, a helical component characterized by $A_H$ and $n_H$. Using Planck 2015 temperature and polarization data with low- and high-$\ell$ likelihoods and CosmoMC/Bayesian inference, the study finds robust nanogauss-scale upper limits, e.g., $B_{1\mathrm{Mpc}}<4.4$ nG (95% CL) for non-helical PMFs when considering compensated modes, with tighter or looser bounds depending on the mode, data combination, and fixed $n_B$. Helical PMFs yield slightly weaker bounds (e.g., $B_{1\mathrm{Mpc}}<5.6$ nG in some cases) due to reduced fluctuations from parity-violating sources. Non-Gaussianity analyses (bispectra for passive/compensated modes) and Alfvén-wave correlations provide complementary constraints, while Faraday rotation with Planck data remains less restrictive. Overall, Planck 2015 delivers a cohesive, cross-validated PMF constraint framework, disfavouring large PMFs and providing tight prospects for distinguishing PMF generation scenarios through spectral-index and helicity investigations.

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 Alfvén 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.

Planck 2015 results. XIX. Constraints on primordial magnetic fields

TL;DR

This Planck 2015 analysis provides a comprehensive set of constraints on primordial magnetic fields (PMFs) by exploiting multiple CMB signatures: magnetically induced power spectra, Faraday rotation, ionization-history heating, non-Gaussianities, and harmonic-space anisotropies from Alfvén waves. PMFs are modeled as a stochastic background with an amplitude and a spectral index , including both compensated and passive modes, and, in helicity-enabled scenarios, a helical component characterized by and . Using Planck 2015 temperature and polarization data with low- and high- likelihoods and CosmoMC/Bayesian inference, the study finds robust nanogauss-scale upper limits, e.g., nG (95% CL) for non-helical PMFs when considering compensated modes, with tighter or looser bounds depending on the mode, data combination, and fixed . Helical PMFs yield slightly weaker bounds (e.g., nG in some cases) due to reduced fluctuations from parity-violating sources. Non-Gaussianity analyses (bispectra for passive/compensated modes) and Alfvén-wave correlations provide complementary constraints, while Faraday rotation with Planck data remains less restrictive. Overall, Planck 2015 delivers a cohesive, cross-validated PMF constraint framework, disfavouring large PMFs and providing tight prospects for distinguishing PMF generation scenarios through spectral-index and helicity investigations.

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 nG (where is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity, and nG for a maximally helical field.For nearly scale-invariant PMFs we obtain nG and 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 nG. A search for preferred directions in the magnetically-induced passive bispectrum yields nG, whereas the the compensated-scalar bispectrum gives nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in and at 70 GHz and gives nG. In our final analysis, we consider the harmonic-space correlations produced by Alfvén 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.

Paper Structure

This paper contains 15 sections, 13 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Cosmic magnetism
  3. Imprints of primordial magnetism
  4. Structure of the paper
  5. Impact of primordial magnetic fields on the CMB power spectra
  6. Magnetic modes
  7. Compensated modes
  8. Passive modes
  9. Impact of non-helical PMFs on the CMB angular power spectra
  10. Compensated modes
  11. Passive modes
  12. Impact of helical PMFs on CMB anisotropies
  13. Constraints from the CMB temperature and polarization power spectra
  14. Likelihood
  15. Constraints with compensated scalar and vector contributions

Figures (5)

  • Figure 1: Magnetically-induced CMB $TT$ (top left), $TE$ (top right), $EE$ (bottom left), and $BB$ (bottom right) power spectra. The solid lines represent primary CMB anisotropies, the dotted lines represent magnetically-induced compensated scalar modes (except for the $BB$ panel, where it represents the lensing contributions and the solid line represents primary tensor modes with a tensor-to-scalar ratio of $r=0.1$), the dashed lines represent vector modes, whereas the dot-dashed lines represent magnetically-induced compensated tensor modes. We consider PMFs with $B_{1\mathrm{Mpc}}=4.5$nG and $n_B=-1$.
  • Figure 2: Dependence of the magnetically-induced CMB power spectrum on the spectral index. For all plotted cases, the amplitude is $B_{1\mathrm{Mpc}}=4.5$nG. The black lines show primary CMB anisotropies; for the other colours we refer to the legend. Left: scalar contributions, right: vector contributions.
  • Figure 3: Magnetically-induced CMB $TT$ (top left), $TE$ (top right), $EE$ (bottom left), and $BB$ (bottom right) power spectra due to passive tensor modes, compared with the ones due to compensated modes. The solid lines represent primary CMB anisotropies, the dotted lines represent magnetically-induced compensated scalar modes (except for the $BB$ panel, where it represents the lensing contribution), the dashed lines represent vector modes, whereas dot-dashed lines represent magnetically-induced passive tensor modes. We consider PMFs with $B_{1\mathrm{Mpc}}=4.5$nG and $n_B=-2.9$.
  • Figure 4: Dependence of the magnetically-induced CMB power spectrum due to passive tensor modes on the spectral index for a GUT-scale PMF (left) and comparison between the two extremes for the time ratio $\tau_\nu/\tau_B$ (right). The black lines show the primary CMB anisotropies; for the other colours we refer to the legend. Solid lines represent PMFs generated at the GUT scale, $\tau_\nu/\tau_B=10^{17}$, whereas dashed lines represent PMFs generated at late times, $\tau_\nu/\tau_B=10^6$.
  • Figure 5: CMB $TT$ (top left), $TE$ (top right), $EE$ (bottom left), and $BB$ (bottom right) power spectra due to helical PMFs compared to the ones due to non-helical PMFs. Solid lines are non-helical predictions, while dashed lines are helical predictions. Blue are the scalar modes, green the vector, and red the compensated tensor modes. We consider PMFs with $B_{1\mathrm{Mpc}}=4.5$nG and $n_B=-1$.