Constraining primordial magnetic fields with distortions of the black-body spectrum of the cosmic microwave background: pre- and post-decoupling contributions
- Departamento de Física Fundamental and IUFFyM, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca (Spain)
- Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85741 Garching (Germany)
Primordial magnetic fields that exist before the photon-baryon decoupling epoch are damped on length scales below the photon diffusion and free-streaming scales. The energy injected into the plasma by dissipation of magnetosonic and Alfv and apos;en waves heats photons, creating a y-type distortion of the black-body spectrum of the cosmic microwave background. This y-type distortion is converted into a μ-type distortion when elastic Compton scattering is efficient. Therefore, we can use observational limits on y- and μ-type distortions to constrain properties of magnetic fields in the early universe. Assuming a Gaussian, random, and non-helical field, we calculate μ and y as a function of the present-day strength of the field, B{sub 0}, smoothed over a certain Gaussian width, k{sub c}{sup −1}, as well as of the spectral index of the power spectrum of fields, n{sub B}, defined by P{sub B}(k)∝k{sup n{sub B}}. For a nearly scale-invariant spectrum with n{sub B} = −2.9 and a Gaussian smoothing width of k{sub c}{sup −1} = 1Mpc, the existing COBE/FIRAS limit on μ yields B{sub 0} < 40 nG, whereas the projected PIXIE limit on μ would yield B{sub 0} < 0.8 nG. For non-scale-invariant spectra, constraints can be stronger. For example, for B{sub 0} = 1 nG with k{sub c}{sup −1} = 1Mpc, the COBE/FIRAS limit on μ excludes a wide range of spectral indices given by n{sub B} > −2.6. After decoupling, energy dissipation is due to ambipolar diffusion and decaying MHD turbulence, creating a y-type distortion. The distortion is completely dominated by decaying MHD turbulence, and is of order y ≈ 10{sup −7} for a few nG field smoothed over the damping scale at the decoupling epoch, k{sub d,} {sub dec} ≈ 290(B{sub 0}/1nG){sup −1}Mpc{sup −1}. The projected PIXIE limit on y would exclude B{sub 0} > 1.0 and 0.6 nG for n{sub B} = −2.9 and -2.3, respectively, and B{sub 0} > 0.6 nG for n{sub B} ≥ 2. Finally, we find that the current limits on the optical depth to Thomson scattering restrict the predicted y-type distortion to be y∼<10{sup −8}.
- OSTI ID:
- 22369826
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2014, Issue 01; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
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