CMB with the background primordial magnetic field

Dai G. Yamazaki

Phys. Rev. D 89, 083528 – Published 18 April 2014

Abstract

We investigate the effects of the background primordial magnetic field (PMF) on the cosmic microwave background (CMB). The sound speed of the tightly coupled photon-baryon fluid is increased by the background PMF. The increased sound speed causes the odd peaks of the CMB temperature fluctuations to be suppressed and the CMB peak positions to be shifted to a larger scale. The background PMF causes a stronger decaying potential and increases the amplitude of the CMB. These two effects of the background PMF on a smaller scale cancel out, and the overall effects of the background PMF are the suppression of the CMB around the first peak and the shifting of peaks to a larger scale. We also discuss obtaining information about the PMF generation mechanisms, and we examine the nonlinear evolution of the PMF by the constraint on the maximum scale for the PMF distributions. Finally, we discuss degeneracies between the PMF parameters and the standard cosmological parameters.

Received 20 February 2014

DOI:https://doi.org/10.1103/PhysRevD.89.083528

Authors & Affiliations

Dai G. Yamazaki^*

National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan

^*yamazaki.dai@nao.ac.jp

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Vol. 89, Iss. 8 — 15 April 2014

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Figure 1
The effects of the background magnetic field on the CMB. The dotted curve is the theoretical result from the WMAP nine-year best-fit parameter in $Λ CDM$ and the tensor mode [64]. (The main papers of the Planck project are under review, so we refrain from using their results.) These standard cosmological parameters are $(Ω_{b}, Ω_{CDM}, n_{s}, 10^{9} Δ_{R}^{2}, H_{0}, τ, r) = (0.0442, 0.210, 0.992, 2.26, 72.6, 0.091, 0.38)$ , where $Ω_{b} h^{2}$ is the baryon density, $Ω_{CDM} h^{2}$ is the CDM density, $n_{s}$ is the scalar spectral index, $10^{9} Δ_{R}^{2}$ is the amplitude of the initial fluctuation, $H_{0}$ is the Hubble parameter, $τ$ is the optical depth, and $r$ is the tensor-to-scalar ratio. The bold curve is the theoretical result with the background PMF effects of (0.0, 3 nG) (without the first-order perturbation of the PMF). In this case, $ρ_{MF} / ρ_{γ} = 0.0161$ .
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Figure 2
The effects of the PMF on the CMB. The dotted curve is the theoretical result from the WMAP nine-year best-fit parameter in $Λ CDM$ and the tensor mode [64]. (The main papers of the Planck project are under review, so we refrain from using their results.) The bold curves in panels (a), (b), (c), and (d) are the theoretical results with the PMF effects of $(n_{B}, B_{λ}, ρ_{MF} / ρ_{γ}) = (- 2.0, 15 nG, 0.00116), (- 2.0, 20 nG, 0.00185), (0.0, 2 nG, 0.00910)$ , and $(0.0, 3 nG, 0.0161)$ , respectively. The dots with the error bars are the results of the CMB observations [64, 65, 66], as shown by the legend in this figure.
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Figure 3
The ratio of the background magnetic field to photon density. The bold, dotted, and dashed curves are $B_{λ} = 10$ , 1, and 0.1 nG, respectively.
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Figure 4
The contribution of the upper-limit wave number of the PMF to the CMB. The dotted curve is the theoretical result from the WMAP nine-year best-fit parameter in $Λ CDM$ and the tensor mode [64]. The bold, dashed, and thin curves are the theoretical results with the PMF effects of $(n_{B}, B_{λ}, k_{\max}, ρ_{MF} / ρ_{γ}) = (- 2.0, 15 nG, 1000 {Mpc}^{- 1}, 0.0240), (- 2.0, 15 nG, 500 {Mpc}^{- 1}, 0.0120)$ , and $(- 2.0, 15 nG, 50 {Mpc}^{- 1}, 0.00120)$ , respectively.
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Figure 5
The contribution of the PMF and the standard cosmological parameters to the CMB. The dotted curves are the theoretical results without PMF effects. The bold curves are the theoretical results with PMF effects of $(n_{B}, B_{λ}, k_{\max}, ρ_{MF} / ρ_{γ}) = (- 2.0, 10 nG, 1500 {Mpc}^{- 1}, 0.0160)$ . The standard cosmological parameters of all curves in this figure except the bold curves of panel (b) are the WMAP nine-year best-fit parameters in $Λ CDM$ and the tensor mode [64]. These standard cosmological parameters are $(Ω_{b}, Ω_{CDM}, n_{s}, 10^{9} Δ_{R}^{2}, H_{0}, τ, r) = (0.0442, 0.210, 0.992, 2.26, 72.6, 0.091, 0.38)$ . The different standard cosmological parameters of the bold curve in the right panel (b) are the baryon density and the CDM density. These parameter values are $(Ω_{b}, Ω_{CDM}) = (0.0461, 0.195)$ .
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