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CMB with the background primordial magnetic field
Mar. 31. 14



Abstract

Dr. Dai G. Yamazaki (Division of Theoretical Astronomy, National Astronomical Observatory of Japan) has released
the overall effects of the background primordial magnetic field (PMF) on the cosmic microwave background (CMB).
He investigates the effects of the background PMF on the CMB. The sound speed of the tightly coupled photonbaryon 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 larger scale. The background PMF causes the 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 suppression of the CMB around the first peak and shifting peaks to large scale. We also discuss obtaining information about the PMF generation mechanisms, and 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.






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The cosmic microwave background (CMB) provides important information about the Universe. The positions of peaks and the amplitude of the CMB temperature perturbations are reflected by the sound speed of the photonbaryon fluid and the changing potential.
Since a magnetic field increases the sound speed of fluid, and affects the evolution of density perturbations, if this amplitude as background is large enough, the magnetic field gives the critical effects on the CMB.
A power law (PL) is one of the most familiar spectra for the various physical processes including the PMF on cosmological scale (see Yamazaki, et al. Phys. Rep. 517, 141, 2012 and references therein).
The main parameters of the PLPMF are the field strength on the coherent scale: &lambda$; ,
B_{λ} and the spectral index: n_{B}.
These parameters also have been tried constraining from the cosmological observations.
Since an average of the strength of the PMF as the background is zero, while an average of the background PMF energy density is a finite value,
previous studies have constrained the background PMF energy density (ρ_{PMF}) from big bang nucleosynthesis (BBN). ρ_{PMF} is proportional to the scale invariant field strength of the PMF (B_{SI})
which is as a function of λ, B_{λ}, n_{B}, and upper and lower scales of the PMF at a its generation time (Yamazaki and Kusakabe, 2012).
From previous studies (Yamazaki and Kusakabe, 2012) ρ_{PMF} for larger n_{B} is comparable to the constrained PMF energy density by the BBN and this influence in the CMB is not negligible.
In this paper, we investigate effects of the background PMF on the CMB as a function of the PLPMF parameters: the field strength on the coherent scale, the spectral index, the maximum scales of the PMF. We also report degeneracies of these PLPMF parameters and the standard cosmological parameters in the PMF influences in the CMB for the first time.

Fig. 1;
The contribution of the PMF and the standard cosmological parameters on the CMB.
The black curves are the theoretical result without PMF effects.
The red curves are the theoretical result with the 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 red curve of Panel (b), which is displayed by moving your mouse on Fig. 1, are the WMAP 9yr best fit parameters in ΛCDM and the tensor mode.These standard cosmological parameters are (Ω_{b}, Ω_{CDM}, n_{s}, 10^{9}Δ^{2}_{R}, 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 red curve in the panel (b) is the baryon density and the CDM density. These parameter values are (Ω_{b}, Ω_{CDM}) = (0.0461, 0.195).

The background PMF increases the sound speed of the tightly coupled photonbaryon fluid, and causes the stronger decaying potential. The overall effect of the background PMF changes amplitudes of the CMB around the first peak stronger than in smaller scale [Fig. 1(a)].
We report the case that k_{max} is assumed to be a free parameter. The energy density of the background PMF is dependent on k_{max}, and k_{max} is dependent on a PMF generation model. Hence, if one determines the k_{max} by constraining the magnetic energy density from the CMB, we obtain information of the PMF generation mechanisms. We also discuss the constraint on the k_{max} as being an examination for the nonlinear evolution of the PMF.
Finally we discuss the possibility of degeneracies between the background PMF, the baryon, and the CDM [Fig. 1(a) and (b)].
Considering the fundamental understanding of the baryon and matter densities effects on the CMB,
we expect the positive correlation between Ω_{b} and the background PMF, and the negative correlation between Ω_{CDM} and the background PMF.
In fact, the affected CMB by the PMF can be adjusted by changing Ω_{b} and Ω_{CDM} as Fig. 1(a) and (b).
In previous constraints on the PMF without the background effects, the degeneracy between the PMF and the standard cosmological parameters are negligible small. If n_{B} and k_{max} are sufficiently small, the ρ_{MF} is too small to affect the CMB, and the previous result is no problem.
However, a lot remains to be established about the PMF, it is too early to discuss the PMF effects and generation mechanisms in such narrow parameter range.
To understand the PMF correctly, we should constrain the background PMF and the standard cosmological parameters simultaneously.
If we promote the effects of the background PMF on the CMB, and constrain them by the latest and future observations, it will permit development of better studies for the generation and evolution of the PMF and provide new insight into the early universe with the PMF.





