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Register a new userPrimordial Magnetic Field Limits from Cosmic Microwave Background Bispectrum of Magnetic Passive Scalar Modes
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Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabatic-like scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} sim 6-9 times 10^{-16}$, for a magnetic field of $B_0 sim 3$ nG, assuming a nearly scale-invariant magnetic spectrum . We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} approx -1.4 times 10^{-16}$. These values are more than $sim 10^6$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of $B_0 sim 2$ nG on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on $B_0$ based on the compensated mode bispectrum.
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Primordial magnetic fields will generate non-Gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-Gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10^{-29} and 10^{-19}, respectively. Observational limits on CMB non-Gaussianity from WMAP data allow us to conservatively set upper limits of a nG, and plausibly sub-nG, on the present value of the primordial cosmic magnetic field. This represents the tightest limit so far on the strength of primordial magnetic fields, on Mpc scales, and is better than limits from the CMB bispectrum and all modes in the CMB power spectrum. Thus, the CMB trispectrum is a new and more sensitive probe of primordial magnetic fields on large scales.
Cosmic magnetic fields are observed to be coherent on large scales and could have a primordial origin. Non-Gaussian signals in the cosmic microwave background (CMB) are generated by primordial magnetic fields as the magnetic stresses and temperature anisotropy they induce depend quadratically on the magnetic field. We compute the CMB scalar trispectrum on large angular scales, for nearly scale-invariant magnetic fields, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately $10^{-29}$ and $10^{-19}$, respectively. The scalar anisotropic stress trispectrum is also calculated in the flat-sky approximation and yields a similar result. Observational limits on CMB non-Gaussianity from the Planck mission data allow us to set upper limits of $B_0 lesssim 0.6 $ nG on the present value of the primordial cosmic magnetic field. Considering the inflationary magnetic curvature mode in the trispectrum can further tighten the magnetic field upper limit to $B_0 lesssim 0.05 $ nG. These sub-nanoGauss constraints from the magnetic trispectrum are the most stringent limits so far on the strength of primordial magnetic fields, on megaparsec scales, significantly better than the limits obtained from the CMB bispectrum and the CMB power spectrum.
We discuss the manner in which the primordial magnetic field (PMF) suppresses the cosmic microwave background (CMB) $B$ mode due to the weak-lensing (WL) effect. The WL effect depends on the lensing potential (LP) caused by matter perturbations, the distribution of which at cosmological scales is given by the matter power spectrum (MPS). Therefore, the WL effect on the CMB $B$ mode is affected by the MPS. Considering the effect of the ensemble average energy density of the PMF, which we call the background PMF, on the MPS, the amplitude of MPS is suppressed in the wave number range of $k>0.01~h$ Mpc$^{-1}$.The MPS affects the LP and the WL effect in the CMB $B$ mode; however, the PMF can damp this effect. Previous studies of the CMB $B$ mode with the PMF have only considered the vector and tensor modes. These modes boost the CMB $B$ mode in the multipole range of $ell > 1000$, whereas the background PMF damps the CMB $B$ mode owing to the WL effect in the entire multipole range. The matter density in the Universe controls the WL effect. Therefore, when we constrain the PMF and the matter density parameters from cosmological observational data sets, including the CMB $B$ mode, we expect degeneracy between these parameters. The CMB $B$ mode also provides important information on the background gravitational waves, inflation theory, matter density fluctuations, and the structure formations at the cosmological scale through the cosmological parameter search. If we study these topics and correctly constrain the cosmological parameters from cosmological observations including the CMB $B$ mode, we need to correctly consider the background PMF.
We present the first cosmological simulations of primordial magnetic fields derived from the constraints by the Cosmic Microwave Background observations, based on the fields gravitational effect on cosmological perturbations. We evolved different primordial magnetic field models with the {enzo} code and compared their observable signatures (and relative differences) in galaxy clusters, filaments and voids. The differences in synchrotron radio powers and Faraday Rotation measure from galaxy clusters are generally too small to be detected, whereas differences present in filaments will be testable with the higher sensitivity of the Square Kilometre Array. However, several statistical full-sky analyses, such as the cross-correlation between galaxies and diffuse synchrotron power, the Faraday Rotation structure functions from background radio galaxies, or the analysis of arrival direction of Ultra-High-Energy Cosmic Rays, can already be used to constrain these primordial field models.
If primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range $10^5 -10^{12}M_{odot}$ is severely constrained by upper limits to the $mu$ distortion in the cosmic microwave background (CMB). This is because inhomogeneities on these scales will be dissipated by Silk damping in the redshift interval $5times 10^4lesssim zlesssim2times 10^6$. If the primordial fluctuations on a given mass scale have a Gaussian distribution and PBHs form on the high-$sigma$ tail, as in the simplest scenarios, then the $mu$ constraints exclude PBHs in this mass range from playing any interesting cosmological role. Only if the fluctuations are highly non-Gaussian, or form through some mechanism unrelated to the primordial fluctuations, can this conclusion be obviated.
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