Cosmic Microwave Background Trispectrum and Primordial Magnetic Field Limits

Abstract

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.Magnetic fields are ubiquitous in the Universe from planets and stars to galaxies and galaxy clusters [1,2], yet the origin and evolution of large-scale magnetic fields remains a puzzle. A popular paradigm is that magnetic fields in collapsed structures could arise from dynamo amplification of seed magnetic fields [2]. The seed field could in turn be generated in astrophysical batteries [3] or due to processes in the early universe [4,5]. Indeed recent γ-ray observations claim to find a lower limit to an all-pervasive intergalactic magnetic field that fills most of the cosmic volume [6], which would perhaps favor a primordial origin. A primordial magnetic field can be generated at inflation [4], or arise out of other phase transitions in the early Universe [5]. As yet there is no compelling mechanism which produces strong coherent primordial fields. Equally, the dynamo paradigm is not without its own challenges in producing sufficiently coherent fields and sufficiently rapidly [2]. Therefore, it is useful to keep open the possibility that primordial magnetic fields originating in the early universe play a crucial role in explaining the observed cosmic magnetism.In this context it is important to investigate every observable signature of the putative primordial magnetic fields. Constraints on large-scale primordial magnetic fields have already been derived using the cosmic microwave background (CMB) power spectrum [7,8] and Faraday rotation [9]. However, the effects of a magnetic field on the CMB are relatively more prominent in its non-Gaussian correlations. This is because magnetic fields induce non-Gaussian signals at lowest order as the magnetic energy density and stress are quadratic in the field. On the other hand, the standard inflationary perturbations, dominated by their linear component, can source non-Gaussian correlations only with higher-order perturbations and thus necessarily produce a small amplitude of CMB non-Gaussianity (cf. [10,11]). Primordial magnetic fields can induce apprec...

PROBING PRIMORDIAL MAGNETIC FIELDS USING Lyα CLOUDS

“…In comparison to bounds on PMFs from CMBR anisotropies (e.g., Figure 1 of Yamazaki et al 2010), for the entire range of spectral indices, we obtain stronger limits on B 0 . Other constraints from bispectrum and trispectrum analyses of CMBR passive scalar modes (Trivedi et al 2010(Trivedi et al , 2012 are 2.4 nG and 0.7 nG, respectively; they have used spectral index value n = −2.8, whereas for n = −2.8 our analysis gives an upper bound on B 0 0.3 nG ( Figure 7). As noted above, these bounds are even better than our previous analysis with the weak-lensing data (Figure 8).…”

“…The impact of large-scale PMFs on CMBR temperature and polarization anisotropies has been studied in detail (e.g., Subramanian & Barrow 1998b, 2002Seshadri & Subramanian 2001;Mack et al 2002;Lewis 2004;Gopal & Sethi 2005;Tashiro & Sugiyama 2006;Sethi & Subramanian 2005;Sethi et al 2008;Sethi & Subramanian 2009;Sethi et al 2010;Kahniashvili & Ratra 2005;Giovannini & Kunze 2008;Yamazaki et al 2008;Seshadri & Subramanian 2009;Trivedi et al 2010Trivedi et al , 2012. Wasserman (1978) demonstrated that PMFs can induce density perturbations in the post-recombination universe.…”

The influence of magnetic fields, turbulence, and UV radiation on the formation of supermassive black holes

“…Note that the amount of AD heating depends on the scaling of B with ρ; it is therefore important to obtain a correct model for this relationship. The current upper limit on the primordial magnetic field is ∼1 nG comoving (Schleicher & Miniati 2011;Trivedi et al 2012), so a 2 nG field would be reached by the ∼2σ upward fluctuations.…”

Reionization constraints on primordial magnetic fields

“…; these considerations put upper bounds on B0 in the range 0.3-1 nG (e.g. Trivedi, Seshadri, & Subramanian 2012, Kahniashvili et al 2010, Shaw & Lewis 2012, Pandey & Sethi 2013, Pandey & Sethi 2012, Lewis 2004, Caprini, Durrer, & Kahniashvili 2004. Bounds obtained from Big Bang Nucleosynthesis constraints give B0 10 −7 G (Suh & Mathews 1999).…”