Constraints on the multi-lognormal magnetic fields from the observations of the cosmic microwave background and the matter power spectrum

Abstract

Primordial magnetic fields (PMFs), which were generated in the early Universe before recombination, affect the motion of plasma and then the cosmic microwave background and the matter power spectrum. We consider constraints on PMFs with a characteristic correlation length from the observations of the anisotropies of the cosmic microwave background and the matter power spectrum. The spectrum of PMFs is modeled with multi-lognormal distributions, rather than power-law distribution, and we derive constraints on the strength $|{\mathbf{B}}_k|$ at each wave number $k$ along with the standard cosmological parameters in the flat Universe and the foreground sources. We obtain upper bounds on the field strengths at $k=10^{-1},10^{-2},10^{-4}$, and $10^{-5}$ Mpc${}^{-1}$ as 4.7 nG, 2.1 nG, 5.3 nG, and 10.9 nG ($2\sigma$ C.L.) respectively, while the field strength at $k=10^{-3}$Mpc${}^{-1}$ turns out to have a finite value as $|{\mathbf{B}}_{k=10^{-3}}|=6.2\pm 1.3$ nG ($1\sigma$ C.L.). This finite value is attributed to the finite values of BB mode data at $\ell >300$ obtained from the QUAD experiment. If we do not include the BB mode data, we obtain only the upper bound on $B_{k=10^{-3}}$.

10 pages, 6 figures. Accepted for publication in Physical Review D, published 26 November 2013

References in corpus (19)

• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• CMB anisotropies from primordial inhomogeneous magnetic fields
• Cosmological Magnetic Field: a fossil of density perturbations in the early universe
• Effects of a Primordial Magnetic Field on Low and High Multipoles of the CMB
• CMB Temperature Anisotropy from Broken Spatial Isotropy due to an Homogeneous Cosmological Magnetic Field
• Primordial magnetic field limits from cosmological data
• The Search for a Primordial Magnetic Field
• Faraday rotation, stochastic magnetic fields and CMB maps
• Constraints on the Evolution of the Primordial Magnetic Field from the Small-Scale Cosmic Microwave Background Angular Anisotropy
• CMB anisotropies due to cosmological magnetosonic waves
• Tight coupling expansion and fully inhomogeneous magnetic fields
• Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects
• Constraining primordial magnetic fields through large scale structure
• Primordial magnetic fields and formation of molecular hydrogen
• Effect of Primordial Magnetic Field on Seeds for Large Scale Structure
• Effects of power law primordial magnetic field on big bang nucleosynthesis
• Constraints on the Primordial Magnetic Field from ${\sigma }_8$
• Neutrino mass effects on vector and tensor CMB anisotropies in the presence of a primordial magnetic field

Cited by in corpus (7)

• Big Bang Nucleosynthesis with an Inhomogeneous Primordial Magnetic Field Strength
• Primordial Magnetic Helicity Constraints from WMAP Nine-Year Data
• Scale-invariant helical magnetic field evolution and the duration of inflation
• The evolution of primordial magnetic field since its generation
• CMB with the background primordial magnetic field
• Evolution of the cosmic matter density field with a primordial magnetic field
• Impact of a primordial magnetic field on cosmic microwave background $B$ modes with weak lensing