CMB anisotropies generated by a stochastic background of primordial magnetic fields with non-zero helicity

Abstract

We consider the impact of a stochastic background of primordial magnetic fields with nonvanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the T B and EB cross-correlation in the CMB pattern. We finally show the impact of including the helical term on the power spectra of CMB anisotropies up to multipoles with ∼ O(10 3 ).

Planck2015 results

“…A non-zero helicity in the PMFs changes the amplitudes of the parity-even power spectra and induces parity-odd cross-correlations between the temperature and B-polarization anisotropies and E-and B-polarization anisotropies (Pogosian et al 2002;Caprini et al 2004;Ballardini et al 2015). Such parity-odd cross-correlators are also generated by Faraday rotation, but only owing to homogeneous PMFs, not owing to the stochastic model for PMFs considered in this paper (Kosowsky et al 2005).…”

“…5 we show the predictions for the magneticallyinduced compensated modes, considering the additional contributions to the sources owing to helicity. We consider the maximally helical case, A H = A B , with equal spectral indices, n B = n H , using the solutions to the helical energy momentum tensor components derived by Ballardini et al (2015). The predictions show no difference in the shape and in the slope of the angular power spectra, with a small shift in the amplitude, which is always smaller for the helical case, at least for scales relevant for the CMB.…”

“…We consider the impact of such PMFs on CMB anisotropies in temperature and polarization. Using the exact expressions for the energy-momentum tensor components including the helical contribution discussed by Ballardini et al (2015), we derive the predictions for the impact of a helical PMF on the CMB power spectra in temperature and polarization.…”

“…As done for the amplitude of the magnetic field in Eq. (2), we can express the amplitude of the helical component on a comoving scale of λ as (Ballardini et al 2015)…”

Constraints on primordial magnetic fields from magnetically-induced perturbations: current status and future perspectives with LiteBIRD and future ground based experiments

“…It is possible to generate fields with an helical contribution by several mechanisms [69][70][71][72] and numerical simulations show how the fields rapidly reach the maximally helical confinguration independentely from the initial conditions [73][74][75][76][77]. Last, but not least, helicity can leave imprints onto the Cosmic Microwave Background [78][79][80][81][82][83].…”