15 research outputs found
Effects of non-linearities on magnetic field generation
Magnetic fields are present on all scales in the Universe. While we
understand the processes which amplify the fields fairly well, we do not have a
"natural" mechanism to generate the small initial seed fields. By using fully
relativistic cosmological perturbation theory and going beyond the usual
confines of linear theory we show analytically how magnetic fields are
generated. This is the first analytical calculation of the magnetic field at
second order, using gauge-invariant cosmological perturbation theory, and
including all the source terms. To this end, we have rederived the full set of
governing equations independently. Our results suggest that magnetic fields of
the order of G can be generated (although this depends on the small
scale cut-off of the integral), which is largely in agreement with previous
results that relied upon numerical calculations. These fields are likely too
small to act as the primordial seed fields for dynamo mechanisms.Comment: 21 pages; v2: minor changes, added references; v3: version accepted
for publication in JCA
Isocurvature initial conditions for second order Boltzmann solvers
We study how to set the initial evolution of general cosmological
fluctuations at second order, after neutrino decoupling. We compute approximate
initial solutions for the transfer functions of all the relevant cosmological
variables sourced by quadratic combinations of adiabatic and isocurvature
modes. We perform these calculations in synchronous gauge, assuming a Universe
described by the CDM model and composed of neutrinos, photons, baryons
and dark matter. We highlight the importance of mixed modes, which are sourced
by two different isocurvature or adiabatic modes and do not exist at the linear
level. In particular, we investigate the so-called compensated isocurvature
mode and find non-trivial initial evolution when it is mixed with the adiabatic
mode, in contrast to the result at linear order and even at second order for
the unmixed mode. Non-trivial evolution also arises when this compensated
isocurvature is mixed with the neutrino density isocurvature mode. Regarding
the neutrino velocity isocurvature mode, we show it unavoidably generates
non-regular (decaying) modes at second order. Our results can be applied to
second order Boltzmann solvers to calculate the effects of isocurvatures on
non-linear observables.Comment: 25+18 pages. No figure
The intrinsic B-mode polarisation of the cosmic mMicrowave background
We estimate the B-polarisation induced in the Cosmic Microwave Background by the non-linear evolution of density perturbations. Using the second-order Boltzmann code SONG, our analysis incorporates, for the first time, all physical effects at recombination. We also include novel contributions from the redshift part of the Boltzmann equation and from the bolometric definition of the temperature in the presence of polarisation. The remaining line-of-sight terms (lensing and time-delay) have previously been studied and must be calculated non-perturbatively. The intrinsic B-mode polarisation is present independent of the initial conditions and might contaminate the signal from primordial gravitational waves. We find this contamination to be comparable to a primordial tensor-to-scalar ratio of r≃10−7 at the angular scale ℓ≃100, where the primordial signal peaks, and r≃5⋅10−5 at ℓ≃700, where the intrinsic signal peaks. Therefore, we conclude that the intrinsic B-polarisation from second-order effects is not likely to contaminate future searches of primordial gravitational waves