We present a detailed analytical study of ultrarelativistic neutrinos in cosmological perturbation theory and of the observable signatures of inhomogeneities in the cosmic neutrino background. We note that modification of perturbation variables that removes all the time derivatives of scalar gravitational potentials from the dynamical equations simplifies their solution notably. The used perturbations of particle number per coordinate, not proper, volume are generally constant on superhorizon scales. In real space the analytical approach can be extended beyond fluid models to neutrinos. The faster cosmological expansion due to the neutrino background affects the acoustic and damping angular scales of the cosmic microwave background (CMB). But we find that equivalent changes can be produced by varying other standard parameters, including the primordial helium abundance. The low-l integrated Sachs-Wolfe effect is also not sensitive to neutrinos. However, the gravity of neutrino perturbations suppresses the CMB acoustic peaks for the multipoles with $l\ensuremath{\gtrsim}200$ while it enhances the amplitude of matter fluctuations on these scales. In addition, the perturbations of relativistic neutrinos generate a unique phase shift of the CMB acoustic oscillations that, for adiabatic modes, cannot be caused by any other standard physics. The origin of the shift is traced to neutrino free-streaming velocity exceeding the sound speed of the photon-baryon plasma. We find that from a high-resolution, low-noise instrument such as CMBPOL the effective number of light neutrino species can be determined with an accuracy of $\ensuremath{\sigma}{(N}_{\ensuremath{\nu}})\ensuremath{\simeq}0.05--0.09,$ depending on the constraints on the helium abundance.

Signatures of relativistic neutrinos in CMB anisotropy and matter clustering

http://www.astro.auth.gr/~tsagas/Publications/Journals/PR/PR2.pdf

Relativistic cosmology and large-scale structure

The progress in the last decade in perturbative quantum field theory at high temperatures and densities, made possible by the use of effective field theories and hard thermal/dense loop resummations in ultrarelativistic gauge theories, is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far is given together with references to a few of the most recent developments and open problems.

https://iopscience.iop.org/article/10.1088/0034-4885/67/3/R05/pdf

Advances in perturbative thermal field theory

We present updated constraints on the free-streaming nature of cosmological neutrinos from cosmic microwave background (CMB) power spectra, baryonic acoustic oscillation data, and local measurements of the Hubble constant. Specifically, we consider a Fermi-like four-fermion interaction between massless neutrinos, characterized by an effective coupling constant $ G_{\rm eff}$, and resulting in a neutrino opacity $\dot{\tau}_\nu\propto G_{\rm eff}^2 T_\nu^5$. Using a conservative prior on the parameter $\log_{10}\left(G_{\rm eff} {\rm MeV}^2\right)$, we find a bimodal posterior distribution. The first of these modes is consistent with the standard $\Lambda$CDM cosmology and corresponds to neutrinos decoupling at redshift $z_{\nu,{\rm dec}} > 1.3\times10^5$. The other mode of the posterior, dubbed the "interacting neutrino mode", corresponds to neutrino decoupling occurring within a narrow redshift window centered around $z_{\nu,{\rm dec}}\sim8300$. This mode is characterized by a high value of the effective neutrino coupling constant, together with a lower value of the scalar spectral index and amplitude of fluctuations, and a higher value of the Hubble parameter. Using both a maximum likelihood analysis and the ratio of the two mode's Bayesian evidence, we find the interacting neutrino mode to be statistically disfavored compared to the standard $\Lambda$CDM cosmology. Interestingly, the addition of CMB polarization and direct Hubble constant measurements significantly raises the statistical significance of this secondary mode, indicating that new physics in the neutrino sector could help explain the difference between local measurements of $H_0$, and those inferred from CMB data. A robust consequence of our results is that neutrinos must be free streaming long before the epoch of matter-radiation equality.

John M. Stewart

Papers

Perturbations in an Expanding Universe of Free Particles