Backreaction Effects of Dissipation in Neutrino Decoupling

Abstract

Dissipative effects during neutrino decoupling in the early universe create a small backreaction on the Hubble rate, and lead to a small rise in temperature and entropy. We use a simplified thermohydrodynamic model, which provides a causal approximation to kinetic theory, in order to estimate the backreaction effects and the entropy production. I. INTRODUCTIONNon-equilibrium processes in the early universe are typically associated with dynamical transitions or particle decouplings. In the case of neutrino decoupling, the standard approach is to treat the process as adiabatic (see e.g.[1]). The small non-equilibrium effects are thus usually neglected, which provides a reasonable approximation. However, given the increasing accuracy of cosmological observations and theoretical modeling, it is worthwhile revisiting the standard equilibrium models of processes such as neutrino decoupling, in order to see whether non-equilibrium corrections can lead to observable consequences. Recently, non-equilibrium corrections in neutrino decoupling have been calculated in a number of papers, using complicated kinetic theory and numerical computations (see [2] for a short review). The corrections are very small, as expected. For example, in [3][4][5] it was found that non-equilibrium effects lead to a small change in the decoupling temperature for neutrinos. Spectral distortions have also been analyzed [6], showing the remarkable fact that they amount to as much as 1% or more for the higher-energy side of the spectrum. Although these corrections in the spectrum, energy density and temperature of the neutrino component have hardly any effect on primordial helium synthesis, yielding a change in the mass fraction of ∼ 10 −4 , they can lead to other effects that may be observable. Thus it is shown that the non-equilibrium increase in neutrino temperature, which leads to an extra injection of energy into the photon spectrum, leads to a shift of equilibrium epoch between matter and radiation which, in turn, modifies the angular spectrum of fluctuations of the cosmic microwave background radiation [7,8].Despite the accuracy of these models in obtaining corrections to the decoupling temperature and distribution function due to non-equilibrium effects, they still make use of the standard Friedman equations for a perfect (i.e nondissipative) fluid. This leads to the physically inconsistent situation in which, say, the energy density and expansion evolve in time like a radiative fluid in equilibrium. One expects that small distortions in the particle equilibrium distribution function should be reflected in the macroscopic (i.e fluid) description, as given by the stress-energy tensor, by adding a bulk viscous pressure to the equilibrium one. Here we consider an alternative thermo-hydrodynamic model of dissipative effects in neutrino decoupling, simple enough to produce analytic solutions for the backreaction effects on the universal scale factor, and estimates for the entropy production due to dissipation. As explained above these effects are...

Cosmological neutrino entropy changes due to flavor statistical mixing

“…The above results does not change the significance and the magnitude of the finite-temperature electromagnetic corrections to the energy density of the γe + e − radiation plasma [15,20,21] or of the finite-temperature QCD corrections [22]. They are of the same order of magnitude of flavor mixing corrections upon the averaged temperature of decoupling for different neutrino species, which also depend on the mixing parameters [22].…”

Neutrinos in cosmology

“…universe was recently proposed in ref. [142]. Though significantly less accurate, it gives a simple intuitive description and qualitatively similar results.…”

“…A simplified hydrodynamic approach to non-equilibrium neutrinos in the early universe was recently proposed in ref. [142]. Though significantly less accurate, it gives a simple intuitive description and qualitatively similar results.…”

The CB energy density through the quantum measurement theory

“…The results depicted from Figs. 1 and 2 does not change the significance and the magnitude of the finite-temperature electromagnetic corrections to the energy density of the γe + e − radiation plasma [20,22,23] or of the finite temperature QCD corrections [1]. They are of the same order of magnitude of flavor mixing corrections upon the averaged temperature of decoupling for different neutrino species, which also depend on the mixing parameters [1].…”

“…The results depicted from Figs. 1 and 2 does not change the significance and the magnitude of the finite-temperature electromagnetic corrections to the energy density of the γe + e − radiation plasma[20,22,23] or of the finite temperature QCD corrections[1]. They are of the same order of magnitude of flavor mixing corrections upon the averaged temperature of decoupling for different neutrino species, which also depend on the mixing parameters [1].The energy dependence of an ensemble of neutrino flavors on the statistical weights can be determined and the role of different flavor energy definitions in obtaining the expressions for cosmological neutrino masses can therefore be discriminated.…”