Acoustic oscillations and viscosity

Abstract

Using a simple thermo-hydrodynamic model that respects relativistic causality, we revisit the analysis of qualitative features of acoustic oscillations in the photon-baryon fluid. The growing photon mean free path introduces transient effects that can be modelled by the causal generalization of relativistic Navier-Stokes-Fourier theory. Causal thermodynamics provides a more satisfactory hydrodynamic approximation to kinetic theory than the quasi-stationary (and non-causal) approximations arising from standard thermodynamics or from expanding the photon distribution to first order in the Thomson scattering time. The causal approach introduces small corrections to the dispersion relation obtained in quasi-stationary treatments. A dissipative contribution to the speed of sound slightly increases the frequency of the oscillations. The diffusion damping scale is slightly increased by the causal corrections. Thus quasi-stationary approximations tend to over-estimate the spacing and under-estimate the damping of acoustic peaks. In our simple model, the fractional corrections at decoupling are $\gtrsim 10^{-3}$.Comment: Improved version with new quantitative estimates and some corrections. We show how quasi-stationary approximations based on expanding the photon distribution to first order in the Thomson time tend to under-estimate the frequency and damping of acoustic oscillation

Cosmological dynamics on the brane

“…If we choose the fundamental 4-velocity u µ such that σ µν = 0, which is the covariant analogue of the longitudinal or conformal Newtonian gauge in metric-based perturbation theory (see [19,20] for further discussion), then the shear propagation equation (51) becomes a constraint determining the brane tidal tensor:…”

Integrability conditions of quasi-Newtonian cosmologies in modified gravity

“…Despite there being no proper Newtonian limit for GR on cosmological scales, recent works on so-called quasi-Newtonian cosmologies [18][19][20] have shown that gravitational physics (such as analysis of nonlinear collapse and structure formation using the Zel'Dovich approximation 21 ) can be studied to a good approximation using such an approach. In, 18 it was shown that non-linear quasi-Newtonian cosmologies are generally covariantly inconsistent in General Relativity.…”

“…Based on the ansatz for the evolution of the gravitational potential introduced by van Elst and Ellis 18 and Maartens' generalisation, 19 we first consider what happens if we modify the stress-energy tensor to include a a general anisotropic stress π ab and extend the general relativistic integrability conditions for the linearized models about the FLRW background. We show that while a general anisotropic source does not lead to integrability conditions that close on time propagation, f (R) gravity is special because of the particular form π ab takes in this case.…”

“…23 This in turn puts strict constraints on the gravitational field. 19,[23][24][25] On the other hand, when linearized around a FriedmannLemaître-Robertson-Walker (FLRW) model, these quasi-Newtonian models are consistent and provide a basis for the study of peculiar velocities in almost FLRW models. 18,19 It has been pointed out 26 that peculiar motion can locally mimic the effects of dark matter in regions of a dust-dominated FRW universe endowed with bulk peculiar velocities.…”

“…This is what is referred to as a quasi-Newtonian (Eulerian) frame. 19,27 The matter pressure and vorticity both vanish in this frame, while the matter energy flux q m a is non-zero, i.e., there is net particle flux due to the tilting of the quasi-Newtonian frame relative to the comoving one. Moreover, both the isotropic and anisotropic pressures of matter vanish to linear order because they arise as second-order effects due to the relative motion a :…”