Abstract
The viscous inhomogeneities of a relativistic plasma determine a further class of entropic modes whose amplitude must be sufficiently small since curvature perturbations are observed to be predominantly adiabatic and Gaussian over large scales. When the viscous coefficients only depend on the energy density of the fluid the corresponding curvature fluctuations are shown to be almost adiabatic. After addressing the problem in a gauge-invariant perturbative expansion, the same analysis is repeated at a non-perturbative level by investigating the nonlinear curvature inhomogeneities induced by the spatial variation of the viscous coefficients. It is demonstrated that the quasiadiabatic modes are suppressed in comparison with a bona fide adiabatic solution. Because of its anomalously large tensor to scalar ratio the quasiadiabatic mode cannot be a substitute for the conventional adiabatic paradigm so that, ultimately, the present findings seems to exclude the possibility of a successful accelerated dynamics solely based on relativistic viscous fluids. If the dominant adiabatic mode is not affected by the viscosity of the background a sufficiently small fraction of entropic fluctuations of viscous origin cannot be a priori ruled out.
Highlights
The first releases of the WMAP data [1] presented convincing evidence that the initial conditions of the Einstein-Boltzmann hierarchy are predominantly adiabatic
Whenever the bulk viscosity does not have a homogeneous background the resulting fluctuations are automatically gauge-invariant and their contribution to the evolution equations of the curvature perturbations reminds us of the familiar source terms arising in connection with the conventional entropic modes customarily constrained by means of the temperature and the polarization anisotropies of the CMB
A second complementary possibility stipulates that the viscous coefficients have a spatial variation but in the presence of a homogeneous background
Summary
The first releases of the WMAP data [1] presented convincing evidence that the initial conditions of the Einstein-Boltzmann hierarchy are predominantly adiabatic. Since the inhomogeneities of the viscous coefficients cause entropic fluctuations of the spatial curvature, the role of viscosity at large scales must either be constrained by the initial data of the Einstein-Boltzmann hierarchy [7] or totally absent. If correct this conclusion would threaten the possibility of an accelerated phase only driven by the viscous coefficients. It will be shown that the largescale fluctuations induced by inhomogeneous viscosities are not necessarily entropic, as argued in the previous paragraph, but they can be very close to adiabatic at large scales ( the terminology quasiadiabatic) provided the viscous coefficients solely depend on the energy density of the relativistic plasma.
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