Magnetization of fluid phonons and large-scale curvature perturbations

The quasinormal mode of a gravitating and magnetized fluid in a spatially flat, isotropic and homogeneous cosmological background is derived in the presence of the fluid sources of anisotropic stress and of the entropic fluctuations of the plasma. The obtained gauge-invariant description involves a system of two coupled differential equations of which the physical content is analyzed in all the most relevant situations. The Cauchy problem of large-scale curvature perturbations during the radiation dominated stage of expansion can be neatly formulated, and its general solution is shown to depend on five initial data assigned when the relevant physical wavelengths are larger than the particle horizon. The consequences of this approach are explored.

Figure 1

The standard adiabatic initial conditions of Eq. (6.5) are illustrated.

Figure 2

Some early departures from the linear approximation are illustrated in the case when the second derivative of the anisotropic stress does not vanish.

Figure 3

Illustrative examples where the initial conditions are dominated by the total anisotropic stress without leading to an early departure from the linear regime as suggested by Fig. 2.

Figure 4

Examples of Cauchy data dominated by the anisotropic stress where initially $\mathcal{R}(x_i)\ne {\mathcal{R}}^{\prime }(x_i)$. The initial conditions are fixed in compliance with Eqs. (6.26).

Figure 5

Illustrative examples of asymmetric initial conditions where ${\sigma }_{\mathrm{t}}(x_i)\ne 0$ and ${\sigma }_{\mathrm{t}}^{\prime }(x_i)\ne {\sigma }_{\mathrm{t}}^{\prime \prime }(x_i)$. As in Fig. 4, the Cauchy data are fixed according to Eqs. (6.26).

Figure 6

The numerical integration corresponding to the Cauchy data of Eqs. (6.27) and (6.28). As in Figs. 4 and 5, the Cauchy data are fixed according to Eqs. (6.26).