Effects of the Sound Speed of Quintessence on the Microwave Background and Large Scale Structure

Abstract

We consider how quintessence models in which the sound speed differs from the speed of light and varies with time affect the cosmic microwave background and the fluctuation power spectrum. Significant modifications occur on length scales related to the Hubble radius during epochs in which the sound speed is near zero and the quintessence contributes a non-negligible fraction of the total energy density. For the microwave background, we find that the usual enhancement of the lowest multipole moments by the integrated Sachs-Wolfe effect can be modified, resulting in suppression or bumps instead. Also, the sound speed can produce oscillations and other effects at wavenumbers $k > 10^{-2}$ h/Mpc in the fluctuation power spectrum.

Figures (5)

• Figure 1: The speed of sound as a function of the scale factor $a$ ($a_{\text{today}}=1$) for a k-essence model studied in Ref.kess. Note the changes in $c_s$ between the last scattering surface and the present epoch triggered by the transformations in the background equation of state.
• Figure 2: Comparison of the lowest multipole moments of the CMB temperature power spectrum for a series of models with $w=-0.8$: (a) $c_s=1$ (dotted); (b) $c_s=1$ until $z=5$ and then $c_s=0$ for $z<5$ (solid); and (c) $c_s=0$ for all $z$ (dot-dashed).
• Figure 3: Comparison of the lowest multipole moments of the CMB temperature power spectrum for a series of models with the same $w(z)$ (in this case, corresponding to the $k$-essence model in Fig. \ref{['fig:fig1']} and Ref.kess) but different $c_s(z)$: (a) $c_s=1$ (dotted); (b) $c_s=1$ for $z> 10$ and $c_s=0$ for $z<10$ (solid); the $k$-essence model shown in Fig. \ref{['fig:fig1']} (dot-dashed); and two variations (short- and long-dashed) with rapid variations in $c_s^2$ (spikes) as described in the text.
• Figure 4: Comparision of higher multipole moments of the CMB temperature power spectrum for the models in Fig. \ref{['fig:fig3']}. The spectra have been normalized so that the amplitudes match at the top of the first acoustic peak.
• Figure 5: Comparison of the shape of the total fluctuation power spectrum, $P(k)$ as a function of wavenumber $k$ for the sequence of models in Fig. \ref{['fig:fig2']}. The normalization of the curves is arbitrary.