Perturbations in a coupled scalar field cosmology

Abstract

I analyze the density perturbations in a cosmological model with a scalar field coupled to ordinary matter, such as one obtains in string theory and in conformally transformed scalar-tensor theories. The spectrum of multipoles on the last scattering surface and the power spectrum at the present are compared with observations to derive bounds on the coupling constant and on the exponential potential slope. It is found that the acoustic peaks and the power spectrum are strongly sensitive to the model parameters. The models that best fit the galaxy spectrum and satisfy the cluster abundance test have energy density $Ω_φ\simeq 0.1$ and a scale factor expansion law $a\sim t^{p}, p\simeq 0.68$.

Figures (9)

• Figure 1: Parameter space for the attractors. In the dark-shaded region the solution $b$ is an attractor; in the other regions the attractors are the solutions $a,c$ or $d$, as labelled. In all the paper we focus on the attractor $b$. The continuous curves mark values of $\Omega _{\phi }$ equal to 0.05,0.1, 0.2, 0.3,...,0.9, top to bottom. The dotted lines are values of $p$ equal to 0.6, 0.65, 2/3, 0.7, 0.8, 1, 1.3, left to right. There exists also a completely equivalent symmetric region with $\beta \rightarrow -\beta$ and $\mu \rightarrow -\mu .$
• Figure 2: Phase space corresponding to $\Omega_{\phi}=0.1, p=0.7$, in MDE.
• Figure 3: Contour plot of the exponent $m_+$ of the fluctuation growth law $\delta _{c}\sim a^{m}$ versus $\Omega _{\phi },p$. The contour levels are for $m=0.9$ (enclosing the white region), down to 0 in steps of 0.1. In the black region $m$ is complex. Notice that for any given $\Omega _{\phi }$ the maximum of $m$ is close to $p=2/3$, especially for small $\Omega _{\phi }$.
• Figure 4: Growth of the dark matter fluctuations for various values of the coupling and $\Omega_{\phi}=0.1$. In the top panel the trend of the horizon length and of two comoving scale (the horizontal lines) show the horizon crossing and the radiation and matter eras. Thick lines: wavelength $\simeq 900$Mpc$/h$. Thin lines: wavelength $\simeq 100$Mpc$/h$.
• Figure 5: $C_{\ell }$ spectrum for various models (actually we plot $[\ell(\ell+1)C_{\ell}/2\pi]^{1/2}$, as customary). Notice the shift of the peak location for the different values of $p$, in agreement with the approximation given in the text. The amplitude decreases for $p\neq 2/3$ (except for values slightly larger than 2/3) and, for a given $p,$ decreases for smaller $\Omega _{\phi }$ , as expected. The data points are from Tegmark's home page (http:// www.sns.ias.edu/ max).