Effects of Cosmological Moduli Fields on Cosmic Microwave Background

Abstract

We discuss effects of cosmological moduli fields on the cosmic microwave background (CMB). If a modulus field φonce dominates the universe, the CMB we observe today is from the decay of φand its anisotropy is affected by the primordial fluctuation in the amplitude of the modulus field. Consequently, constraints on the inflaton potential from the CMB anisotropy can be relaxed. In particular, the scale of the inflation may be significantly lowered. In addition, with the cosmological moduli fields, correlated mixture of adiabatic and isocurvature fluctuations may be generated, which results in enhanced CMB angular power spectrum at higher multipoles relative to that of lower ones. Such an enhancement can be an evidence of the cosmological moduli fields, and may be observed in future satellite experiments.

Figures (4)

• Figure 1: Evolution of the gravitational potential at the superhorizon scale for the case where $\delta\tilde{\phi}_{\rm i}\neq 0$ and $\tilde{\Psi}_{\rm i}=0$. The horizontal axis is the scale factor $a$ whose normalization is arbitrary, and the vertical axis is $\tilde{\Psi}^{(\delta\phi)}$ normalized by $\tilde{S}_{\rm i}$. The lines (A) and (B) correspond to cases with different initial modulus amplitude; $\bar{\phi}_{\rm i}^2$ for the line (A) is 10 times larger than that of (B).
• Figure 2: The CMB angular power spectrum $C_l^{(\delta\phi)}$ for the case with the correlated isocurvature perturbation in the baryonic sector (dashed line), as well as $C_l$ for purely adiabatic (solid line) and purely baryonic isocurvature (dotted line) cases. For the cosmological parameters, we use $h=0.65$, $\Omega_{\rm b}h^2=0.019$, $\Omega_{\rm m}=0.4$aph0007187, and the flat universe is assumed. (Here, $h$ is the present expansion rate of the universe in units of 100 km/sec/Mpc, and $\Omega_{\rm b}$ and $\Omega_{\rm m}$ are present density parameters for baryon and non-relativistic matter, respectively.) We used the normalization $[l(l+1)C_{l}/2\pi]_{l=10}=1$.
• Figure 3: The CMB angular power spectrum $C_l$ for $R=0$ (solid), $R=4.5$ (dashed), and $R=9$ (dotted). The overall normalization of $C_l$ is determined such that the $\chi^2$ variable is minimized. Scale-invariance is assumed both for $\Psi_{\rm i}$ and $S_{\rm i}$. The values of the cosmological parameters are the same as those used in Fig. \ref{['fig:comparison']}.
• Figure 4: The $\chi^2$ variable as a function of $R$. The overall normalization of $C_l$ is chosen so that the $\chi^2$ variable is minimized. We take $\Omega_{\rm b}h^2=0.019$, and several values of $h$ and $\Omega_{\rm m}$aph0007187.