Double Inflation and the Low CMB Quadrupole

Abstract

Recent released WMAP data show a low value of quadrupole in the CMB temperature fluctuations, which confirms the early observations by COBE. In this paper we consider a model of two inflatons with different masses, $V(φ_1,φ_2)={1\over 2}m_1^2φ_1^2 + {1 \over 2} m_2^2 φ_2^2$, $m_1>m_2$ and study its effects on CMB of suppressing the primordial power spectrum $P(k)$ at small $k$. Inflation is driven in this model firstly by the heavier inflaton $φ_1$, then the lighter field $φ_2$. But there is no interruption in between. We numerically calculate the scalar and tensor power spectra with mode by mode integrations, then fit the model to WMAP temperature correlations TT and the TE temperature-polarization spectra. Our results show that with $m_1\sim 10^{14}$ GeV and $m_2\sim 10^{13}$ GeV, this model solves the problems of flatness {\it etc.} and the CMB quadrupole predicted can be much lower than the standard power-law $Λ$CDM model.

Figures (4)

• Figure 1: Initial power spectra and slow rolling parameters as a function of $\ln(k/k_f)$. $N(k_f)=59.6$
• Figure 2: CMB anisotropies with primordial spectra shown in Fig.\ref{['fig:fig2']} . The error bars are taken the same as Ref.Spergel. The upper and lower dashed lines show the 1-$\sigma$ confidence levels for lognormal distributions with cosmic variance limits. The middle solid lines show the models with the lowest quadrupoles.
• Figure 3: Two-dimesional contours in the $\ln(k_f/k_c)$-- $\Omega_{\Lambda}$ plane for our grids of model. $k_c \approx 1.6 \times 10^{-3}$ Mpc$^{-1}$. The regions of different color show 68.3%, 95% and 99.7% confidence respectively.
• Figure 4: One-dimesional marginalized distributions for the values of $\ln(k_f/k_c)$.