Constraints on Natural Inflation from Cosmic Microwave Background

Abstract

We study constraints on the natural inflation model from the cosmic microwave background radiation (CMBR). Inflaton φfor the natural inflation has a potential of the form V=Λ^4[1-\cos(φ/\sqrt{2}f_φ)], which is parametrized by two parameters f_φand Λ. Various cosmological quantities, like the primordial curvature perturbation and the CMBR anisotropy, are determined as functions of these two parameters. Using recent observations of the CMBR anisotropy by BOOMERANG and MAXIMA (as well as those from COBE), constraints on the parameters f_φand Λare derived. The model with f_φlower than 8.5\times 10^{18} (5.4\times 10^{18}, 4.5\times 10^{18}) GeV predicts a power spectrum with index n_{\rm S} smaller than 0.95 (0.9, 0.85) which suppresses the CMBR anisotropy for smaller angular scale. With such a small n_{\rm S}, height of the second acoustic peak can become significantly lower than the case of the scale-invariant Harrison-Zeldovich spectrum.

Figures (3)

• Figure 1: $n_{\rm S} (k_{\rm COBE})$ as a function of $f_\phi$. The best-fit value of $\Lambda$ for the COBE-scale normalization is used.
• Figure 2: CMBR anisotropy for the $l$-th multipole. The vertical axis is $\tilde{C}_l\equiv [l(l+1)/2\pi]C_l$. Here, we take $f_\phi= 10\times 10^{18}$ GeV (solid), $8\times 10^{18}$ GeV (dashed), $6\times 10^{18}$ GeV (dotted), and $4\times 10^{18}$ GeV (dot-dashed), and the best-fit values of $\Lambda$ for the COBE-scale normalization are used.
• Figure 3: Constraint on the parameters $f_\phi$ and $\Lambda$. The shaded regions are for $\chi^2\leq 43$ for (a) $\tau=0$ (no reionization), (b) $\tau=0.2$, and (c) $\tau=0.4$. The dotted lines are contours of constant $\sigma_8$ (0.4, 0.6, 0.8, 1.0, 1.2, and 1.4, from below).