We investigate if the observed small and nearly scale-invariant primordial cosmic perturbation, i.e., the perturbation amplitude $P_{\zeta }\sim {10}^{-9}$ and the spectral index $n_s\simeq 0.965$, is typical in the landscape of vacua after imposing anthropic selections on them. We consider the situation where the universe begins from a metastable vacuum driving a precedent inflation, a curvature-dominated open universe is created by tunneling, and the curvature energy is inflated away by new inflation. We argue that the initial inflaton field value is homogeneous but typically nonzero because of the quantum fluctuation of long wavelength modes created during the precedent inflation, and only the universe which accidentally has a small inflaton field value is anthropically selected. We show that this bias, together with certain distributions of inflation model parameters that are physically well motivated, makes the observed small and nearly scale-invariant spectrum typical.

• Received 1 April 2019

DOI:https://doi.org/10.1103/PhysRevD.100.023510