An Open Universe from Inflation

Abstract

We present a natural scenario for obtaining an open universe (${\Omega }_0<1$) through inflation. In this scenario, there are two epochs of inflationary expansion---an epoch of `old inflation,' during which the inflaton field is stuck in a false vacuum, followed by an epoch of `new inflation,' during which the inflaton field slowly rolls toward its true minimum. During the first epoch, inflation solves the smoothness and horizon problems. Then an open universe (with negative spatial curvature) is created by the nucleation of a single bubble. In effect $\Omega$ is instantaneously `reset' to zero. During the subsequent `new' inflation $\Omega$ rises toward unity. The value of $\Omega$ today is calculable in terms of the parameters of the potential, and we show that obtaining values significantly different from zero or unity (though within the range $0<\Omega <1$) does not require significant fine tuning. We compute the spectrum of density perturbations by evolving the Bunch-Davies vacuum modes across the bubble wall into its interior.

60 pages + 3 figures. Uses PHYZZX macro package. In this revised version we replace the numerical results of the previous version with exact analytic solutions. Some minor mistakes are corrected and there is some new material.

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