Abstract
We consider an open universe created by bubble nucleation, and study possible effects of an "ancestor vacuum" (de Sitter space in which bubble nucleation occurred) on the present universe. We compute vacuum expectation values of energy-momentum tensor for a minimally coupled scalar field, carefully taking into account the effect of the ancestor vacuum by the Euclidean prescription. In the study of the time evolution, an important role is played by the so-called supercurvature mode, which is non-normalizable on a spatial slice of open universe and decays in time most slowly. We point out that vacuum energy of a quantum field can be regarded as dark energy if mass of the field is of order the present Hubble parameter or smaller. We obtain preliminary results for the dark energy equation of state w(z) as a function of the redshift.
Highlights
In a theory with multiple vacua, nucleation of bubbles of a true vacuum can occur due to quantum tunneling
We point out that the vacuum energy of the quantum field can be regarded as dark energy if mass of the field is of order the present Hubble parameter or smaller
If there is a field with mass of order the present Hubble parameter H0 or smaller, the supercurvature mode of this field will be essentially frozen until today
Summary
In a theory with multiple vacua, nucleation of bubbles of a true vacuum can occur due to quantum tunneling. As long as the mass of the scalar field is smaller than the Hubble parameter in our universe, the field value for the supercurvature mode remains nearly constant. This is the well-known freezing of the superhorizon fluctuations; supercurvature modes can always be considered to be outside the horizon. If there is a field with mass of order the present Hubble parameter H0 or smaller, the supercurvature mode of this field will be essentially frozen until today This gives us an interesting possibility for the realization of dark energy. In Appendix D, we present the details on the matching of the wave functions of the scalar field across different eras
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