Alexander Vilenkin

Creation of Universes from Nothing

If inflation is eternal, then the beginning of our local universe, about 14 billion years ago, was preceded by an unknown number of ancestor bubble universes.

Predictions from quantum cosmology.

If the cosmological evolution is followed back in time, we come to the initial singularity where the classical equations of general relativity break down. This led many people to believe that in order to understand what actually happened at the origin of the universe, we should treat the universe quantum-mechanically and describe it by a wave function rather than by a classical spacetime. This quantum approach to cosmology was initiated by DeWitt [1] and Misner [2], and after a somewhat slow start has become very popular in the last decade or so. The picture that has emerged from this line of development [3, 4, 6, 5, 7, 8, 9] is that a small closed universe can spontaneously nucleate out of nothing, where by ‘nothing’ I mean a state with no classical space and time. The cosmological wave function can be used to calculate the probability distribution for the initial configurations of the nucleating universes. Once the universe nucleated, it is expected to go through a period of inflation, which is a rapid (quasi-exponential) expansion driven by the energy of a false vacuum. The vacuum energy is eventually thermalized, inflation ends, and from then on the universe follows the standard hot cosmological scenario. Inflation is a necessary ingredient in this kind of scheme, since it gives the only way to get from the tiny nucleated universe to the large universe we live in today.

Many worlds in one

A generic prediction of inflation is that the thermalized region we inhabit is spatially infinite. Thus, it contains an infinite number of regions of the same size as our observable universe, which we shall denote as O regions. We argue that the number of possible histories which may take place inside of an O region, from the time of recombination up to the present time, is finite. Hence, there are an infinite number of O regions with identical histories up to the present, but which need not be identical in the future. Moreover, all histories which are not forbidden by conservation laws will occur in a finite fraction of all O regions. The ensemble of O regions is reminiscent of the ensemble of universes in the many-world picture of quantum mechanics. An important difference, however, is that other O regions are unquestionably real.

A measure of the multiverse

I review recent progress in defining a probability measure in the inflationary multiverse. General requirements for a satisfactory measure are formulated and recent proposals for the measure are clarified and discussed.

Solutions to the cosmological constant problems

We critically review several recent approaches to solving the two cosmological constant problems. The old problem is the discrepancy between the observed value of

A gravitational analogue of the Aharonov-Bohm effect

Lambda

Prediction and explanation in the multiverse

and the large values suggested by particle physics models. The second problem is the time coincidence between the epoch of galaxy formation

A quantum measure of the multiverse

t_G

The Very Early Universe

and the epoch of

Quantum Creation of Universes

Lambda