High-Energy Astrophysics American and Soviet Perspectives/Proceedings from the U.S.-U.S.S.R. Workshop on High-Energy Astrophysics (1991) / Chapter Skim
Currently Skimming:
CAN A MAN-MADE UNIVERSE BE ACHIEVED BY QUANTUM TUNNELING WITHOUT AN INITIAL SINGULARITY?
CAN A MAN-MADE UNIVERSE BE ACHIEVED BY QUANTUM TUNNELING WITHOUT AN INITIAL SINGULARITY?
Pages 153-173
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 153... ...
ALAN H GUTH Massachusetts Institute of Technology and Harvard~mithsonian Center for Astrophysics ABSTRACT Essentially all modern particle theories suggest the possible existence of a false vacuum state-a metastable state with an energy density that cannot be lowered except by means of a very slow phase transition.
|
From page 154... ...
The mass Is much larger than the present mass of the visible universe, because most of the energy is lost to gravitational potential energy as the universe expands. W~ the advent of grand unified theories (GUTS and inflationary cosmology, however, a much simpler recipe for a universe can now be formulated.
|
From page 155... ...
particle theory contains a scalar field ~ with a potential energr density similar to that shown in Figure 1. The state ~ = ¢' is the state of minimum energy density, and therefore is the true vacuum.
|
From page 156... ...
The net effect is to create a huge gravitational repulsion, causing the universe to go into a period of exponential expansion. TlIE NEW INFLATIONARY UNIVERSE While the original form of the inflationary universe model (Gush 1981)
|
From page 157... ...
The piston chamber is filled with false vacuum, and is surrounded by true vacuum. When the piston is pulled out the energy density remains constant, so the additional energy must be furnished Or the force needed to pull the piston against the negative pressure of the false vacuum.
|
From page 158... ...
For typical grand unified theory numbers, this enormous expansion requires only about 10-32 see of inflation. During this inflationary penod, the density of any particles that may have been present before inflation is diluted so much that it becomes completely negligible.
|
From page 159... ...
by introducing a scalar field potential with a flat plateau, as was shown in Figure 1. This leads to a "slow-rollover" phase transition, in which quantum fluctuations destabilize the false vacuum, starting the scalar field to roll down the hill of the potential energy diagram.
|
From page 160... ...
This success of inflation, however, occurs only at a pnce: for the magnitude of the density fluctuations to turn out correctly, the scalar field that drives inflation must be coupled incredibly wealOy. For a simple A¢4 meow, for example, me value of ~ must be about 10-~2.
|
From page 161... ...
If the region of false vacuum is large enough, one expects that it would undergo inflation. An observer in the outside true vacuum region, on the other hand, would see the false vacuum region as a region of negative pressure.
|
From page 162... ...
The energy of the fictitious particle is related to the mass of the physical false vacuum bubble. As can be seen in the potential energy diagram, there are three lauds of solutions.
|
From page 163... ...
For small values of the surface energy density (a << /, this critical mass is given simply by Mcr = 41rX_3 where X is the rate of the exponential expansion tie., scale factor oc expects ) , which is related to the false vacuum energy density pf by X 3 Pf ~ For typical GUT parameters, MCr ~ 10 kg.
|
From page 164... ...
the exponential expansion of the false vacuum region, which occurs as one moves upward and to the left in the diagram, is completely hidden by the distortion of the metric. The physical meaning of a spacetime diagram of this type can be seen most clearly by examining a sequence of equal-time slices.
|
From page 165... ...
~ summarize, the false vacuum bubble appears from the outside to be a black hole. From me inside, however, it appears lo be an inflating region of false vacuum, with new space being created as the region expands.
|
From page 166... ...
The reason stems from the intrinsic nonuniformity, on very large scales, of the decay of the false vacuum (Aryal and Vilenldn, 1987~. This process occurs exponentially, lye most other decay processes, but for inflation to be successful the parameters must be arranged so that the ~ I have studied a simplified but exactly soluble model of a slow-rot/over phase transition with S.-Y.
|
From page 167... ...
Although an initial singulantr is often hypothesized to have been present at the big bang, there do not appear to be any initial singularities available today. So we ask whether it is possible to intervene in some way, to modify the early stages of this picture, so that an inflationary universe could be produced without an initial singularity.
|
From page 168... ...
Since the bubble is not expanding rapidly, the Penrose theorem does not preclude its production by classical processes, without an initial singularity. We have not explored in detail the mechanisms by which such a region might be created, but presumably it could be created either by supercooling from high temperatures or perhaps by compressing a gas of fermions that couple to the scalar field.
|
From page 169... ...
We have used our definition of the action to estimate the tunneling amplitude as a function of the various parameters in the problem, and we have found that it behaves very reasonably: the tunneling action decreases monotonically to zero as the bubble mass M approaches the critical mass MCr at which tunneling would not be necessary, and it diverges monotonically as the gravitational constant G ~ O The action is negative definite by the standard sign conventions, but we argue that, regardless of the sign of the action, the tunneling probability is always exponentially suppressed.
|
From page 170... ...
, as long as Gcr2 Is smaller than or comparable to pf' and M is not too near Mu. For typical grand unified theory parameters, this would give an outrageously small tunneling probability, such as 10-~° .
|
From page 171... ...
o A new universe can in principle be created in a hypothetical laboratory, without an initial singularity, by a process of quantum tunneling. Work in these areas is continuing, and we hope to get a better idea of what exactly is needed in order to create an inflationary universe.
|
From page 172... ...
1m. Quantum Nucleation of False Vacuum Bubbled Physical Review D 41: 2638-2645.
|
From page 173... ...
Physics Lettem 108B: 103-107. Starobinsky, ~ A 198Z Dynamics of Phase Transition in the New Inflationary Universe Scenario and Generation of Perturbations.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.