No Boundary Wave Function of the Universe
Predictions (cont'd)
Quantum Transitions Between Classical Histories: Bouncing Cosmologies [151]
(with T. Hertog) In a quantum theory of gravity spacetime geometry behaves classically when the quantum probababilities are high for histories of geometry that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This perspective on classicality has the following general consequences: (a) Classical histories of geometry and field are generally available only in limited patches of the configuration space on which the wave function lives. (b) In a given patch states generally predict an ensemble of possible classical histories with probabilities for the individual histories in the ensemble. (c) In between patches classical predictability breaks down and is replaced by quantum evolution connecting classical histories in different patches. (d) Classical predictability can break down on scales well below the Planck scale, and with no breakdown in the classical equations of motion. We support these conclusions by using a simple minisuperspace model to analyze the predictions of the no-boundary quantum state for bouncing classical histories --- histories that contract from a large size to a minimum radius and then reexpand to again become large. We find that classicality can break down near the bounce even when its size is much larger than the Planck length. There are ensembles of classical histories on either side of the bounce which are related by time symmetry. The evolution of the quantum state through the bounce supplies quantum probabilities for how a classical history on one side transitions to another on the opposite side. We describe how (a)-(d) could affect our understanding of black hole evaporation.
Arrows of Time in the Bouncing Universes of the No-Boundary Quantum State [147]
(with T. Hertog) We derive the arrows of time of our universe that follow from the NBWF in a minisuperspace model. Arrows of time are viewed four-dimensionally as properties of the four-dimensional Lorentzian histories of the universe. Probabilities for these histories are predicted by the NBWF. For histories with a regular `bounce' at a minimum radius we find that fluctuations are small at the bounce and grow in the direction of expansion on either side. The arrow of time defined by the growth in fluctuations points in one direction over the whole of a recollapsing spacetime but is bidirectional in a bouncing spacetime. We argue that the electromagnetic, thermodynamic, and psychological arrows of time are aligned with the fluctuation arrow. The implications of a bidirectional arrow of time for causality are discussed.
Accelerated Expansion from Negative Lambda [154]
Quantum Probabilities for Inflation from Holography [153]
Vector Fields in Holographic Cosmology [151]
(with S.W. Hawking and T. Hertog) The evolution of the universe is determined by its quantum state. The wave function of the universe obeys the constraints of general relativity and in particular the Wheeler-DeWitt equation (WDWE). For non-zero Lambda of either sign, we show that solutions of the WDWE at large volume have two domains in which geometries and fields are asymptotically real. In one the histories are Euclidean asymptotically anti-de Sitter, in the other they are Lorentzian asymptotically classical de Sitter. A cosequence of this asymptotic structure is that even theories with a negative cosmological constand can predict our observations of an inflating universe. Further, the asymptotic structure of solutions of the WDWE implies that the leading order in \hbar quantum probabilities for classical, asymptotically de Sitter histories can be obtained from the action of asymptotically anti-de Sitter configurations. This leads to a promising universal connection between quantum cosmology and holography. The first two papers above describe similar models from different starting points. The third extends the results to Maxwell fields.
Anthropic Bounds on Lambda from the No-Boundary Quantum State [152]
(with T. Hertog) We show that anthropic selection emerges inevitably in the general framework for prediction in quantum cosmology. There the predictions of anthropic reasoning depend on the prior implied by the universe's quantum state. To illustrate this we compute the probabilities specified by the no-boundary wave function for our observations at the present time of the values of Lambda and Q in an inflationary landscape model in which both quantities vary. Within the anthropic range of values the no-boundary state yields an approximately flat distribution on Lambda and strongly favors small values of Q. This restores Weinberg's successful prediction of Lambda.
Real Tunneling Geometries [90]
(with G.W. Gibbons) This paper examines the predictions of the "no boundary" initial condition for the present large-scale topology and geometry. Finite-action real tunneling solutions of Einstein consist of Euclidean geometries joined to a Lorentzian l geometry across a spacelike surface of vanishing extrinsic curvature. The classification of such solutions is discussed and general constraints on their topology derived. For example, it is shown that, if the Euclidean Ricci tensor is positive, then a real tunneling solution can nucleate only a single connected Lorentzian spacetime (the unique conception theorem). Explicit examples of real tunneling solutions driven by a cosmological constant are exhibited and their implications for cosmic baldness described. It is argued that the most probable spacetime predicted by the real tunneling solutions of the NBWF has the topology RxS3 with the deSitter metric.
Number of Time Dimensions [timedim]
An excerpt giving a simple argument why the classical spacetimes predicted by the No-Boundary quantum state can have no more than one time-dimension.
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