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Register a new userProbabilities in the Bousso-Polchinski multiverse
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Added by
Delia Schwartz-Perlov
Publication date
2006
fields
Physics
and research's language is
English
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Using the recently introduced method to calculate bubble abundances in an eternally inflating spacetime, we investigate the volume distribution for the cosmological constant $Lambda$ in the context of the Bousso-Polchinski landscape model. We find that the resulting distribution has a staggered appearance which is in sharp contrast to the heuristically expected flat distribution. Previous successful predictions for the observed value of $Lambda$ have hinged on the assumption of a flat volume distribution. To reconcile our staggered distribution with observations for $Lambda$, the BP model would have to produce a huge number of vacua in the anthropic range $DeltaLambda_A$ of $Lambda$, so that the distribution could conceivably become smooth after averaging over some suitable scale $deltaLambdallDeltaLambda_A$.
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We investigate the phenomenology of the Watcher measure in the Bousso-Polchinski landscape. We study a small toy landscape analytically. The results are sufficient to allow us to extrapolate watcher phenomenology to much larger landscapes. We compare our results to other measures which have been applied to BP landscapes containing googles of vacua. Under certain well motivated conditions, watcher phenomenology coincides with the causal patch prescription, but not Lindes volume weighted measure.
Predictions in an eternally inflating multiverse are meaningless unless we specify the probability measure. The scale-factor cutoff is perhaps the simplest and most successful measure which avoid catastrophic problems such as the youngness paradox, runaway problem, and Boltzmann brain problem, but it is not well defined in contracting regions with a negative cosmological constant. In this paper, we propose a new measure with properties similar to the scale-factor cutoff which is well defined everywhere. The measure is defined by a cutoff in the 4-volume spanned by infinitesimal comoving neighborhoods in a congruence of timelike geodesics. The probability distributions for the cosmological constant and for the curvature parameter in this measure are similar to those for the scale factor cutoff and are in a good agreement with observations.
To make predictions for an eternally inflating multiverse, one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by Boltzmann brains - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.
Topology-changing transitions between vacua of different effective dimensionality are studied in the context of a 6-dimensional Einstein-Maxwell theory. The landscape of this theory includes a $6d$ de Sitter vacuum ($dS_6$), a number of $dS_4 times S_2$ and $AdS_4 times S_2$ vacua, and a number of $AdS_2 times S_4$ vacua. We find that compactification transitions $dS_6 to AdS_2 times S_4$ occur through the nucleation of electrically charged black hole pairs, and transitions from $dS_6$ to $dS_4 times S_2$ and $AdS_4 times S_2$ occur through the nucleation of magnetically charged spherical black branes. We identify the appropriate instantons and describe the spacetime structure resulting from brane nucleation.
We study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS$_2$ metric becomes a solution of a deformed AP model. In particular, the dilaton potential is deformed from a simple quadratic form to a hyperbolic function-type potential similarly to integrable deformations. A specific solution is a deformed black hole solution. Because the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears, the holographic interpretation is far from trivial. The Hawking temperature is the same as the undeformed case but the Bekenstein-Hawking entropy is modified due to the deformation. This entropy can also be reproduced by evaluating the renormalized stress tensor with an appropriate counter term on the regularized screen close to the singularity.
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