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Landscape Predictions from Cosmological Vacuum Selection
Raphael Bousso and I-Sheng Yang*
Department of Physics and Center for Theoretical Physics
University of California, Berkeley, CA 94720, U.S.A.
and
Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, U.S.A.
In BP models with hundreds of fluxes, we compute the effects of cosmological dynamics on the
probability distribution of landscape vacua. Starting from generic initial conditions, we find that
most fluxes are dynamically driven into a different and much narrower range of values than expected
from landscape statistics alone. Hence, cosmological evolution will access only a tiny fraction of
the vacua with small cosmological constant. This leads to a host of sharp predictions. Unlike
other approaches to eternal inflation, the holographic measure employed here does not lead to
"staggering", an excessive spread of probabilities that would doom the string landscape as a solution
to the cosmological constant problem.I. INTRODUCTION
The task of making predictions in the landscape of
string theory represents an enormous challenge. We must
survey the metastable vacua in the theory and find the
relative abundance of various low-energy properties. But
vacua without observers will not be observed. The great
variability of low energy physics in the string landscape
demands novel methods for capturing such selection ef-
fects.
Interposed between these two tasks is a third problem,
which will be the focus of this paper: vacuum selection
by cosmological dynamics. It is not enough for a vacuum
to exist in theory. It will be relevant only if it can be dy-
namically realized from generic initial conditions, either
as regions in spacetime or branches of a wavefunction.
The former viewpoint insists on treating spacetime
semiclassically on a global scale. This has no operational
meaning, since no observer can see beyond his own hori-
zon [1]. Moreover, it leads to problematic infinities and
ambiguities that have plagued the definition of measures
in eternal inflation; see, e.g., Refs. [2, 3, 4, 5, 6, 7, 8]
for discussions and some recent proposals. Thus, the
global viewpoint seems poised to suffer the same fate as
the ether: a false convenience increasingly recognized as
a burden. (A similar conclusion was reached earlier by
studying quantum aspects of black holes [9, 10], and it
seems natural indeed that it should extend to cosmology.)
One of us recently proposed a "holographic" mea-
sure [7] that refers only to a single causally connected
region, or causal diamond. In Ref. [11], it was shown that
this measure not only overcomes problems that plagued
anthropic predictions of the cosmological constant, but
is able to maintain this success when specific anthropic
conditions are traded for the much weaker assumption
that observers require merely free energy.*bousso@lbl.gov, jingking@berkeley.edu
Here we apply a different aspect of the proposal of
Ref. [7]. We focus not on anthropic selection, but on
cosmological selection. We shall find that dynamical ef-
fects can significantly suppress or enhance the probabil-
ity of observing a given vacuum, and they can interfere
with anthropic selection in some models. However, unlike
another recently proposed measure [5], the holographic
measure does not lead to excessively uneven probabil-
ity distributions that would render the string landscape
ineffective at solving the cosmological constant problem.
We will follow Ref. [12] in modelling the string land-
scape as arising from a large number of possible four-form
flux configurations. We mainly consider a model with
250 fluxes, with fixed charges of order 1/30. This yields
a large number of metastable vacua, of which 10121 have
vacuum energy comparable to the observed value. Of
these, however, we find that only 1080 are accessed by a
typical worldline, starting from generic initial conditions.
The selected ensemble is characterized by 250 probabil-
ity distributions over the integers, one for each flux. The
distributions differ in many cases, drastically from the
distributions one would have obtained by simply restrict-
ing the landscape to vacua with small cosmological con-
stant. Thus, cosmological selection leads to thousands
of distinct predictions. Many correspond to probabilities
that are so close to 0 or 1 that even a single conflicting
observation would rule out the model.
The specific predictions we obtain apply only to the toy
model we study, but they do allow us to draw more gen-
eral lessons. Most importantly, our results demonstrate
that cosmological dynamics can be a powerful constraint.
It reduces the effective size of the landscape drastically,
leading to a large number of strong predictions. Another
general lesson is that fast decays happen first. In natu-
ral models, it takes hundreds or thousands of tunneling
events to get from a generic initial vacuum to a vacuum
with observers. Any metastable internal configuration
that gives rise to a relatively fast decay channel but is
unlikely to arise late in the decay chain will not be ob-
served.
In the real string landscape, the selection effects will
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Bousso, Raphael; Bousso, Raphael & Yang, Sheng. Landscape predictions from cosmological vacuum selection, article, April 23, 2007; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc893822/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.