Cosmological Constant in
the Multiverse
Vladimir Burdyuzha
Astro-Space Center, Lebedev Physical Institute,
Russian Academy of Sciences, Moscow
Miami-2008, December, Lago Mar
Which are scenario for the
Multiverse
1.A.Linde and A.Vilenkin proposed computer
models of eternal inflation in which uni-verses
from separate “big bangs” widened in
disconnection regions of space-time.
2.Universes may produce inside black holes
putting out shoots and expanding in a new
region of space-time (A.Guth, L.Smolin).
3. Other universes may exists in additional
space measures (L. Randall, R.Sundrum).
Which is scenario for the Multiverse
The present understanding of inflationary
cosmology suggests that our Universe is one
among an infinite numbers of“pockets” in an
eternally inflating multiverse.
A new cosmological paradigm
Accordingly to the new cosmological paradigm
the multiverse is an eternally growing fractal
consisting of infinitely many exponentially
large parts with different coupling constants,
particles masses, the effective cosmological
constant and other constants of nature. These
parts were called mini-universes (A.Linde,
A.Vilenkin) or “pocket universes” (A.Guth)
The Multiverse
The general structure of the multiverse is naturally
extremely complicated one cannot describe the
growing fractal in the simplest terms. Fortunately,
inflation makes each part of the multiverse locally
homogeneous and practically independent of each
other. The fundamental theory admits a wide range of
possible values of the “constants of nature” and
geometries and naturally we can only hope to obtain
the probability of observing a local part of
multiverse with a given set of properties.
Our Universe
It is natural to assume that our Universe is located in a
random place of the multiverse and that some
probability distribution exists for the typically
observed values of the cosmological parameters.
Predicting which physics we should expect to observe
within our region of such multiverse is a major
challenge for theoretical physics. The attempt to build
a calculus for such predictions is complicated in part
by the need to regulate the diverging space time
volume of the mutiverse. A number of different
approaches were made.
A vacuum component
Each of these pockets contains an infinite
nearly homogeneous and isotropic universe.
The fundamental theory admits a landscape of
metastable vacua each may be characterized
by different physical parameters (A.Guth, A.
Vilenkin, 2008)
A vacuum component of our
Universe
The vacuum component of our
Universe
Before T ~150 MeV in our Universe the
vacuum component is changed by jumps
since in it density energy carried a negative
contributions condensates of quantum fields
(the Universe lost symmetry). After 150 MeV
the vacuum component hardened (the last
quark-gluon phase transition) and it became
cosmological constant.
That may select a universe from
cosmological landscape
V. Kozlov and I.Volovich (2006) showed that
solution of the Klein-Gordon equation on
Friedmann type manifold with finite action
exists. These solutions have a discrete mass
spectrum and they could select a universe from
cosmological landscape. Therefore, the
anthropic principle may be added this
mathematical assertion (it may be necessity!)
A wave function of H. Everett
Introduction of an universal wave function of
H. Everett as we suggest allows to discuss
vacuum components of the multiverse. At first
we identify these components with Wheeler
space-time foam. During time branches of the
Everett wave function will become
independent ones and then they will become
classical realities.