Cosmological Constant in the Multiverse

1. Cosmological Constant in the Multiverse Vladimir Burdyuzha Astro-Space Center, Lebedev Physical Institute, Russian Academy of Sciences, Moscow Miami-2008, December, Lago Mar

2. 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).

3. 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.

4. 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)

5. 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.

6. 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.

7. 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)

8. A vacuum component of our Universe

9. 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.

10. 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!)

11. 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.