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Zenith Grant Awardee

Dr. Alexander Vilenkin

Tufts University


Jaume Garriga, <i>Universitat de Baecelona</i><br>Vitaly Vanchurin, <i>Tufts University</i>

Project Title

Probabilities in the Landscape

Project Summary

Models of cosmic inflation, combined with recent developments in string theory, point to a new cosmological paradigm, where distant parts of the universe have diverse properties and different particle physics. Inflationary scenarios, which explain the observed homogeneity of the universe, predict that on very large scales the universe is very inhomogeneous, with vast regions still in the state of exponential inflationary expansion, and "normal" regions like ours constantly being formed. The cosmological and particle physics parameters, such as the dark energy density or elementary particle masses, may have different values in different parts of such an eternally inflating universe. These variable parameters cannot be predicted with certainty, and one can only hope to determine their probability distributions. The proposed research will focus on the conceptual and technical problems that have been encountered in the calculation of probabilities in the eternally inflating universe. We shall also consider applications of the general theory to specific observables, such as the dark energy and dark matter densities, the magnitude of density fluctuations that seeded the structure formation in the universe, and the neutrino masses.

Technical Abstract

String theory appears to admit a multitude of vacua with different values of the effective constants of nature. In combination with inflationary dynamics, this results in a ?Multiverse? where the entire landscape of vacua is explored. How are the different vacua distributed in the Multiverse? And what are the probabilities for us to observe given values of the constants? These fundamental questions are the target of the present proposal.

The characterization of the distribution of vacua faces conceptual and technical difficulties. The volume of all types of regions in the inflationary multiverse is infinite, and a regularization prescription is needed for determining volume fractions in different vacua. Recently, we proposed a regularization, which is independent of gauge and of initial conditions. The uniqueness of this proposal should be investigated further. Moreover, new analytical and numerical tools should be developed to describe the complicated dynamics of eternal inflation. The calculation of probabilities for observations requires also the investigation of selection effects, and the comparison of ?alternate universes? with different low energy constants. We will also consider application to specific observables, such as the amplitude of density perturbations, the dark matter mass per photon, neutrino masses, and the cosmological constant.

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