The initial conditions of the universe: how much isocurvature is allowed?

We investigate the constraints imposed by the current data on correlated mixtures of adiabatic and non-adiabatic primordial perturbations. We discover subtle flat directions in parameter space that tolerate large (~60%) contributions of non-adiabatic fluctuations. In particular, larger values of the baryon density and a spectral tilt are allowed. The cancellations in the degenerate directions are explored and the role of priors elucidated.Comment: 4 pages, 4 figures. Submitted to PR

Open inflation and the singular boundary

The singularity in Hawking and Turok's model (hep-th/9802030) of open inflation has some appealing properties. We suggest that this singularity should be regularized with matter. The singular instanton can then be obtained as the limit of a family of ``no-boundary'' solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking boundary term. Unrelated to this question, we also point out that gravitational backreaction improves the behaviour of scalar perturbations near the singularity. As a result, the problem of quantizing scalar perturbations and gravity waves seems to be very well posed.Comment: 7 page

Constraints on isocurvature models from the WMAP first-year data

We investigate the constraints imposed by the first-year WMAP CMB data extended to higher multipole by data from ACBAR, BOOMERANG, CBI and the VSA and by the LSS data from the 2dF galaxy redshift survey on the possible amplitude of primordial isocurvature modes. A flat universe with CDM and Lambda is assumed, and the baryon, CDM (CI), and neutrino density (NID) and velocity (NIV) isocurvature modes are considered. Constraints on the allowed isocurvature contributions are established from the data for various combinations of the adiabatic mode and one, two, and three isocurvature modes, with intermode cross-correlations allowed. Since baryon and CDM isocurvature are observationally virtually indistinguishable, these modes are not considered separately. We find that when just a single isocurvature mode is added, the present data allows an isocurvature fraction as large as 13+-6, 7+-4, and 13+-7 percent for adiabatic plus the CI, NID, and NIV modes, respectively. When two isocurvature modes plus the adiabatic mode and cross-correlations are allowed, these percentages rise to 47+-16, 34+-12, and 44+-12 for the combinations CI+NID, CI+NIV, and NID+NIV, respectively. Finally, when all three isocurvature modes and cross-correlations are allowed, the admissible isocurvature fraction rises to 57+-9 per cent. The sensitivity of the results to the choice of prior probability distribution is examined.Comment: 20 pages, 24 figures. Submitted to PR

A prescription for probabilities in eternal inflation

Some of the parameters we call ``constants of Nature'' may in fact be variables related to the local values of some dynamical fields. During inflation, these variables are randomized by quantum fluctuations. In cases when the variable in question (call it $\chi$) takes values in a continuous range, all thermalized regions in the universe are statistically equivalent, and a gauge invariant procedure for calculating the probability distribution for $\chi$ is known. This is the so-called ``spherical cutoff method''. In order to find the probability distribution for $\chi$ it suffices to consider a large spherical patch in a single thermalized region. Here, we generalize this method to the case when the range of $\chi$ is discontinuous and there are several different types of thermalized region. We first formulate a set of requirements that any such generalization should satisfy, and then introduce a prescription that meets all the requirements. We finally apply this prescription to calculate the relative probability for different bubble universes in the open inflation scenario.Comment: 15 pages, 5 figure