The wave function discord

Linde's proposal of a Euclidean path integral with the ``wrong'' sign of Euclidean action is often identified with the tunneling proposal for the wave function of the universe. However, the two proposals are in fact quite different. I illustrate the difference and point out that recent criticism by Hawking and Turok does not apply to the tunneling proposal.Comment: 7 pages, 2 figure

The No-Boundary Wave Function and the Duration of the Inflationary Period

For the simplest minisuperspace model based on a homogeneous, isotropic metric and a minimally coupled scalar field we derive analytic expressions for the caustic which separates Euklidean and Minkowskian region and its breakdown value \p_*. This value represents the prediction of the no-boundary wave function for the scalar field at the beginning of inflation. We use our results to search for inflationary models which can render the no-boundary wave function consistent with the requirement of a sufficiently long inflationary period.Comment: 11 pages, TUM-HEP-206/94, 2 figures (added as uu-encoded postscript file

Scaling of cosmic string loops

We study the spectrum of loops as a part of a complete network of cosmic strings in flat spacetime. After a long transient regime, characterized by production of small loops at the scale of the initial conditions, it appears that a true scaling regime takes over. In this final regime the characteristic length of loops scales as $0.1 t$, in contrast to earlier simulations which found tiny loops. We expect the expanding-universe behavior to be qualitatively similar. The large loop sizes have important cosmological implications. In particular, the nucleosynthesis bound becomes $G\mu \lesssim 10^{-7}$, much tighter than before.Comment: Added discussion of gravitational wave bounds; other minor change

Non-linear dynamics of cosmic strings with non-scaling loops

At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions l_{min}. To understand the late time behavior we propose a very simple analytical model of strings with a non-scaling population of loops. The complicated non-linear dynamics is described by only a single parameter N ~ 2/(1-C(l_{min})) where C(l) is a correlation function of the string tangent vectors. The model predicts an appearance of two new length scales: the coherence length \xi ~ t/N^2 and the cross-correlation length \chi ~ t/N. At the onset of evolution N ~ 10 and at late times N is expected to grow logarithmically due to cosmological stretching and emission of small loops. The very late time evolution might be modified further when the gravitational back-reaction scale grows larger than l_{min}.Comment: 5 pages, minor corrections, accepted for publication in Physical Review

Ultra high energy neutrinos from hidden-sector topological defects

We study Topological Defects (TD) in hidden (mirror) matter as possible sources of ultra-high energy neutrinos. The hidden/mirror and ordinary matter are assumed to interact very weakly through gravity or superheavy particles. An inflationary scenario is outlined in which superheavy defects are formed in hidden/mirror matter (and not in ordinary matter), and at the same time the density of mirror matter produced at the end of inflation is much smaller than that of ordinary matter. Superheavy particles produced by hidden-sector TD and the products of their decays are all sterile in our world. Only mirror neutrinos oscillate into ordinary neutrinos. We show that oscillations with maximal mixing of neutrinos from both worlds are possible and that values of $\Delta m^2$, needed for for solution of solar-neutrino and atmospheric-neutrino problems, allow the oscillation of ultra-high energy neutrinos on a timescale of the age of the Universe. A model of mass-degenerate visible and mirror neutrinos with maximal mixing is constructed. Constraints on UHE neutrino fluxes are obtained. The estimated fluxes can be 3 orders of magnitude higher than those from ordinary matter. Detection of these fluxes is briefly discussed.Comment: Revtex, 31 page

WKB Wave Functions with the Induced Gravity Theory

The Wheeler-DeWitt equation for the induced gravity theory is constructed in the minisuperspace approximation, and then solved using the WKB method under three types of boundary condition proposed respectively by Hartle & Hawking (``no boundary''), Linde and Vilenkin (``tunneling from nothing''). It is found that no matter how the gravitational and cosmological ``constants'' vary in the classical models, they will acquire constant values when the universe comes from quantum creation, and that, in particular, the resulting tunneling wave function under the Linde or Vilenkin boundary condition reaches its maximum value if the cosmological constant vanishes.Comment: 10 pages, no figure, LaTex fil

Iso-curvature fluctuations through axion trapping by cosmic string wakes

We consider wake-like density fluctuations produced by cosmic strings at the quark-hadron transition in the early universe. We show that low momentum axions which are produced through the radiation from the axionic string at an earlier stage, may get trapped inside these wakes due to delayed hadronization in these overdense regions. As the interfaces, bordering the wakes, collapse, the axions pick-up momentum from the walls and finally leave the wake regions. These axions thus can produce large scale iso-curvature fluctuations. We have calculated the detailed profile of these axionic density fluctuations and discuss its astrophysical consequences.Comment: 23 pages, 4 figures, RevTe

Schroedinger Wheeler-DeWitt Equation In Multidimensional Cosmology

We study multidimensional cosmology to obtain the wavefunction of the universe using wormhole dominance proposal. Using a prescription for time we obtain the Schroedinger-Wheeler-DeWitt equation without any reference to WD equation and WKB ansatz for WD wavefunction. It is found that the Hartle-Hawking or wormhole-dominated boundary conditions serve as a seed for inflation as well as for Gaussian type ansatz to Schroedinger-Wheeler-DeWitt equation.Comment: 10 Pages, LaTeX, no figur

Effects of friction on cosmic strings

We study the evolution of cosmic strings taking into account the frictional force due to the surrounding radiation. We consider small perturbations on straight strings, oscillation of circular loops and small perturbations on circular loops. For straight strings, friction exponentially suppresses perturbations whose co-moving scale crosses the horizon before cosmological time $t_*\sim \mu^{-2}$ (in Planck units), where $\mu$ is the string tension. Loops with size much smaller than $t_*$ will be approximately circular at the time when they start the relativistic collapse. We investigate the possibility that such loops will form black holes. We find that the number of black holes which are formed through this process is well bellow present observational limits, so this does not give any lower or upper bounds on $\mu$. We also consider the case of straight strings attached to walls and circular holes that can spontaneously nucleate on metastable domain walls.Comment: 32 pages, TUTP-93-

Tunneling in quantum cosmology: numerical study of particle creation

We consider a minisuperspace model for a closed universe with small and positive cosmological constant, filled with a massive scalar field conformally coupled to gravity. In the quantum version of this model, the universe may undergo a tunneling transition through an effective barrier between regions of small and large scale factor. We solve numerically the minisuperspace Wheeler--De Witt equation with tunneling boundary conditions for the wave function of the universe, and find that tunneling in quantum cosmology is quite different from that in quantum mechanics. Namely, the matter degree of freedom gets excited under the barrier, provided its interaction with the scale factor is not too weak, and makes a strong back reaction onto tunneling. In the semiclassical limit of small values of cosmological constant, the matter energy behind the barrier is close to the height of the barrier: the system ``climbs up'' the barrier, and then evolves classically from its top. These features are even more pronounced for inhomogeneous modes of matter field. Extrapolating to field theory we thus argue that high momentum particles are copiously created in the tunneling process. Nevertheless, we find empirical evidence for the semiclassical-type scaling with the cosmological constant of the wave function under and behind the barrier.Comment: 29 pages, 17 figure