The successful anthropic prediction of the cosmological constant depends crucially on the assumption of a flat prior distribution. However, previous calculations in simplified landscape models showed that the prior distribution is staggered, suggesti
ng a conflict with anthropic predictions. Here we analytically calculate the full distribution, including the prior and anthropic selection effects, in a toy landscape model with a realistic number of vacua, $N sim 10^{500}$. We show that it is possible for the fractal prior distribution we find to behave as an effectively flat distribution in a wide class of landscapes, depending on the regime of parameter space. Whether or not this possibility is realized depends on presently unknown details of the landscape.
Charge carriers moving at the speed of light along a straight, superconducting cosmic string carry with them a logarithmically divergent slab of electromagnetic field energy. Thus no finite local input can induce a current that travels unimpeded to i
nfinity. Rather, electromagnetic back-reaction must damp this current asymptotically to nothing. We compute this back-reaction and find that the electromagnetic fields and currents decline exactly as rapidly as necessary to prevent a divergence. We briefly discuss the corresponding gravitational situation.
Using recent simulation results, we provide the mass and speed spectrum of cosmic string loops. This is the quantity of primary interest for many phenomenological signatures of cosmic strings, and it can be accurately predicted using recently acquire
d detailed knowledge of the loop production function. We emphasize that gravitational smoothing of long strings does not play any role in determining the total number of existing loops. We derive a bound on the string tension imposed by recent constraints on the stochastic gravitational wave background from pulsar timing arrays, finding $Gmu leq 2.8times 10^{-9}$. We also provide a derivation of the Boltzmann equation for cosmic string loops in the language of differential forms.
Core-collapse supernovae emit on the order of 3x10^53 ergs in high-energy neutrinos over a time of order 10 seconds, and so decrease their mass by about 0.2 solar mass. If the explosion is nearly spherically symmetric, there will be little gravitatio
nal wave emission. Nevertheless, the sudden decrease of mass of the progenitor may cause a change in the gravitational time delay of signals from a nearby pulsar. We calculate the change in arrival times as successive pulses pass through the neutrino shell at different times, and find that the effect may be detectable in ideal circumstances.
Anthropic reasoning is a critical tool to understand probabilities, especially in a large universe or multiverse. According to anthropic reasoning, we should consider ourselves typical among members of a reference class that must include all subjecti
vely indistinguishable observers. We discuss here whether such a reference class, which we assume must include computer simulations, must also include computers that replay previous simulations, magnetic tapes that store but do not run the simulation, and even abstract mathematical functions. We do not see any clear criterion for excluding these anomalous observers, but their presence is deeply troubling to the idea of anthropic reasoning.
An eternally inflating universe produces an infinite amount of spatial volume, so every possible event happens an infinite number of times, and it is impossible to define probabilities in terms of frequencies. This problem is usually addressed by mea
ns of a measure, which regulates the infinities and produces meaningful predictions. I argue that any measure should obey certain general axioms, but then give a simple toy model in which one can prove that no measure obeying the axioms exists. In certain cases of eternal inflation there are measures that obey the axioms, but all such measures appear to be unacceptable for other reasons. Thus the problem of defining sensible probabilities in eternal inflation seems not be solved.
Using a new parallel computing technique, we have run the largest cosmic string simulations ever performed. Our results confirm the existence of a long transient period where a non-scaling distribution of small loops is produced at lengths depending
on the initial correlation scale. As time passes, this initial population gives way to the true scaling regime, where loops of size approximately equal to one-twentieth the horizon distance become a significant component. We observe similar behavior in matter and radiation eras, as well as in flat space. In the matter era, the scaling population of large loops becomes the dominant component; we expect this to eventually happen in the other eras as well.
