Energy conditions allow eternal inflation

Eternal inflation requires upward fluctuations of the energy in a Hubble volume, which appear to violate the energy conditions. In particular, a scalar field in an inflating spacetime should obey the averaged null energy condition, which seems to rule out eternal inflation. Here we show how eternal inflation is possible when energy conditions (even the null energy condition) are obeyed. The critical point is that energy conditions restrict the evolution of any single quantum state, while the process of eternal inflation involves repeatedly selecting a subsector of the previous state, so there is no single state where the conditions are violated. </p

Cosmic String Cusps with Small-Scale Structure: Their Forms and Gravitational Waveforms

We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties of the small-scale structure. We further argue that the presence of structure at cusps under most circumstances leads to the formation of loops at the size of the smallest scales. On the other hand we show that the gravitational waveform of a cusp remains generally unchanged; the primary effect of small-scale structure is to smooth out the sharp waveform emitted in the direction of cusp motion.Comment: RevTeX, 8 pages. Replaced with version accepted for publication by PR

Spatially Averaged Quantum Inequalities Do Not Exist in Four-Dimensional Spacetime

We construct a particular class of quantum states for a massless, minimally coupled free scalar field which are of the form of a superposition of the vacuum and multi-mode two-particle states. These states can exhibit local negative energy densities. Furthermore, they can produce an arbitrarily large amount of negative energy in a given region of space at a fixed time. This class of states thus provides an explicit counterexample to the existence of a spatially averaged quantum inequality in four-dimensional spacetime.Comment: 13 pages, 1 figure, minor corrections and added comment

Induced vacuum energy-momentum tensor in the background of a d-2 - brane in d+1 - dimensional space-time

Charged scalar field is quantized in the background of a static d-2 - brane which is a core of the magnetic flux lines in flat d+1 - dimensional space-time. We find that vector potential of the magnetic core induces the energy-momentum tensor in the vacuum. The tensor components are periodic functions of the brane flux and holomorphic functions of space dimension. The dependence on the distance from the brane and on the coupling to the space-time curvature scalar is comprehensively analysed.Comment: 32 pages, 3 figures, journal version, some references adde

Quantum interest in two dimensions

The quantum interest conjecture of Ford and Roman asserts that any negative-energy pulse must necessarily be followed by an over-compensating positive-energy one within a certain maximum time delay. Furthermore, the minimum amount of over-compensation increases with the separation between the pulses. In this paper, we first study the case of a negative-energy square pulse followed by a positive-energy one for a minimally coupled, massless scalar field in two-dimensional Minkowski space. We obtain explicit expressions for the maximum time delay and the amount of over-compensation needed, using a previously developed eigenvalue approach. These results are then used to give a proof of the quantum interest conjecture for massless scalar fields in two dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR

Scaling in Numerical Simulations of Domain Walls

We study the evolution of domain wall networks appearing after phase transitions in the early Universe. They exhibit interesting dynamical scaling behaviour which is not yet well understood, and are also simple models for the more phenomenologically acceptable string networks. We have run numerical simulations in two- and three-dimensional lattices of sizes up to 4096^3. The theoretically predicted scaling solution for the wall area density A ~ 1/t is supported by the simulation results, while no evidence of a logarithmic correction reported in previous studies could be found. The energy loss mechanism appears to be direct radiation, rather than the formation and collapse of closed loops or spheres. We discuss the implications for the evolution of string networks.Comment: 7pp RevTeX, 9 eps files (including six 220kB ones

Quantum energy inequalities and local covariance II: Categorical formulation

We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated.Comment: 27 pages, LaTeX. Further discussion added. Version to appear in General Relativity and Gravitatio

Cosmic F- and D-strings

Macroscopic fundamental and Dirichlet strings have several potential instabilities: breakage, tachyon decays, and confinement by axion domain walls. We investigate the conditions under which metastable strings can exist, and we find that such strings are present in many models. There are various possibilities, the most notable being a network of (p,q) strings. Cosmic strings give a potentially large window into string physics.Comment: 27 pages, 5 figures; v. 5: JHEP style, added comments in section 2.

An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning

An anthropic principle has made it possible to answer the difficult question of why the observable value of cosmological constant ($\Lambda\sim 10^{-47}$ GeV${}^4$) is so disconcertingly tiny compared to predicted value of vacuum energy density $\rho_{SUSY}\sim 10^{12}$ GeV${}^4$. Unfortunately, there is a darker side to this argument, as it consequently leads to another absurd prediction: that the probability to observe the value $\Lambda=0$ for randomly selected observer exactly equals to 1. We'll call this controversy an infrared divergence problem. It is shown that the IRD prediction can be avoided with the help of a Linde-Vanchurin {\em singular runaway measure} coupled with the calculation of relative Bayesian probabilities by the means of the {\em doomsday argument}. Moreover, it is shown that while the IRD problem occurs for the {\em prediction stage} of value of $\Lambda$, it disappears at the {\em explanatory stage} when $\Lambda$ has already been measured by the observer.Comment: 9 pages, RevTe

The circular loop equation of a cosmic string with time-varying tension in de Sitter spacetimes

In this work the equation of circular loops of cosmic string possessing time-dependent tension is studied in the de Sitter spacetime. We find that the cosmic string loops with initial radius $r(t_{0})>0.707L$, L de Sitter radius, should not collapse to form a black holes. It is also found that in the case of $r(t_{0})<0.707L$ a loop of cosmic string whose tension depends on some power of cosmic time can not become a black hole if the power is lower than a critical value which is associated with the initial size of the loop.Comment: 6 page