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Quantum inequalities are constraints on how negative the weighted average of the renormalized stressenergy tensor of a quantum field can be. A null-projected quantum inequality can be used to prove the averaged null energy condition, which would then rule out exotic phenomena such as wormholes and time machines. In this work we derive such an inequality for a massless minimally coupled scalar field, working to first order of the Riemann tensor and its derivatives. We then use this inequality to prove the averaged null energy condition on achronal geodesics in a curved background that obeys the null convergence condition. [ABSTRACT FROM AUTHOR]

We analyze the shapes of cosmic string loops found in large-scale simulations of an expanding-universe string network. The simulation does not include gravitational backreaction, but we model that process by smoothing the loop using Lorentzian convolution. We find that loops at formation consist of generally straight segments separated by kinks. We do not see cusps or any cusplike structure at the scale of the entire loop, although we do see very small regions of string that move with large Lorentz boosts. However, smoothing of the string almost always introduces two cusps on each loop. The smoothing process does not lead to any significant fragmentation of loops that were in non-self-intersecting trajectories before smoothing. [ABSTRACT FROM AUTHOR]

Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. Such inequalities in curved spacetime can be used to disprove the existence of exotic phenomena, such as closed timelike curves. Starting with a general result of Fewster and Smith, we derive a quantum inequality for a minimally coupled scalar field on a geodesic in a spacetime with small curvature, working to first order in the Ricci tensor and its derivatives. Since only the Ricci tensor enters, there are no first-order corrections to the flat-space quantum inequality on paths which do not encounter any matter or energy. [ABSTRACT FROM AUTHOR]

Quantum inequalities are bounds on negative time averages of the energy density of a quantum field. They can be used to rule out exotic spacetimes in general relativity. We study quantum inequalities for a scalar field with a background potential (i.e., a mass that varies with spacetime position) in Minkowski space. We treat the potential as a perturbation and explicitly calculate the first-order correction to a quantum inequality with an arbitrary sampling function, using general results of Fewster and Smith. For an arbitrary potential, we give bounds on the correction in terms of the maximum values of the potential and its first three derivatives. The techniques we develop here will also be applicable to quantum inequalities in general spacetimes with small curvature, which are necessary to mle out exotic phenomena. [ABSTRACT FROM AUTHOR]

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 infinity. Rather, electromagnetic backreaction must damp this current asymptotically to nothing. We compute this backreaction 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. [ABSTRACT FROM AUTHOR]

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 acquired detailed knowledge of the loop production function. We emphasize that gravitational smoothing of long strings plays a negligible 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 Gµ=2.8×10-9. We also provide a derivation of the Boltzmann equation for cosmic string loops in the language of differential forms. [ABSTRACT FROM AUTHOR]

Core-collapse supernovae emit on the order of 3×1053 ergs in high-energy neutrinos over a time of order 10 seconds, and so decrease their mass by about 0.2M?. If the explosion is nearly spherically symmetric, there will be little gravitational-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. [ABSTRACT FROM AUTHOR]

The averaged null energy condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. Exotic spacetimes, such as those allow wormholes or the construction of time machines are possible in general relativity only if ANEC is violated along achronal geodesies. Starting from a conjecture that flat-space quantum inequalities apply with small corrections in spacetimes with small curvature, we prove that ANEC is obeyed by a minimally coupled, free quantum scalar field on any achronal null geodesic surrounded by a tubular neighborhood whose curvature is produced by a classical source. [ABSTRACT FROM AUTHOR]

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 means 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 to be solved. [ABSTRACT FROM AUTHOR]

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 nonscaling 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. [ABSTRACT FROM AUTHOR]

Eternally inflating universes lead to an infinite number of Boltzmann brains but also an infinite number of ordinary observers. If we use the scale factor measure to regularize these infinities, the ordinary observers dominate the Boltzmann brains if the vacuum decay rate of each vacuum is larger than its Boltzmann brain nucleation rate. Here, we point out that nucleation of small black holes should be counted in the vacuum decay rate, and this rate is always larger than the Boltzmann brain rate, if the minimum Boltzmann brain mass is more than the Planck mass. We also discuss nucleation of small, rapidly inflating regions, which may also have a higher rate than Boltzmann brains. This process also affects the distribution of the different vacua in eternal inflation. [ABSTRACT FROM AUTHOR]

We compare the spectrum of the stochastic gravitational wave background produced in several models of cosmic strings with the common-spectrum process recently reported by NANOGrav. We discuss theoretical uncertainties in computing such a background, and show that despite such uncertainties, cosmic strings remain a good explanation for the potential signal, but the consequences for cosmic string parameters depend on the model. Superstrings could also explain the signal, but only in a restricted parameter space where their network behavior is effectively identical to that of ordinary cosmic strings. [ABSTRACT FROM AUTHOR]

We determine the distribution of cosmic string loops directly from simulations, rather than determining the loop production function and inferring the loop distribution from that. For a wide range of loop lengths, the results agree well with a power law exponent -2.5 in the radiation era and -2 in the matter era, the universal result for any loop production function that does not diverge at small scales. Our results extend those of Ringeval et al. [Cosmological evolution of cosmic string loops, J. Cosmol. Astropart. Phys. 02 (2007) 023.]: we are able to run for 15 times longer in conformal time and simulate a volume 300-2400 times larger. At the times they reached, our simulation is in general agreement with the more negative exponents they found, -2.6 and -2.4. However, our simulations show that this was a transient regime; at later times, the exponents decline to the values above. This provides further evidence against models with a rapid divergence of the loop density at small scales, such as "model 3" used to analyze LIGO data and predict LISA sensitivity. [ABSTRACT FROM AUTHOR]

A network of cosmic strings would lead to gravitational waves which may be detected by pulsar timing or future interferometers. The details of the gravitational wave signal depend on the distribution of cosmic string loops, which are produced by intercommutations from the scaling network of long strings. We analyze the limits imposed by energy conservation, i.e., by the fact that the total amount of string flowing into loops cannot exceed the amount leaving the long strings. We show that some recent suggestions for the cosmic string loop production rate and distribution are ruled out by these limits. As a result, gravitational waves based on such suggestions, in particular "model 3" used in LIGO data analysis, are not to be expected. [ABSTRACT FROM AUTHOR]

To understand the properties of a possible cosmic string network requires knowledge of the structures on long strings, which control the breaking off of smaller loops. These structures are influenced by backreaction due to gravitational wave emission. To gain an understanding of this process, we calculate the effect of gravitational backreaction on the "helical breather," an infinite cosmic string with a helical standing wave. We do the calculation analytically to first order in the amplitude of the oscillation. Our results for the rate of loss of length agree with the total power emitted from this system as calculated by Sakellariadou. We also find a rotation of the generators of the string that leads to an advancement of the phase of the oscillation in addition to that produced by the loss of length. [ABSTRACT FROM AUTHOR]

We present the results of computational gravitational backreaction on simple models of cosmic string loops. These results give us insight into the general behavior of cusps and kinks on loops, in addition to other features of evolution. Kinks are rounded off via an asymmetric and divergent correction to the string direction. The result is that cusps emerge in the place of kinks, but the resulting smooth string section has a small amount of energy. Existing cusps persist, but quickly lose strength as backreaction removes energy from the string surrounding the cusp. Both kinks and cusps have their location in space shifted slightly with each oscillation. [ABSTRACT FROM AUTHOR]

We find the leading-order effect of gravitational backreaction on cosmic strings for points near kinks and cusps. Near a kink, the effect diverges as the inverse cube root of the distance to the kink and acts in a direction transverse to the world sheet. Over time, the kink is rounded off, but only regions fairly close to the kink are significantly affected. Near cusps, the effect diverges inverse linearly with the distance to the cusp and acts against the direction of the cusp motion. This results in a fractional loss of string energy that diverges logarithmically with the distance of closest approach to the cusp. [ABSTRACT FROM AUTHOR]

We do a start-to-finish calculation of the stochastic gravitational wave background to be expected from cosmic strings. We start from a population of string loops taken from simulations, smooth these by Lorentzian convolution as a model of gravitational backreaction, calculate the average spectrum of gravitational waves emitted by the string population at any given time, and propagate it through a standard model cosmology to find the stochastic background today. Except for modeling back reaction as smoothing, we take into account all known effects, including changes in the number of cosmological relativistic degrees of freedom at early times and the possibility that some energy is in rare bursts that we might never have observed. [ABSTRACT FROM AUTHOR]

We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational backreaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, backreaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" (maximally symmetric) loop evaporates without changing shape, but for all other loops in this class, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, it will evaporate before its kinks are significantly changed; if it is far from square, the opening out of the kinks is much faster than evaporation of the loop. [ABSTRACT FROM AUTHOR]

Core-collapse supernovae emit on the order of 3×1053 ergs in high-energy neutrinos over a time of order 10 seconds, and so decrease their mass by about 0.2M⊙. If the explosion is nearly spherically symmetric, there will be little gravitational-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. [ABSTRACT FROM AUTHOR]