Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps

Gravitons and Lightcone Fluctuations II: Correlation Functions

A model of a fluctuating lightcone due to a bath of gravitons is further investigated. The flight times of photons between a source and a detector may be either longer or shorter than the light propagation time in the background classical spacetime, and will form a Gaussian distribution centered around the classical flight time. However, a pair of photons emitted in rapid succession will tend to have correlated flight times. We derive and discuss a correlation function which describes this effect. This enables us to understand more fully the operational significance of a fluctuating lightcone. Our results may be combined with observational data on pulsar timing to place some constraints on the quantum state of cosmological gravitons.Comment: 16 pages and two figures, uses eps

A quantum weak energy inequality for the Dirac field in two-dimensional flat spacetime

Fewster and Mistry have given an explicit, non-optimal quantum weak energy inequality that constrains the smeared energy density of Dirac fields in Minkowski spacetime. Here, their argument is adapted to the case of flat, two-dimensional spacetime. The non-optimal bound thereby obtained has the same order of magnitude, in the limit of zero mass, as the optimal bound of Vollick. In contrast with Vollick's bound, the bound presented here holds for all (non-negative) values of the field mass.Comment: Version published in Classical and Quantum Gravity. 7 pages, 1 figur

Minimum target prices for production of direct acting antivirals and associated diagnostics to combat Hepatitis C Virus

Combinations of direct-acting antivirals (DAAs) can cure hepatitis C virus (HCV) in the majority of treatment-naïve patients. Mass treatment programs to cure HCV in developing countries are only feasible if the costs of treatment and laboratory diagnostics are very low. This analysis aimed to estimate minimum costs of DAA treatment and associated diagnostic monitoring. Clinical trials of HCV DAAs were reviewed to identify combinations with consistently high rates of sustained virological response across hepatitis C genotypes. For each DAA, molecular structures, doses, treatment duration, and components of retrosynthesis were used to estimate costs of large-scale, generic production. Manufacturing costs per gram of DAA were based upon treating at least 5 million patients per year and a 40% margin for formulation. Costs of diagnostic support were estimated based on published minimum prices of genotyping, HCV antigen tests plus full blood count/clinical chemistry tests. Predicted minimum costs for 12-week courses of combination DAAs with the most consistent efficacy results were: US$122 per person for sofosbuvir+daclatasvir; US$152 for sofosbuvir+ribavirin; US$192 for sofosbuvir+ledipasvir; and US$115 for MK-8742+MK-5172. Diagnostic testing costs were estimated at US$90 for genotyping US$34 for two HCV antigen tests and US$22 for two full blood count/clinical chemistry tests. Conclusions: Minimum costs of treatment and diagnostics to cure hepatitis C virus infection were estimated at US$171-360 per person without genotyping or US$261-450 per person with genotyping. These cost estimates assume that existing large-scale treatment programs can be established. (Hepatology 2015;61:1174–1182

Cosmological and Black Hole Horizon Fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps