Viable inflationary models ending with a first-order phase transition

We investigate the parameter space of hybrid inflation models where inflation terminates via a first-order phase transition causing nucleation of bubbles. Such models experience a tension from the need to ensure nearly scale invariant density perturbations, while avoiding a near scale-invariant bubble size distribution which would conflict observations. We perform an exact analysis of the different regimes of the models, where the energy density of the inflaton field ranges from being negligible as compared to the vacuum energy to providing most of the energy for inflation. Despite recent microwave anisotropy results favouring a spectral index less than one, we find that there are still viable models that end with bubble production and can match all available observations. As a by-product of our analysis, we also provide an up-to-date assessment of the viable parameter space of Linde's original second-order hybrid model across its full parameter range.Comment: 9 pages, 7 figures. Revised version: corrections to description of the historical development of the models. v3: Minor corrections to match version accepted by PR

Implications of Spontaneous Glitches in the Mass and Angular Momentum in Kerr Space-Time

The outward-pointing principal null direction of the Schwarzschild Riemann tensor is null hypersurface-forming. If the Schwarzschild mass spontaneously jumps across one such hypersurface then the hypersurface is the history of an outgoing light-like shell. The outward-- pointing principal null direction of the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null infinity) null hypersurface-forming. If the Kerr parameters of mass and angular momentum spontaneously jump across one such asymptotic hypersurface then the asymptotic hypersurface is shown to be the history of an outgoing light-like shell and a wire singularity-free spherical impulsive gravitational wave.Comment: 16 pages, TeX, no figures, accepted for publication in Phys. Rev.

Light-like Signals in General relativity and Cosmology

The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the surface by its imbedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de sitter univers and Minkowskian space-time.Comment: 21 pages, latex, no figure

Estimating drizzle drop size and precipitation rate using two-colour lidar measurements

A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution. The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions

Detecting Early Galaxies Through Their 21-cm Signature

New observations over the next few years of the emission of distant objects will help unfold the chapter in cosmic history around the era of the first galaxies. These observations will use the neutral hydrogen emission or absorption at a wavelength of 21-cm as a detector of the hydrogen abundance. We predict the signature on the 21-cm signal of the early generations of galaxies. We calculate the 21-cm power spectrum including two physical effects that were neglected in previous calculations. The first is the redistribution of the UV photons from the first galaxies due to their scattering off of the neutral hydrogen, which results in an enhancement of the 21-cm signal. The second is the presence of an ionized hydrogen bubble near each source, which produces a cutoff at observable scales. We show that the resulting clear signature in the 21-cm power spectrum can be used to detect and study the population of galaxies that formed just 200 million years after the Big Bang.Comment: 5 pages, 3 figures, submitted to MNRAS Let

Spline-based modelling of trends in the force of HIV infection, with application to the UNAIDS Estimation and Projection Package

Objective: We previously developed a flexible specification of the UNAIDS Estimation and Projection Package (EPP) that relied on splines to generate time-varying values for the force of infection parameter. Here, we test the feasibility of this approach for concentrated HIV/AIDS epidemics with very sparse data and compare two methods for making short-term future projections with the spline-based model. Methods: Penalised B-splines are used to model the average infection risk over time within the EPP 2011 modelling framework, which includes antiretroviral treatment effects and CD4 cell count progression, and is fit to sentinel surveillance prevalence data with a Bayesian algorithm. We compare two approaches for future projections: (1) an informative prior related to equilibrium prevalence and (2) a random walk formulation. Results: The spline-based model produced plausible fits across a range of epidemics, which included 87 subpopulations from 14 countries with concentrated epidemics and 75 subpopulations from 33 countries with generalised epidemics. The equilibrium prior and random walk approaches to future projections yielded similar prevalence estimates, and both performed well in tests of out-of-sample predictive validity for prevalence. In contrast, in some cases the two approaches varied substantially in estimates of incidence, with the random walk formulation avoiding extreme changes in incidence. Conclusions: A spline-based approach to allowing the force of infection parameter to vary over time within EPP 2011 is robust across a diverse array of epidemics, including concentrated ones with limited surveillance data. Future work on the EPP model should consider the impact that different modelling approaches have on estimates of HIV incidence

Peeling properties of lightlike signals in General Relativity

The peeling properties of a lightlike signal propagating through a general Bondi-Sachs vacuum spacetime and leaving behind another Bondi-Sachs vacuum space-time are studied. We demonstrate that in general the peeling behavior is the conventional one which is associated with a radiating isolated system and that it becomes unconventional if the asymptotically flat space-times on either side of the history of the light-like signal tend to flatness at future null infinity faster than the general Bondi-Sachs space-time. This latter situation occurs if, for example, the space-times in question are static Bondi-Sachs space- times.Comment: 14 pages, LaTeX2

Detection of gravitational waves from the QCD phase transition with pulsar timing arrays

If the cosmological QCD phase transition is strongly first order and lasts sufficiently long, it generates a background of gravitational waves which may be detected via pulsar timing experiments. We estimate the amplitude and the spectral shape of such a background and we discuss its detectability prospects.Comment: 7 pages, 5 figs. Version accepted by PR