There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multiband photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: {Omega}{sub M} = 0.263 {+-} 0.042 (stat) {+-} 0.032 (sys) for a flat {Lambda}CDM model; and w = -1.023 {+-} 0.090 (stat) {+-} 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.

The Supernova Legacy Survey: Measurement of Omega_m, Omega_l and w from the First Year Data Set

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1397398

Cosmological Inflation and Large-Scale Structure

In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation method. The first one (Loess) is a nonparametric approach that allows to obtain smoothed curves with no prior knowledge of the functional relationship between variables nor of the cosmological quantities. The second one (Simex) takes into account the effect of measurement errors on a variable via a simulation process. For the reconstructions we use as raw data the Union2.1 Type Ia Supernovae compilation, as well as recent Hubble parameter measurements. This work aims to illustrate the approach, which turns out to be a self-sufficient technique in the sense we do not have to choose anything by hand. We examine the details of the method, among them the amount of observational data needed to perform the locally weighted fit which will define the robustness of our reconstruction. In view of our results, we believe that our proposal offers a promising alternative for reconstructing global trends of cosmological data when there is little intuition on the relationship between the variables and we also think it even presents good prospects to generate reliable mock data points where the original sample is poor.

Nonparametric reconstruction of the cosmic expansion with local regression smoothing and simulation extrapolation

Dark energy models with tracker properties have gained attention due to the large range of initial conditions leading to the current value of the dark energy density parameter. A well-motivated family of these models are the so-called $\alpha$-attractors, which show the late time behavior of a cosmological constant. In the present paper we perform a model-selection analysis of a variety of $\alpha$-attractor potentials in comparison with a non-flat $\Lambda$CDM model. Specifically, we compute the Bayes Factor for the L-Model, the Oscillatory Tracker Model, the Recliner Model, and the Starobinsky Model, while considering the non-flat $\Lambda$CDM as the base model. Each model is tested through a Bayesian analysis using observations relevant to the current accelerated expansion: we employ the latest SNe Ia data, combined with cosmic clocks, the latest BOSS release of BAO data, and the Planck Compressed 2018 data. The produced Markov Chains for each model are further compared through a Bayesian evidence analysis. From the latter we conclude that the Oscillatory Tracker Model is preferred by data (even if weakly) over the non-flat $\Lambda$CDM model. Our results also suggest at the L-model is the least favoured version of the $\alpha$-attractor models considered.

Bayesian evidence for $\alpha$-attractor dark energy models

Bayesian evidence for α-attractor dark energy models

� in the range 0 < ˜ < 3, being so consistent with previous probes; we also determined the deceleration parameter q0 and the redshift of transition to accelerated expansion. Besides we present an updated analysis of the model with CMB5-year data and CMB7-year data, as well as with the baryon acoustic peak BAO. From the statistics with CMB it turns out that the model does not describe in a feasible way the far far epoch of recombination of the universe, but is in very good concordance for epochs as far as z � 8.1 till present.

https://iopscience.iop.org/article/10.1088/1475-7516/2011/08/023/pdf

Probing bulk viscous matter-dominated models with gamma-ray bursts

We present a sample of 81 Gamma-Ray Bursts (GRBs) observed by Fermi-GBM for which we compute the distance moduli and use them to constrain effective dark energy models. To overcome the circularity problem affecting the use of GRBs as distance indicators, we calibrate the Amati relation of our sample by employing a cosmology-independent technique. Specifically, the latest observational Hubble parameter data are used to approximate the cosmic expansion through a Bezier parametric curve. We subsequently obtain the distance moduli of the GRBs and include it in a suite of recent cosmological (Planck Compressed 2018 and 2012 BOSS release of BAO data) and local (Pantheon SNIa) observations of the expansion history to compute Bayesian posterior constraints for the standard cosmological model $\Lambda$CDM, $\omega$CDM, and for the CPL parametrization. We highlight the advantages that our dataset and method represent over other recent GRB data.

Ariadna Montiel

Papers

Nonparametric reconstruction of the cosmic expansion with local regression smoothing and simulation extrapolation

Bayesian evidence for $\alpha$-attractor dark energy models

Bayesian evidence for α-attractor dark energy models

Probing bulk viscous matter-dominated models with gamma-ray bursts

Improving sampling and calibration of GRBs as distance indicators