Gerard t Hooft

Hawking particles emitted by a black hole are usually found to have thermal spectra, if not exactly, then by a very good approximation. Here, we argue differently. Locally, Hawking particles are thermal, but globally not: the Hawking particles emerging from one hemisphere of a black hole are 100 % entangled with the Hawking particles emerging from the other hemisphere. Consequently, their thermal fluctuations are identical, so if a rare event takes place on one hemisphere, the same event will be seen at the antipodal point on the other hemisphere. We explain why such bizarre behaviour is demanded by the requirement that black hole evaporation is described by a unitary scattering matrix. Region I and the diametrically opposite region II of the Penrose diagram represent antipodal points in a CPT relation, as was suggested before. On the horizon itself, antipodal points are identified, as long as there is no matter falling in. A candidate instanton is proposed to describe the formation and evaporation of virtual black holes of the type described here.

Ivan Arraut, Kaddour Chelabi

The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the non-linear formulations of massive gravity. When the gravitational effects are taken into account, and the observers are located at the Vainshtein radius, this degeneracy corresponds to a multiplicity of Vainshtein scales, all of them connected through the broken generators of the theory.

Michele Moresco, Lucia Pozzetti, Andrea Cimatti, Raul Jimenez, Claudia Maraston, Licia Verde, Daniel Thomas, Annalisa Citro, Rita Tojeiro, David Wilkinson

Deriving the expansion history of the Universe is a major goal of modern cosmology. To date, the most accurate measurements have been obtained with Type Ia Supernovae and Baryon Acoustic Oscillations, providing evidence for the existence of a transition epoch at which the expansion rate changes from decelerated to accelerated. However, these results have been obtained within the framework of specific cosmological models that must be implicitly or explicitly assumed in the measurement. It is therefore crucial to obtain measurements of the accelerated expansion of the Universe independently of assumptions on cosmological models. Here we exploit the unprecedented statistics provided by the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 to provide new constraints on the Hubble parameter $H(z)$ using the em cosmic chronometers approach. We extract a sample of more than 130000 of the most massive and passively evolving galaxies, obtaining five new cosmology-independent $H(z)$ measurements in the redshift range $0.3<z<0.5$, with an accuracy of $\sim$11-16\% incorporating both statistical and systematic errors. Once combined, these measurements yield a 6\% accuracy constraint of $H(z=0.4293)=91.8\pm5.3$ km/s/Mpc. The new data are crucial to provide the first cosmology-independent determination of the transition redshift at high statistical significance, measuring $z_{t}=0.4\pm0.1$, and to significantly disfavor the null hypothesis of no transition between decelerated and accelerated expansion at 99.9\% confidence level. This analysis highlights the wide potential of the cosmic chronometers approach: it permits to derive constraints on the expansion history of the Universe with results competitive with standard probes, and most importantly, being the estimates independent of the cosmological model, it can constrain cosmologies beyond -and including- the $\Lambda$CDM model.

Stephen W. Hawking, Malcolm J. Perry, Andrew Strominger

It has recently been shown that BMS supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian spacetimes. These laws require black holes to carry a large amount of soft ($i.e.$ zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This paper gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of the horizon. Charge conservation is used to give an infinite number of exact relations between the evaporation products of black holes which have different soft hair but are otherwise identical. It is further argued that soft hair which is spatially localized to much less than a Planck length cannot be excited in a physically realizable process, giving an effective number of soft degrees of freedom proportional to the horizon area in Planck units.

Robert H. Brandenberger, Yi-Fu Cai, Sumit R. Das, Elisa G.M. Ferreira, Ian A. Morrison, Yi Wang

We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a cosmological "singularity" - a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled region near the boundary, we reconstruct the bulk fluctuations after the singularity crossing making use of generic properties of boundary-to-bulk propagators. Finally, we extract the spectrum of the fluctuations at late times given some initial spectrum. We find that the spectral index is unchanged, but the amplitude increases due to the squeezing of the fluctuations during the course of the evolution. This investigation can teach us important lessons on how the spectrum of cosmological perturbations passes through a bounce which is singular from the bulk point of view but which is resolved using an ultraviolet complete theory of quantum gravity.