General Relativity & Quantum Cosmology

Gravitational scattering provides valuable insight into classical dynamics and is likely of fundamental importance in quantum gravity.  However, a complete framework for gravitational scattering does not yet exist.  The lack of a clear framework hinders progress; for example, different groups have reported different results for the loss of angular momentum in post-Minkowskian scattering.  In this talk I will report on recent work 2303.17124 with Compere and Wei constructing a general framework for classical gravitational scattering of finite-sized massive bodies in four spacetime dimensions.  We formulate assumptions and definitions such that the five asymptotic regions (past/future timelike/null infinity and spatial infinity) share a single Bondi-Metzner-Sachs (BMS) group of symmetries and associated charges and derive global conservation laws stating that the total change in charge is balanced by the corresponding radiative flux.  Our assumptions are compatible with all known properties of scattering spacetimes, including certain logarithmic corrections that invalidate common falloff assumptions.  Among the new implications are rigorous definitions for quantities like initial/final spin, scattering angle, and impact parameter in multi-body spacetimes, without the use of any preferred background structure.  We show that spin is supertranslation-invariant, while impact parameter is not.  To complement these derivations I will emphasize a helpful "puzzle piece" diagram that faithfully represents all five asymptotic regions, illustrating their roles in the scattering problem.

Zoom link:  https://pitp.zoom.us/j/94358515412?pwd=cUFocVNjQ1pqUmp4MDN0RmRLbjE0QT09

In addition to the now-well known “Hubble tension”, in recent years a second tension has emerged: the $S_8$ tension. This is a measure of the homogeneity of the Universe. Specifically, $S_8$ is defined as $(\Omega_{\mathrm matter}/0.3)^{0.5} \sigma_8$ where $\sigma_8$ is the standard deviation of the density fluctuation in an 8 $h^{-1}$ Mpc radius sphere. As with the Hubble tension, there is disagreement, at greater than 4 $\sigma$ significance between what is predicted by extrapolating the fluctuations in the Cosmic Microwave Background forward to the present day, and what is measured by multiple probes of the inhomogeneity in the nearby Universe. I will discuss the diverse lines of evidence for the tension, showing it is not restricted to one probe, but is seen in weak gravitational lensing, peculiar velocities and redshift-space distortions and cluster abundances. I will conclude by discussing prospects for future measurements.

Local measurements of the expansion rate of the local universe differ from predictions of simple models fitted to large-scale cosmological measurements, at a statistically significant level. Sample variance (often called cosmic variance) is a key component of errors placed on measurements made from a small data set. For the Hubble constant, which parametrises the expansion rate, the size of the patch of the Universe covered by recent supernovae observations has a radius of 300Mpc. The smaller the patch, the larger the patch-to-patch fluctuations and the larger the error on the measured value of H0 from sample variance. Using the H0 measurement from supernovae as an example, I will consider a number of different ways to estimate sample variance using techniques developed for multiple uses, and show that they all approximately agree. The sample variance error on H0 measurements from the recent Pantheon supernovae sample is +/-1 kms^-1Mpc^-1, insufficient to explain the Hubble tension in a standard Lambda-CDM universe. This will demonstrate methods for comparing variations in expansion rate in the universe and what we mean by saying the universe is expanding (on average), or that galaxies move apart with particular velocities.

I present an unprecedented template-based search for stimulated emission of Hawking radiation (or Boltzmann echoes) by combining the gravitational wave data from 65 binary black hole merger events observed by the LIGO/Virgo collaboration. With a careful Bayesian inference approach, I found no statistically significant evidence for this signal in either of the 3 Gravitational Wave Transient Catalogs GWTC-1, GWTC-2 and GWTC-3. However, the data cannot yet conclusively rule out the presence of Boltzmann echoes either, with the Bayesian evidence ranging within 0.3-1.6 for most events, and a common (non-vanishing) echo amplitude for all mergers being disfavoured at only 2:5 odds. The only exception is GW190521, the most massive and confidently detected event ever observed, which shows a positive evidence of 9.2 for stimulated Hawking radiation. An optimal combination of posteriors yields an upper limit of A<0.42 (at 90% confidence level) for a universal echo amplitude, whereas A∼1 was predicted in the canonical model. The next generation of gravitational wave detectors such as LISA, Einstein Telescope, and Cosmic Explorer can draw a definitive conclusion on the quantum nature of black hole horizons.

It has been proposed that quantum-gravitational effects may change the near-horizon structure of black holes, e.g. firewalls or ultra-compact objects mimicking black holes. Also, a Lorentz-violating theory as a candidate of quantum gravity, e.g. the Horava-Lifshitz theory, changes the causal structure of black holes due to the superluminal propagation of excited modes. The late-time part of the gravitational wave ringdown from a black hole is significantly affected by those effects, and the emission of gravitational wave echoes may be induced. The black hole quasi-normal (QN) modes are affected by the change of the horizon structure, which results in the drastic modification of the late-time signal of the gravitational wave. In this talk, I will discuss how the gravitational wave echo can be modeled and how the echo model is reasonable from an entropic point of view by counting QN modes to estimate the black hole entropy.

Holography has profoundly transformed our understanding of quantum gravity in spacetimes with asymptotic negative curvature. Its implications for cosmology are equally profound, suggesting that time is emergent and that our universe has a dual description in terms of a three-dimensional quantum field theory. This talk will outline key features of holographic cosmology, from the perspective it offers for the cosmic singularity to the strategies it presents for computing cosmological observables. Recent results for the de Sitter wavefunction will be discussed and their interpretation in the language of three-dimensional conformal field theory.

If relativistic gravitation has a quantum description, it must be meaningful to consider a spacetime metric in a genuine quantum superposition. Here I present a new operational framework for studying “superpositions of spacetimes” via model particle detectors. After presenting the general approach, I show how it can be applied to describe a spacetime generated by a BTZ black hole in a superposition of masses and how such detectors would respond. The detector exhibits signatures of quantum-gravitational effects reminiscent of Bekenstein’s seminal conjecture concerning the quantized mass spectrum of black holes in quantum gravity. I provide further remarks in distinguishing spacetime superpositions that are genuinely quantum-gravitational, notably with reference to recent proposals to test gravitationally-induced entanglement, and those in which a putative superposition can be re-expressed in terms of dynamics on a single, fixed spacetime background.

The constrained Hamiltonian formalism is the basis for canonical quantization techniques. However, there are disagreements surrounding the notion of a gauge transformation in such a formalism. The standard definition of a gauge transformation in the constrained Hamiltonian formalism traces back to Dirac: a gauge transformation is a transformation generated by an arbitrary combination of first-class constraints. On the basis of this definition, Dirac argued that one should extend the form of the Hamiltonian in order to include all of the gauge freedom. However, Pitts (2014) argues that in some cases, a first-class constraint does not generate a gauge transformation, but rather "a bad physical change". Similarly, Pons (2005) argues that Dirac's analysis of gauge transformations is "incomplete" and does not provide an account of the symmetries between solutions. Both authors conclude that extending the Hamiltonian in the way suggested by Dirac is unmotivated. If correct, these arguments could have implications for other issues in the foundations of the constrained Hamiltonian formalism, including the Problem of Time. In this talk, I use a geometric formulation of the constrained Hamiltonian formalism to show that one can motivate the extension to the Hamiltonian independently from consideration of the gauge transformations, and I argue that this supports the standard definition of a gauge transformation without falling prey to the criticisms of Pitts (2014) and Pons (2005). Therefore, in order to maintain that first-class constraints do not generate gauge transformations, one must reject the claim that the constrained Hamiltonian formalism is fully described by the geometric picture; I suggest two avenues for doing so.

The success of the AdS/CFT correspondence motivates a holographic approach for spacetime beyond AdS, including our own universe. One possible method involves using an asymptotically-AdS holography and introducing a finite radial cutoff by inserting an End-of-World (EoW) brane. However, previous studies have shown that this leads to nonlocal effects on the boundary and violates entanglement sub-additivity. In this work, we address these issues by examining a two-particle scattering process through the lens of holographic quantum tasks. Our findings suggest that connectedness of entanglement wedge does indeed require nonlocal domain of dependence, but that violation of sub-additivity can be avoided. We also discuss an important question that arises from our results, namely whether the non-locality on the EoW brane is real or apparent. We argue that it is the latter. This talk is based on ongoing work with Takato Mori.