General Relativity & Quantum Cosmology

We consider a natural extension of general relativity, by the addition of a term which is a topological invariant when the cosmological constant is in fact constant.  Allowing the cosmological constant to vary, we discover it is endowed with a natural dynamics, which also includes a mechanism to suppress its value.   A key role in hiding the consequences of a dynamical cosmological constant is played by the torsion of the spacetime connection.

As a dynamical variable, the varying cosmological constant turns out to be canonically conjugate to a measure of intrinsic, cosmological time, given by the Chern-Simons invariant of the Ashtekar connection (which we originally studied with Chopin Soo).  As a result, a small quantum universe that "knows what time it is" does not know the value of the cosmological constant, and visa versa.   This leads to some novel scenarios for the early universe.

This is joint work in progress with Stephon Alexander, Joao Magueijo and Robert Sims.

Since the first detection two years ago, gravitational waves have promised to revolutionize the physics and astrophysics of compact objects. But to understand what these gravitational waves are telling us, we need to understand how these relativistic binary systems form in the first place.  In this talk, I will describe the various astrophysical pathways for forming the binary mergers detected by LIGO/Virgo, and how specific features of the gravitational waves (such as the eccentricities and spins) can illuminate the formation histories of these exotic objects.  In particular, I will discuss how black holes can undergo multiple mergers in dense star clusters, creating a second generation of black holes more massive (and with potentially greater spins) than those formed through the collapse of isolated stars.

As a proxy for a Quantum Gravity theory, String Theory introduces new degrees of freedom and symmetries that should play a major role in the physics of the early universe. We motivate the introduction of these ingredients as we review some of the issues of the inflationary paradigm. Among these new ingredients, T-duality may help us to solve the Big Bang singularity and yield a different cosmological scenario. Thus, we review how this has been thought in the context of Double Field Theory, which aims to build a covariant field theory under T-duality's group, and consider its cosmological applications. 

I will discuss recent developments in the theory of relativistic turbulence, from both pure physics and astronomical perspectives. Turbulence in relativistic fluids and plasmas has applicability in high energy density physics, in early-universe cosmology, and in high energy astrophysics. I will focus on its connections with multi-messenger astrophysics, particularly in the context of binary neutron star (BNS) mergers, and the electromagnetic signals that accompany their gravitational wave emission. My talk will include (1) an overview of methods used to simulate and characterize relativistic turbulence, (2) implications of dynamo theory to the dynamics of BNS mergers, (3) new ideas emerging in the theory of "radiation-mediated" relativistic turbulence, and (4) efforts in modeling the prompt and afterglow emission from GW-170817.

The gravitational waves from a binary inspiral carry unique information about the internal structure of compact objects. This information is of major interest for neutron stars, offering the possibility for advancing our understanding matter and fundamental interactions in unexplored regimes. I will discuss the imprints of an object’s internal structure, and in particular neutron star matter, on the gravitational waves generated during an inspiral, methods for analytically modeling these effects, and what we have learned from GW170817. I will also outline future prospects and challenges.

We  find an  approximation of  the induced spatial distance on a Cauchy hypersurface using only the causal structure and local volume element. The approximation can be made arbitrarily precise for a globally hyperbolic spacetime with compact Cauchy hypersurfaces. This prescription has a discrete analog which we use to evaluate the induced spatial distance in a continuum-like causal set.  As expected, because of  discrete asymptotic silence, this gives a poor approximation to the continuum distance in the "UV".  For larger distances, on the other hand, the approximation works very well, as long as the discreteness scale is significantly smaller than the extrinsic and intrinsic curvature scale of the spatial hypersurface. This paves the way for obtaining detailed spatial geometric information from the causal structure, which has implications for the continuum approximation of causal set theory. 

The unexpected diversity of planetary systems has posed challenges to our classical understanding of planetary formation. For instance, Jupiter sized planets have been detected with short orbital periods of a few days in misaligned orbits with respect to the spin-axis of their host stars. I will first describe the statistical implication of detecting misaligned hot Jupiters and will suggest how dynamical interactions between an outer perturber and the inner planet, can naturally lead to the formation of such misaligned hot Jupiters. Next, I will discuss a similar dynamical process in the outer Solar System, far away from our Sun, which could cause the observed clustering of extreme trans-Neptunian objects. This can constrain properties of a possible outer planet, Planet Nine, in our own Solar System. 

I discuss the canonical degrees of freedom of metric Einstein gravity on a null surface. The constraints are interpreted as conservation equations of a boundary current. Gravitational fluxes are identified, and the Hamiltonians of diffeomorphism symmetry are discussed. Special attention is given to the role of a modification of the phase space at the boundary of the null surface. Based on 1802.06135 with Laurent Freidel.

The large j asymptotic behavior of 4-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large j asymptotic behavior is determined by critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are phases asymptotically, whose exponents equal to Regge action of gravity. The amplitude also contains critical configurations corresponding to non-degenerate split signature 4-simplices and degenerate vector geometries.  

Conventional equations of state suggest that in complete gravitational collapse a singular state of matter with infinite density could be reached finally to a black hole, the characteristic feature of which is its apparent horizon, where light rays are first trapped. The loss of information to the outside world this implies gives rise to serious difficulties with well-established principles of quantum mechanics and statistical physics.

The formation of a gravitational vacuum condensate star with a p=−ρ interior solves these problems and remarkably, actually follows from Schwarzschild's second paper over a century ago. The surface tension of the condensate star surface is the difference of equal and opposite surface gravities between the exterior and interior Schwarzschild solutions. The First Law is then recognized as a purely mechanical classical relation at zero temperature and zero entropy. The Schwarzschild time of such a non-singular gravitational condensate star is a global time, fully consistent with unitary time evolution in quantum theory.

The advent of BH imaging by the EHT and Gravitational Wave Astronomy with LIGO should allow for observational tests of the gravastar hypothesis, particularly in the discrete surface modes of oscillation and GW resonances or “echoes,” which may be observable by advanced LIGO and successor GW detectors.

Dr. Avery Broderick will provide a highly accessible and interesting lecture on the Event Horizon Telescope (EHT) and international efforts to interpret horizon-resolving images of numerous supermassive black holes. Black holes are among the most powerful and mysterious phenomena in the universe. Almost every galaxy has at its core a supermassive black hole, millions or even billions of times more massive than our sun. Despite composing a small fraction of the galactic mass budgets, they set the stage for astrophysical dramas that dictate the fates of their hosts. Though black holes are in theory the ultimate manifestation of strong gravity’s impact on the visible universe, placing these exotic phenomena on concrete empirical footing has been impossible - until now.

This talk will explore the applications of the computing power of numerical relativity to gravitational theories beyond general relativity. Specifically, I will consider dynamical Chern-Simons gravity, which has roots in string theory and loop quantum gravity. I will discuss our  formalism and efforts to simulate binary black holes in this theory to generate waveforms LIGO and LISA. Additionally, I will discuss the generation of numerical black hole solutions in this theory, and applications to probing black hole shadows with the Event Horizon Telescope.