General Relativity & Quantum Cosmology

In this talk, we first introduce the basic idea of asymptotic safety and discuss its application to quantum gravity. We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. It is shown that the beta functions admit two possible fixed points: One is the asymptotically safe fixed point, and the other is the asymptotically free one. The corresponding critical exponents to these fixed points are evaluated.

Next, we argue that asymptotically safe gravity could be an effective theory emerging from the spontaneous symmetry breaking in an ultraviolet (UV) theory. We consider a UV theory invariant under SO(4) local Lorentz symmetry and diffeomorphism. In particular, we impose the degenerate limit (zero eigenvalues of vierbein) on the action and then show that only spinor fields can be dynamical. We will discuss prospects whether or not this UV theory could be a fundamental theory underlying asymptotically safe gravity.

Zoom Link: https://pitp.zoom.us/j/94422371986?pwd=a25pS3cyUmJkNWJHL3hic1NhNlozQT09

In this talk, I would like to discuss gravitational waves in gravitational effective field theories. In particular, I will focus on gravitational waves propagating on a black hole background, and will show that the coefficients of the higher-dimension operators in the EFT can be constrained by causality considerations. I will also comment on observability of these higher-dimension operators in gravitational wave detections.

Zoom Link: https://pitp.zoom.us/j/94226476006?pwd=MEdHWG9oQ2dwQ2hXMUd2ZEFFQnRjZz09

By considering the photon-graviton scattering amplitude at low-energy including loops from the Standard Model, I will argue how we can infer constraints on the Regge behaviour of the gravitational scattering amplitude. I will also comment on implications to other gauge fields in four and higher dimensions and application to the Weak Gravity Conjecture and connections with causality considerations.

Zoom Link: https://pitp.zoom.us/j/91414100213?pwd=Z3g5SmRPb2xjUXEweGtjUC83WCtKdz09

We discuss the minimal coupling of gauge fields to the dual graph lattice of Causal Dynamical Triangulations (CDT) as a preliminary step towards the investigation of more realistic systems of gravity coupled to bosonic and fermionic matter. We first introduce the CDT approach and how the gravity and gauge fields are discretized, for general dimensions and gauge groups, focusing on some of the algorithmic complications which arise. Next, we discuss some results from 2D simulations of CDT coupled to U(1) and SU(2) gauge groups, where we studied both gravity and gauge-related observables and the ones related to gauge fields, comparing them to analogous simulations in the flat case.

In this talk, I will explain the construction of a (1+1) spacetime with a wormhole and its conversion into a time-machine spacetime. Then, I will describe a massless scalar quantum field theory in such spacetime. I focus in comparing this quantization of the field in the time-machine spacetime with the quantization on the two-dimensional Einstein cylinder, the emergence of a zero mode and its regularization.

Zoom link:  https://pitp.zoom.us/j/94856731951?pwd=MnFNZjlkUHVVWkRRQTIxR0o0TDFnUT09

I will present an argument that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise within the theory, even if they are not its basis. I will argue in particular that an apparent alternative to causal sets, viz. a certain sort of discrete Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way. For it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.

Zoom Link: https://pitp.zoom.us/j/96897602807?pwd=VkJ3VTAwYjhaTnJ3Z2ZVclZFYXErZz09

The gravitational radiation from the ringdown of a binary black hole merger is described by the solution of the Teukolsky equation, which predicts both the temporal and angular dependence of the emission. Many studies have explored the temporal feature of the ringdown wave through black hole spectroscopy. In this work, we further study the spatial distribution, by introducing a global fitting procedure over both temporal and spatial dependences, to propose a more complete test of General Relativity. We show that spin-weighted spheroidal harmonics are the better representation of the ringdown angular emission patterns compared to spin-weighted spherical harmonics. The differences are distinguishable in numerical relativity waveforms. We also study the correlation between progenitor binary properties and the excitation of quasinormal modes, including higher-order angular modes, overtones, prograde and retrograde modes. Specifically, we show that the excitation of retrograde modes is dominant when the remnant spin is anti-aligned with the binary orbital angular momentum. This study seeks to provide an analytical strategy and inspire the future development of ringdown test using real gravitational wave events.

In this talk I will outline recent attempts to probe black holes in the strong gravity regime. The access to gravitational wave emission from binary black hole mergers and images of supermassive black holes allow for new tests of general relativity. After reviewing recent activities, I will outline how quasi-normal modes and shadow images can be used to study possible deviations from general relativity. Finally, I will discuss open problems that need to be addressed in the future.