We describe how the original 2d CDT model has been generalized in various ways: to a multicomponent W3 algebra model based on the exceptional Jordan algebra and to a four-dimensional CDT model. Remarkably, under certain assumptions, both these generalisations lead to the same modified Friedmann equation where the present expansion of our universe is driven not by the cosmological constant, but...
The model of Causal Dynamical Triangulations (CDT) is a background-independent and diffeomorphism-invariant approach to quantum gravity, which provides a lattice regularization of the formal gravitational path integral. The framework does not involve any coordinate system and employs only geometric invariants. For a Universe with toroidal spatial topology, we can introduce coordinates using...
We understand reasonably well how to construct a discrete causal set that approximates a given spacetime manifold. The vast majority of causal sets, though, are not at all continuum-like, and if we take the discrete description to be fundamental, we must somehow suppress these "bad" sets. I will discuss some recent progress in showing that a very large class of non-manifoldlike sets is very...
I will give an overview of quantum dynamics in causal set theory. Because of the fundamental (causal) non-locality of causal sets, the dynamics is best described in the language of histories or the path integral formulation. The approach, to date, has been broadly two pronged: the first uses a continuum-inspired partition function and the discrete Einstein Hilbert action while the second uses...
We explore some properties of de Sitter spacetime, emphasizing the Euclidean perspective, including the path integral over the sphere. We consider the problem in various dimensions.
Spin foams and Regge gravity can be formulated as Lorentzian path integrals.
But which configurations should be included in these Lorentzian path integrals, and how should one evaluate these highly oscillatory integrals?
Using a simple configuration describing a cosmological spacetime, I will illustrate how these path integrals may be able to address the conformal factor problem and...
We consider two different kinds of loop models coupled to causal dynamical triangulations, a dense and a dilute one, and describe a mapping onto certain random tree models in which the weights of individual trees depend on their height in addition to their size, in the dilute case. We explain that this height coupling is non-trivial in the sense that it influences the fractal structure of the...
Tensor models were introduced in the early 1990s as a generalization of matrix models, generating Feynman diagrams in one-to-one correspondence with higher-dimensional dynamical triangulations. However, there was initially no way to fix the topology of the diagrams, and no way to construct a large-N limit. The latter was only discovered in 2010, leading to a number of analytical results. In...
In preparation for a lattice Monte Carlo study, I consider some simpler theories related to Quadratic Gravity and Asymptotic Safety. In particular, I discuss why the logarithmic running of coupling constants is different than that which has been discussed in the literature. In addition, I explore the apparent necessity of a strongly coupled region, independent of the behavior of the running couplings.
The talk examines possible answers to the question raised in functional integral based formulations of Quantum Gravity. These include Lorentzian signature perturbation theory and non-perturbative settings starting from the Euclidean propagation kernel. In the latter framework the "no-boundary" proposal is reexamined in relation to the (non-)normalizability of ground state wave function(s)....
Smolin's weak Newton constant limit of 4D Euclidian signature vacuum general relativity, mathematically a consisten U(1)$^3$ deformation of SU(2) quantum gravity, has recently been shown to be quantum integrable, that is, the canonical quantisation programme can be completed. An explicit quantum representation of the Bergmann Komar "group" (the "exponentiation" of the hypersurface deformation...
I will first highlight the main open questions in cosmology and give some examples of how one could address them in the context of quantum gravity. I will then argue that cosmology, in particular in the gravitational-wave astronomy era, can provide a powerful way of testing quantum gravity.
An atom defect attached to the surface of a vibrating, micron-scale membrane can experience accelerations comparable to the surface gravity of a neutron star. As one example application, we show how one can feasibly generate and detect photons from the electromagnetic vacuum as a result of the non-inertial membrane motion. In another existing table-top set-up comprising a non-linear...
The canonical quantization of gravity relies on its Hamiltonian formulation in an appropriate phase space. A geometric approach to the Hamiltonian treatment of singular field theories is very useful, especially when the spacetime manifold has boundaries. In the present talk I will quickly review these geometric methods, illustrate how they work with a very quick derivation of the real Ashtekar...
A classic result of canonical general relativity, going back to Dirac, shows that general covariance and deformation symmetries of spatial hypersurfaces are equivalent only when the Hamiltonian and diffeomorphism constraints are imposed. A recent mathematical analysis by Blohmann, Schiavina and Weinstein has revealed the appearance of a higher algebraic structure with an L-infinity bracket in...
After reviewing how geometric actions capture the dynamics of
asymptotically anti-de Sitter and flat spacetimes in three dimensions,
the construction is extended to four dimensions where it yields BMS4
invariant dual field theories.
Based on arxiv: 1707.08887, arxiv: 2211.07592
I will review work towards a statistical mechanical account of black hole entropy -- and causal horizon entropy more generally -- within causal set theory.
The Killing operator $K_{ab}[v]=\nabla_a v_b + \nabla_b v_a$ is the generator of gauge symmetries (linearized diffeomorphisms) $h_{ab}\mapsto h_{ab} + K_{ab}[v]$ in linearized gravity. A linear local gauge-invariant observable is a differential operator $I[h]$ such that $I[K[v]] = 0$ for any gauge parameter field $v_a$. A set $\{I_i[h]\}$ of such observables is complete if the simultaneous...
Black holes tell us that, at the Planck scale, information in spacetime should be coarse-grained.
Carefully studying the foundations of quantum mechanics, one also hits upon coarse grained
structures, but they are classical. Quantum behavior automatically comes about when taking
the continuum limit. This suggests that the logic applied in CDT should also be classical logic.
This may...
