This series consists of talks in the area of Quantum Gravity.
We study in the context of loop quantum cosmology the effect of the analytic continuation that sends the Barbero-Immirzi parameter to a purely imaginary value. We show that this construction leads once again to a bouncing scenario, in which however the contracting and expanding phases on each side of the bounce are not symmetrical. Moreover, the minimal volume reached by the universe and the critical matter density become naturally independent of the Barbero-Immirzi parameter.
I will discuss why the search for B-Mode Polarization of the Cosmic Microwave Background (CMB) is very important for early universe cosmology, but that a discovery of such a polarization mode is in no way a confirmation of inflationary cosmology.
We isolate an important physical distinction between gauge symmetries which exist at the level of histories and states, and those which exist at the level of histories and not states. This distinction is characterised explicitly using a generalized Hamilton-Jacobi formalism within which a non-standard prescription for the observables of classical totally constrained systems is developed. These ideas motivate a `relational quantization' procedure which is different from the standard `Dirac quanization'.
We prove that the $\lambda\phi^4_4$ quantum field theory on noncommutative Moyal space is, in the limit of infinite noncommutativity, exactly solvable in terms of the solution of a non-linear integral equation. The proof involves matrix model techniques which might be relevant for 2D quantum gravity and its generalisation to coloured tensor models of rank $\geq 3$.
The authors have revealed a fundamental structure which has been hidden within the Wheeler-DeWitt (WDW) constraint of four dimensional General Relativity (GR) of Lorentzian signature in the Ashtekar self-dual variables. The WDW equation can be written as the commutator of two geometric entities, namely the imaginary part of the Chern-Simons functional Q and the local volume element V(x) of 3-space.
Thermodynamical aspects of gravity have been a tantalising puzzle for more than forty years now and are still at the center of much activity in semiclassical and quantum gravity. We shall explore the possibility that they might hint toward an emergent nature of gravity exploring the possible implications of such hypothesis. Among these we shall focus on the possibility that Lorentz invariance might be only a low energy/emergent feature by discussing viable theoretical frameworks, present constraints and open issues which make this path problematic.
I will describe the relationship between radiated energy and entanglement entropy of massless fields at future null infinity (the "Page curve") in two-dimensional models of black hole evaporation. I will use this connection to derive a general feature of any unitary-preserving evaporation scenario: the Bondi mass of the hole must be non-monotonic. Time permitting, I will comment on time scales in such scenarios.
Locally covariant quantum field theory (LCQFT) has proven to be a very successful framework for QFT on curved spacetimes. It is natural to ask, how far these ideas can be generalized and if one can learn something about quantum gravity, using LCQFT methods. In particular, one can use the relative Cauchy evolution to formulate the notion of background independence. Recently we have proven that background independence in this sense holds for effective quantum gravity, formulated as a perturbative QFT.
After the seminal work of Connes and Tretkoff on the Gauss-Bonnet theorem for the noncommutative 2-torus and its extension by Fathizadeh and myself, there have been significant developments in understanding the local differential geometry of these noncommutative spaces equipped with curved metrics. In this talk, I will review a series of joint works with Farzad Fathizadeh in which we compute the scalar curvature for curved noncommutative tori and prove the analogue of Weyl's law and Connes' trace theorem.