General Relativity & Quantum Cosmology

The functional Renormalization Group is a continuum method to study quantum field theories in the non-perturbative regime. In Yang-Mills theory, it can be used to relate fully nonperturbative low-order correlation functions in particular gauges to observables such as confinement order parameters. As a special application, we determine the order of the phase transition and the critical temperature for various gauge groups (SU(N), N=3,.,12, Sp(2) and E(7)). This also allows to investigate what determines the order of the deconfinement phase transition. Furthermore we study the non-perturbative effective potential for the field strength, where we observe the formation of a gluon condensate in the vacuum.

Why is a vertical column of gas at thermal equilibrium slighly hotter at the bottom than a the top? My answer in this talk will be that time runs slower in a deeper gravitational potential, and temperature is nothing but the (inverse) speed of time. Specifically, I will (i) introduce Rovelli's notion of thermal time, (ii) use it to provide a "principle" characterization of thermal equilibrium in stationary spacetimes, and (iii) effortlessly derive the Tolman-Ehrenfest relation. This approach contrasts with the "constructive" accounts of thermal equilibrium in curved spacetimes given in the literature, and vindicates the time-temperature relationship cropping up in the Hawking-Unruh and Kubo-Martin-Schwinger relations.

In the context of loop quantum gravity and spin foam models, the simplicity constraints are essential in that they allow to write general relativity as a constrained topological theory. I will first recall the spin foam quantization procedure and focus more particularly on the step consisting in implementing the simplicity constraints. Then, I will present the U(N) framework initially developed for SU(2) intertwiners. Finally, I will show how we can apply this new framework to impose the simplicity constraints in the context of 4d Euclidean gravity and present new solutions defined in term of U(N) coherent states.

An ultraviolet complete quantum gravity theory is formulated in which vertex functions in Feynman graphs are entire functions and the propagating graviton is described by a local, causal propagator. A scalar-tensor action describes classical gravity theory. The cosmological constant problem is investigated in the context of the ultraviolet complete quantum gravity. Also investigated are black holes and cosmology.

The Exact Renormalization Group (ERG) is a technique which can be fruitfully applied to systems with local interactions that exhibit a large number of degrees of freedom per correlation length. In the first part of the talk I will give a very general overview of the ERG, focussing on its applications in quantum field theory (QFT) and critical phenomena. In the second part I will discuss how a particular extension of the formalism suggests a new understanding of correlation functions in QFTs, in general, and gauge theories in particular.

Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting models expanded about a suitable pseudofree theory [differing from a free theory by an $O(\hbar^2)$ term]. This procedure not only provides acceptable solutions for models for which no acceptable solution currently exists, e.g., $\varphi^4_n$, for spacetime dimension $n\ge4$, but offers a new, divergence-free solution, for less-singular models as well, e.g., $\varphi^4_n$, for $n=2,3$.

Over the last decade there has been strong interest in the theory and phenomenology of particle propagation in quantum spacetime. The main results concern possible Planck-scale modifications of the "dispersion" relation between energy and momentum of a particle. I review results establishing that these modifications can be tested using observations of gamma rays from sources at cosmological distances. And I report recent progress in the understanding of the implications of spacetime expansion for such studies. I also discuss recent preliminary results suggesting that the same Planck-scale modifications of the dispersion relation might have an unexpected role in gravitational collapse.

In my talk I would like to discuss the present status of Doubly Special Relativity. DSR is an extension of Special Relativity aimed at describing kinematics of particles and fields in the regime where (quantum) gravity effects might become relevant. I will discuss an interplay between DSR physics and mathematics of Hopf algebras.

A brief introduction to the notorious "cosmological constant problem" is given. Then, a particular approach is discussed, which has been developed by Volovik and the present speaker over the last years and which goes under the name of q-theory. This approach provides a possible solution of the main cosmological constant problem, why is |Lambda|^(1/4) negligible compared to the energy scales of the electroweak standard model (not to mention the Planck energy)? The next problem is, of course, the small but nonzero value of the actual cosmological constant, responsible for the observed "accelerating universe." This problem can also be addressed in the framework of q-theory. In fact, the observed value Lambda ~ (meV)^4 may correspond to the remnant vacuum energy density of dynamical processes taking place at a cosmic age set by the mass scale M ~ E_ew of ultramassive particles with electroweak interactions. A first estimate of the required value of the energy scale E_ew ranges from 3 to 9 TeV. If correct, this estimate implies the existence of new TeV-scale physics beyond the standard model.

Combining the principles of general relativity and quantum theory still remains as elusive as ever. Recent work, that concentrated on one of the points of contact (and conflict) between quantum theory and general relativity, suggests a new perspective on gravity. It appears that the gravitational dynamics in a wide class of theories - including, but not limited to, standard Einstein's theory - can be given a purely thermodynamic interpretation. In this approach gravity appears as an emergent phenomenon, like e.g., gas or fluid dynamics. I will describe the necessary background, key results and their implications as suggested by my recent work in this area.