Wednesday, March 20, 2019

Implications of a dynamical cosmological constant

Tuesday, Mar 19th

Lee Smolin, Perimeter Institute
Title: Implications of a dynamical cosmological constant 
PDF of the talk (10M)
Audio+Slides of the talk (28M)
By Jorge Pullin, LSU

Experimental cosmologists have determined that 95% of the content of the universe is not made up of ordinary matter. The vast majority of the universe consists of strange forms of matter known as dark matter and dark energy. Some people believe that in reality there is no such matter, but a modification of Einstein's general relativity is needed to explain the universe in large scales. That is, just ordinary matter with a new theory of gravity.

The cosmological constant was a term Einstein added to his equations in 1917 in a futile attempt to make the universe static (at the time it was not known the universe expands). The extra terms it implies in the equations has a behavior similar to dark energy.

Cosmologists have proposed several generalizations of Einstein's theory involving extra fields and constants in order to attempt to explain dark energy and dark matter. However, more complex theories tend to depend on extra parameters that need to be determined, limiting their predictive power. Essentially one can adjust parameters to fit any observed behavior. Also, there is a high degree of arbitrariness in how one can modify Einstein's theory.

The aim of this talk is to introduce a basic principle for the creation of generalized theories that does not involve extra fields. To give more details we have to discuss some basic concepts. Most classical equations of motion, like those of general relativity, can be derived from what is known as an "action principle". The "action" is a function of the variables of the theory such that if one requires that it be a minimum (or a maximum), the equations of the theory follow. That is, the condition for minimization (or maximization) is that the equations of the theory hold. It turns out one can add to the action of a theory some terms such that the resulting equations of motion remain unchanged. Such terms (usually multiplied times a constant) are called "topological terms". The proposal of this talk is to add to the action such terms but allow the constant that multiplies them (called "cosmological constant" in the talk, generalizing the idea of Einstein) to change with time and even possibly space. So if the term were constant we would just recover the usual Einstein theory, but when it is not, one gets a new theory.

Three such theories are proposed in the talk, with various properties discussed. In particular, the geometry they imply is more general than that of Einstein's theory, in addition to a metric to describe space-time another quantity called torsion appears. This is still early days for these theories and various properties are being worked out. In particular, cosmological models have been studied. It appears that the one of the considered "cosmological constants" appears to be clumped around ordinary matter. This is just like dark matter behaves, it tends to clump around galaxies, modifying the orbits of outer stars (this is how dark matter was detected, the stars did not move as they were supposed to given the mass of the galaxy). More complex concepts, like black holes, are yet to be worked out in the new theories as well as several other properties, but some initial glimmers of interesting possibilities are emerging.

Tuesday, March 19, 2019

Towards loop quantum gravity effective dynamics

Tuesday, Feb. 19th

Andrea Dapor, LSU
Title: Toward LQG effective dynamics 
PDF of the talk (250K)
Audio+Slides of the talk (57M)
By Jorge Pullin, LSU

The dynamics of loop quantum gravity is quite complex. This is understandable, as it should reproduce in the classical limit the dynamics of general relativity which in itself is quite complex. This has led investigators to concentrate on situations with a lot of symmetry, in order to achieve simplifications. One of those simplifications is loop quantum cosmology, which studies homogeneous and isotropic spacetimes, i.e. spacetimes that are the same at all points and in all directions. This might seem like too drastic a simplification, but the dynamics of our universe at large scales is well approximated by it.

Imposing a symmetry in the quantum theory is not easy. One has to choose a subset of quantum states that are symmetric and study the action of quantum operators on them. All these operations take place in the full theory and therefore can potentially be as complex as dealing with it in generality. This led people to seek a further approximation: impose the symmetry in the classical theory and only then quantize. The problem is that when one imposes the symmetry at a classical level, general relativity simplifies too much and a lot of the techniques of loop quantum gravity are not applicable anymore. Nevertheless people proceeded by using techniques analogous to those of loop quantum gravity. The resulting construction is known as loop quantum cosmology and has been studied for over a decade.

This talk dealt with the first approach, namely choose a set ofsuitably symmetric states in the quantum theory and study the action of the quantum operators on them. Remarkably some portions of loop quantum cosmology can be retrieved from this approach, but not quite. Some of the quantum operators differ. The talk studied the resulting quantum cosmologies. The picture that emerges is rather different from traditional loop quantum cosmology. There one has that the Big Bang, the singularity that arises at the origin of the universe when all matter is concentrated at a point, is replaced by a Big Bounce in which there is high -but finite- density of matter. If one studies the evolution back in time one can go past the Bounce and one emerges into a previous universe that eventually becomes big and classical like the one we live in. So the picture that emerges is that our universe originated in a large classical universe like ours that contracted, increased in density, became highly quantum, bounced at a finite density, and started to expand eventually becoming classical again. The modified dynamics of the approach followed in the talk leads to a different picture. Our universe starts in a large but highly quantum universe that is highly symmetric (it is known as De Sitter spacetime), it eventually bounces and starts expanding until it becomes the classical universe we live in. The talk also explored the implications for the singularity inside black holes and showed that the modified dynamics leads to a transition in which the black hole explodes into a "white hole" where everything that went into the black hole comes out. This behavior had been suggested by other approaches, but the details differ. The whole approach relies on a conjecture about how the chosen symmetric states in the full theory behave. Proving the conjecture is a future challenge awaiting.

Thursday, February 7, 2019

Modified loop quantum cosmology

Tuesday, Feb. 5th

Parampreet Singh, LSU
Title: Modified loop quantum cosmologies 
PDF of the talk (2M)
Audio+Slidesof the talk (52M)
By Jorge Pullin, LSU

Due to the complexity of the Einstein equations candidates for theories of quantum gravity are fairly complex. In fact, we still do not have good control of the quantum Einstein equations in loop quantum gravity. One possibility to make progress is to consider situations with high symmetry, where most degrees of freedom are frozen and one analyzes only a few. Unfortunately, freezing degrees of freedom in the quantum theory is fairly complex.

An alternative approach is to freeze the degrees of freedom at a classical level and then quantize the resulting theory. This technique is known as "minisuperspace" approach. It is not guaranteed that results obtained in this approach will mimic those of the full theory in a symmetric situation but at least it gives an idea of what is possible to expect.

One of the most studied minisuperspaces is that of homogeneous cosmologies, where all degrees of freedom are frozen with the exception of the size of the universe. In loop quantum gravity this approach is known as loop quantum cosmology.

When one quantizes theories, even as simple as the ones one considers in homogeneous minisuperspaces, there are quantization ambiguities. In a recent talk, an alternative quantization of loop quantum cosmology to the traditional one exploiting one of those ambiguities was presented.

This talk presented a thorough analysis of the alternative quantization, partly using the so-called "effective" approach in which one writes down classical equations of motion that are supposed to capture the modifications that the quantum theory introduces in the behavior of the universe. The stability of the solutions was discussed with and without cosmological constant and the behavior of inflation in various types of models was presented. The elimination of the big bang singularity was analyzed in various scenarios that lead to different types of singularity. The emerging picture is of a universe that starts in a deep quantum state and then "bounces" into a large classical universe like the one we live in.

2+1 D loop quantum gravity on the edge

Tuesday, Jan. 22nd

Barak Shoshany, Perimeter Institute
Title: 2+1D loop quantum gravity on the edge 
PDF of the talk (9M)
Audio+Slidesof the talk (32M)
By Jorge Pullin, LSU

A technique for studying quantum field theories that has been very successfully applied to the Yang-Mills theories of particle physics is discretization. In it, one replaces the differential equations for the theory for equations in finite differences. Among other things, this makes them amenable to treat them using computers.

A problem that arises when trying to apply these techniques in gravity is that the discretization tends to clash with the symmetries of the theory. In theories of gravity of geometric type, like general relativity, points in space-time can be smoothly moved around, a symmetry known as diffeomorphisms. The rigid nature of discretization breaks that symmetry.

This talk addresses this problem through a technique known as coarse graining. In it, one breaks physical systems into subsystems and characterizes the latter through observable quantities that are invariant under the symmetries of the theory. This leads to observables associated with the edges of the region, hence the title of the talk. The coarse graining allows to introduce discretizations compatible with the symmetries of general relativity. This is shown in detail in this talk for the 2+1 dimensional case.

One of the features found is that when piecing together the domains of the coarse graining, the edge degrees of freedom cancel out and one is left only with corner degrees of freedom that can be thought as "particle excitations". The space of quantum states is that of ordinary loop quantum gravity (spin networks) with the addition of the particle excitations. The work shows that spin networks can be obtained by classically discretizing general relativity. This opens possibilities for studying the classical limit and the dynamics. Work is in progress to generalize the results to 3+1 dimensions.

Thursday, December 6, 2018

Quantum theory of charged isolated horizons

Tuesday, Dec. 4th

Konstantin Eder, Hanno Sahlmann, FAU Erlangen
Title: Quantum theory of charged isolated horizons 
PDF of the talk (600K)
Audio+Slides of the talk (32M)

By Jorge Pullin, LSU

Thermodynamics is the branch of physics that deals with systems about which we have incomplete information. A prototypical thermodynamics system is a gas: we will never be able to follow the motion of all the molecules of a gas, there are too many. One describes such systems using macro variables. Some are well known like the volume, the pressure or the temperature. A less well known macro variable is the entropy, which is a measure of our ignorance about the system. When physical systems interact the total entropy always increases.
It came as a surprise when Bekenstein proposed that black holes had a thermodynamic description. Since the area of the horizon of a black hole is proportional to its mass and everything that falls into the black hole cannot get out, it means that when something interacts with a black hole its mass always grows. And since we cannot know what is in the interior of a black hole, the area of the horizon is a measure of that ignorance. So Bekenstein suggested that the entropy of a black hole was proportional to its area. The thermodynamic picture got completed when in 1975 Hawking showed that if one took into account quantum effects, black holes radiated as a black body with a given temperature.

Loop quantum gravity provides a detailed explanation of the entropy of a black hole. In loop quantum gravity finite surfaces can in principle have zero area. They get endowed with "quanta of area" when they are pierced by the loops that characterize the quantum states. A surface can be endowed with a certain value of the area by many different loop quantum gravity states. So just giving the area we have a certain ignorance of the quantum state that gave rise to it. A detailed counting of that ignorance is therefore a notion of entropy and it has been shown that it is proportional to the area.

This talks extends these results to the case in which black holes are in the presence of quantum fields, more specifically Yang-Mills fields, which are the theories that describe particle physics. It shows that the entropy is still proportional to the area, but that higher order corrections may depend on the charges of the Yang-Mills fields. This provides a nice consistency test that shows that the entropy is still mainly proportional to the area even if one is in a non-vacuum situation with the presence of fields.

Wednesday, November 28, 2018

A holographic description for boundary gravitons in 4D

Tuesday, Nov 20

Bianca Dittrich, Perimeter Institute
Title: A holographic description for boundary gravitons in 4D 
PDF of the talk (5M)
Audio+Slides< of the talk (38M)
By Jorge Pullin, LSU

Holography has become a central concept in gravity. It is the idea that the description of gravity in a region of spacetime can be mapped to the description of a quantum field theory on the boundary of the spacetime. It originated in string theory as part of the "Maldacena conjecture" but it proved to be a more fundamental concept that does not require string theory for its formulation.

In this talk, holography was first reviewed in the context of three dimensional spacetimes, where the theory of gravity is much simpler than in four space-time dimensions, as spacetimes are locally flat in 3D. In particular, the example of the torus was discussed in detail. It was presented how to use Regge calculus (an approximation to general relativity using a triangulation in terms of simplices) to construct the boundary theory.

The talk then moved to four dimensional spacetimes starting with the simpler example of the flat sector of gravity where one only considers flat spacetimes. Again, the boundary theory was constructed using Regge calculus and the example of the three torus was discussed. It concluded with some future directions for the full theory, discussion of the symmetry group of the theory at infinity and possible implications for black hole entropy.

Wednesday, October 24, 2018

A unified geometric framework for boundary charges and dressings

Tuesday, Oct 23rd

Aldo Riello, Perimeter Institute
Title: A unified geometric framework for boundary charges and dressings 
PDF of the talk (2M)
Audio+Slides of the talk (41M)
By Jorge Pullin, LSU (with some help from Aldo)

The electromagnetic force and all the subatomic interactions are described by a class of theories known as “gauge theories”. Even gravitation, in its modern formulation due to Einstein, is a gauge theory of sorts, although a more complicated one. The mathematical formulation of these theories is characterized by peculiar redundancies, as if the simplest way to describe the system is through a plethora of different descriptions rather than through a single “true” one. This is most often seen as a mathematical quirk rather than as a hint of some deep property of nature. This talk explores the latter possibility and build on the idea that the rationale for gauge theories must be found not so much in some property of a single system taken in isolation, but rather in the way systems can come together and talk to each other. The first hint of this can be found in the fact that the natural objects populating a gauge theory (“observables”) are intrinsically nonlocal and therefore can’t be easily localized in a given region, without carefully keeping track of what happens at its boundaries. The simplest example of this phenomenon can be found in the electron, that can never be separated from its electric field, which in turn can be detected even at a distance from the electron. This talk presents a novel mathematical framework that by embracing the relational perspective unifies many seemingly unrelated aspects of gauge theories and might – in its future developments – clarifies the analogous but harder conceptual issues one finds on their way to quantum gravity.