Black hole collapse and bounce in effective loop quantum gravity

 Tuesday, November 24th

Edward Wilson-Ewing, University of New Brunswick

Black hole collapse and bounce in effective loop quantum gravity
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By Jorge Pullin, LSU

Stars are balls of fluid that are try to contract through their own gravitational attraction but are kept form doing so by burning nuclear fuel, which also makes them shine. When the fuel gets exhausted they start to contract. Depending on the details, the contraction can become uncontrollable, leading to an object so dense that gravity is so intense that not even light can escape from them. That is what is known as black hole. The matter continues to contract inside the black hole and eventually get highly concentrated. In classical general relativity, this leads to a "singularity", a point where density is infinite. It is expected that quantum gravity will eliminate such singularities, replacing them by a highly quantum region of high curvature.

Loop quantum gravity has led to scenarios of that nature. These investigations are pursued by restricting strongly the degrees of freedom of the problem before quantizing, this makes quantization possible. In this talk one of such proposals was considered. The particular freezing of degrees of freedom requires choosing certain coordinate systems that simplify the equations. This allows to treat the problem including the presence of matter. This in turn opens the possibility of studying how the matter collapses, forms the black hole, and then, since things never become singular, the matter explodes into a "white hole", the time reversal of a black hole. This opens new possibilities for understanding the ultimate fate of black holes and what happens to the information that falls into a black hole, is it lost or is it recovered? Further research will shed light on these issues.

Quantum gravity at the corner

 Tuesday, October 27th

Marc Geiller, ENS Lyon

Quantum gravity at the corner 
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By Jorge Pullin, LSU

Many physical theories are described in terms of more variables than needed. That includes field theories like general relativity. For an analogy consider a pendulum. We can describe it by giving the x,y coordinates of the bob, even though everything is completely characterized if one just gives the angle of the pendulum wire with respect to the vertical. When one has extra variables there may exist many sets of values of them that correspond to the same physical situation. In the pendulum x=1,y=1 and x=2,y=2 both correspond to the wire at 45 degrees. So it is said that these theories have symmetries in the sense that many mathematical configurations correspond to the same physical situation. These are mathematical, not physical symmetries. However, if one considers bounded regions of space-time those mathematical symmetries translate into physical symmetries and into conserved quantities. For instance the electric charge. To define electric charge one needs to define a region it is contained in.

More recently the concept has appeared in physics that one can describe what is happening in a region of space-time by describing what is happening at its boundary. An example of this is the so called AdS/CFT or Maldacena conjecture in string theory. This applies to a specific type of space-times called anti de Sitter (AdS) and it says that the description of gravity in the space-time is equivalent to a special type of field theory called conformal field theory (CFT)  that lives on the boundary of the space-time. This property of encoding the information of a space-time in its boundary is known as "holography" by analogy with the optical phenomenon where three dimensional images are captured on a two dimensional photograph.

This talk addressed studying bounded regions of space-time, more precisely bounded regions of a spatial slice of a space-time, where the boundary is two dimensional and is called "corner" in math. It was explored what is the most general set of symmetries that one can formulate and their implications in the corners. It was observed that certain properties of loop quantum gravity, like the quantization of the areas, arise naturally in this context. This way of viewing things opens a new approach to loop quantum gravity that may offer connections with the ideas of holography in string theory.

I benefited from discussions with Ivan Agulló while preparing this text.

Effective Spin Foams & the Flatness Problem

 Tuesday, September 29th

Hal Haggard, Bard College

Effective Spin Foams & the Flatness Problem
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by Jorge Pullin, LSU

The spin foam approach to quantum gravity emanates from loop quantum gravity and from treating space-time as a whole. Initially, loop quantum gravity was formulated in what is known as the "canonical" approach in which space-time is treated as a bunch of spaces that evolve. Space is represented by quantum states known as spin networks that are networks of lines with intersections and with numbers associated to them. If you can imagine one of those spatial networks sweeping forward in time, the result looks like a foam, hence the name spin foams. How the spin networks evolve as they sweep forward determines the dynamics of the theory, something known as "the vertex", because it involves the creation of new intersections in the spin network. There have been over time several proposals for such vertices, trying to capture as best as possible the quantum dynamics of general relativity

Regge Calculus is an approach to classical general relativity. In it, space-times are approximated by flat sections, pretty much like a geodesic dome approximates a sphere through its flat sections. It has the advantage that it cuts down the infinite number of degrees of freedom of a field theory like general relativity to a finite number. Due to this it can also be used to treat the theory numerically.

This talk used a Regge Calculus approach to define a new "vertex" for spin foams. It inherits the convenience of Regge Calculus as a computational tool. Several numerical experiments were carried out successfully and there are proposals for new ones to come.

Gravitational waves with a cosmological constant

 Tuesday, September 1st

Maciej Kolanowski, Warsaw University

Lost in translation -- energy in the de Sitter universe
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By Jorge Pullin, LSU

One normally tries to think of space-time as space with an extra dimension. But time has a particular nature. This gives space-time unique properties that ordinary three dimensional space does not have. One of them is the nature of infinity. In space-time there are more than one infinity. Objects that travel at speeds slower than light (like humans) finish their lives in a certain infinity, whereas objects that travel at the speed of light, like electromagnetic or gravitational waves end in a different infinity, known as null infinity. 

Infinity is important because it is the point where discussions of energy in gravitational physics are meaningful. By sitting at infinity one ensures that one includes all the energy involved in the universe. Discussions of energy are important, for instance, in the context of gravitational waves. We know that binary systems in astronomy emit gravitational waves that carry energy to infinity and that determines that the systems' orbits inspiral and eventually merge. This has been verified dramatically in the last few years with the discovery of gravitational waves by interferometric detectors like the LIGO detectors.

The discussion of infinity in space-time changes when one has a cosmological constant present. This is important because our best measurements today indicate that indeed we live in a universe with a cosmological constant. This requires revisiting the definitions of energy and conserved quantities in space-time. This talk dealt with this point. It presented new definitions for the emitted energy and compared with other ones already present in the literature.

Alleviating tensions in the cosmic microwave background using loop quantum cosmology

Tuesday, Feb. 18th.
Brajesh Gupt/Abhay Ashtekar, TACC/PSU

Title: Alleviating tensions in the CMB using LQC.
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By Jorge Pullin, LSU

The cosmic microwave background is radiation that reaches us from the big bang. Its wavelength (temperature) is incredibly uniform. If one looks in one direction in the sky and then another, the temperature is the same to one part in 100,000. But the tiny temperature differences between microwaves coming from different directions have been measured and they are not completely random. If one looks in one direction in the sky and then considers the ring of all possible directions a certain angle away from the original one and one averages the temperature along the ring, one does not get zero, as would be the case if the deviations were random. If one plots that deviation as a function of the angle, one obtains a curve with clear features (Credit NASA/WMAP team):

Remarkably, this curve can be rather straightforwardly predicted by the so called inflationary model. In it, the universe suffers a period of rapid expansion. If one considers a quantum field living in the universe in its simplest state (the vacuum) at the beginning of inflation and one evolves it through inflation, the field will develop correlations and those correlations are the ones observed. In the above figure the red dots are experimental points obtained by the WMAP satellite of NASA and the green curve is the prediction of inflation. The agreement is astonishing.

In spite of the agreement, there are some anomalies. If you look at the curve for large angles (left of the diagram) the points do not align as well as in the rest. Another anomaly is the lensing amplitude anomaly. It appears when one studies more complicated correlations than the one discussed before. That one was what is called the "two point" correlation function for the two directions in the sky one looks at. There are more complicated correlations involving three and four points. In the latter, the predictions of standard inflation scenario in the standard cosmological model do not square as well with observations, though the discrepancies are small.

Loop quantum gravity slightly modifies the predictions of inflation. In loop quantum gravity the Big Bang gets replaced by a "bounce" from a previous universe. In such a scenario, there is no good reason to put the quantum field in its simplest state at the outset of inflation. It would be much more naturally to either put it at the bounce or at the beginning of the previous universe. It turns out that things do not change much if one chooses one or the other of those options. The important thing is that by the time inflation starts, the field is not in a vacuum anymore and that modifies the correlations one sees in the cosmic microwave background.

This talk argued that the different correlations that loop quantum gravity predicts actually allow to solve the two anomalies we described above. Loop quantum gravity is not the only model that explains the anomalies, but compared to others, it is much cleaner in that includes essentially no free parameters to tweak and it is therefore more remarkable that it agrees with nature than other models with more freedom to tweak.

Effect of ambiguities in loop cosmology on primordial power spectrum

Tuesday, Feb. 4th.
Parampreet Singh, LSU

Title: Effect of ambiguities in loop cosmology on primordial power spectrum
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By Jorge Pullin, LSU.


Cosmology is the study of the universe as a whole. You might ask, how can they study the universe, such a complicated system? The answer: very coarsely. One ignores many degrees of freedom and concentrates on a few. In its simplest incarnation, the study of cosmology is what is known as a minisuperspace approximation. One freezes all degrees of freedom except a handful. In the simplest case, one only concentrates on the universe's size. Since this is just one number, the equations for it become very simple.

However, we would like to study more features of the universe. To this aim, a technique used is known as perturbations. One assumes that the universe is simple enough that one can concentrate on its size, this will constitute the "background" on which small deviations are considered. One can then write equations for those small deviations that are simple enough to deal with. Such approach has led to spectacular predictions.

Perhaps the most striking ones ar the predictions for the anisotropies of the cosmic microwave background.  This is composed by light that arrivesat the Earth after traveling all the way from the Big Bang. Because the universe has expanded in the meantime, it has "cooled" (its wavelength havs become larger) and that is why we receive it as microwaves, which have comparatively large wavelengths compared to ordinary light. It turns out if one looks into two different directions of the sky the "temperature" (wavelength) of the microwaves that are incoming are exactly the same. They agree to one part in 100,000. The tiny disagreements however, are not random in nature, they have patterns in their structure. And those patterns have been measured with microwave satellites. And they agree remarkably well with the predictions of perturbation theory.

 Loop quantum cosmology is the application of loop quantum gravity techniques to cosmology. The resulting quantum cosmologies have been studied with tiny perturbations living in them. The results are that the predictions are almost the same of the classical theory, but with some deviations that at the moment are unobservable experimentally.

When one quantizes theories, there is not a single procedure you can follow. Different procedures lead to slightly different theories, with different predictions. This talk concentrated on how such differences in the treatment of the background solution impact the predictions on the anisotropies of the cosmic microwave background. The main conclusion is that, in spite of the ambiguities in the quantization, the resulting predictions exhibit robustness, enhancing our confidence on their physical plausibility. These predictions are perhaps the closest we are to an experimental test of quantum gravity so it is very important that they do not have significant ambiguities in them.