Sunday, March 25, 2018

Cosmological non Gaussianity from loop quantum cosmology

Tuesday, Mar 6th

Ivan Agullo, LSU
Title: Non-Gaussianity from LQC 
PDF of the talk (22M)
Audio+Slides [.mp4 19MB]
By Jorge Pullin,  LSU

The standard picture of cosmology is that the universe started in the "big bang" and then underwent a period of rapid expansion, called inflation. During those initial moments, densities are very high and matter is fused into a primordial "soup" that is opaque, light cannot travel through it. As the universe expands and cools, eventually electrons and protons form atoms and the universe becomes transparent to light. The afterglow of that initial phase can then travel freely through the universe and eventually reaches us. Due to the expansion of the universe that light "cools" (its frequency is lowered). In the 1960's to Bell Telephone Co. engineers were working on a microwave antenna and discovered a noise they could not get rid of. That noise was the afterglow of the Big Bang, that by then had cooled off into microwaves. That afterglow has been measured with increasing precision using satellites. It is remarkably homogeneous, if one looks into two different directions of the universe, the difference in temperature (frequency) of the microwave radiation is equal to one part in 100,000. The diagram below has those temperature differences magnified 100,000 times to make them visible, different colors correspond to different temperatures. The whole celestial sphere is mapped into the oval.
At first, it appears that the distribution of temperature is sort of random. But it is not, it has a lot of structure. To characterize the structure, one picks a direction and then moves away from it a certain angle and draws a circle of all directions forming the same angle with the original direction one picked. One then averages the temperature along the circle.  Then one averages the result for all possible initial choices of direction. If the distribution were truly random, if one plotted the average computed as a function of the angle, one would get a constant, no angle would be preferred over others. But what one gets is shown in the following diagram,
In the vertical are the averages, in the horizontal, the angles. The dots are experimental measurements. The continuous curve is what one gets if one evolves a quantum field through the inflationary period, starting from the most "quiescent" quantum state possible at the beginning, called "the vacuum state". The incredibly good agreement between theory and experiment is a great triumph of the inflationary model. The quantity plotted above is technically known as the "two point correlation". Loop quantum cosmology slightly changes the predictions of standard inflation, mostly for very large angles. There, the experimental measurements have a lot of uncertainty and are not able to tell us if loop quantum cosmology or traditional inflation give a better result. Perhaps in a few years better measurements will allow us to distinguish between them. If loop quantum cosmology is favored it would be a tremendously important experimental confirmation. But we are not there yet.

One can generalize the construction we made with two directions and an angle between them to three directions and three angles between them, and so on for higher number of directions. These would be known technically as the three point correlation, four point correlation, etc. If the distribution of temperatures were given by a probabilistic distribution known as a Gaussian, all the higher order correlations are determined by the two point correlation, there is no additional information in them. 

In this talk a study of the three point correlations for loop quantum cosmology was presented. It was shown that non-Gaussianities appear. That is, the three point correlation is not entirely determined by the two point one. Satellites are able to measure non-Gaussianities. In the talk it was shown that depending on the values chosen for the quantum fields at the beginning of the universe, the non-Gaussianities predicted by loop quantum gravity can be made compatible with experiment. This is not strictly speaking an experimental confirmation since one had a parameter one could adjust. But the good news is that the values needed to fit the data appear very natural. Again, future measurement should place tighter bounds on all this.

Image credits: Cosmic microwave background Wikipedia page.

Quantum spacetimes on a quantum computer

Tuesday, Mar 20th

Keren Li, Tsinghua University
Title: Quantum spacetime on a quantum simulator 
PDF of the talk (3M)
Audio+Slides [.mp4 11MB]

By Jorge Pullin, LSU

In loop quantum gravity the quantum states are labeled by objects known as "spin networks". These are graphs in space with intersections. If one evolves a spin network in time one gets a "spin foam". If one had a static situation, the various spatial slices of a spin foam would be the same, as shown in the figure,
If one were in a dynamical situation, new vertices are created,
To compute the probability of transitioning from a spin network to another is what calculations in spin foams are about. The details of these computations resemble computations people do in quantum mechanics of systems with spins. This allows to make a parallel between these computations and the ones that are involved in setting up a quantum computer, specifically the qubits that are constructed using nuclear magnetic resonance systems (NMR). In this talk it was described how the evolution of a very simple spin foam known as the tetrahedron can be simulated on an NMR quantum computer of four qubits and how the experimental measurements reproduce very well theoretical calculations of spin foam models.

Tuesday, February 6, 2018

Using symmetries to determine the dynamics

Tuesday, Feb 6th

Ilya Vilensky, Florida Atlantic University
Title: The unique form of dynamics in LQC 
PDF of the talk (0.5M)
Audio+Slides [.mp4 11MB]

By Jorge Pullin, LSU

Loop quantum cosmology is the application of ideas of loop quantum gravity to the context of cosmology, where one freezes most degrees of freedom and studies just a few large scale ones, like the volume of the universe or its anisotropy. Loop quantum cosmology is not "derived" from loop quantum gravity, in the sense of choosing in the full theory quantum states that are very symmetric with only a few degrees of freedom and study their evolution. That is at the moment, too complicated. In loop quantum cosmology one first freezes the degrees of freedom one wishes to ignore and then proceeds to quantize the remaining ones. It is not clear that this coincides with "quantizing and then freezing". It is therefore important to run cross checks to make sure that at least within the approximation considered, things are consistent.

In spite of the enormous simplification one obtains when one first freezes most degrees of freedom and then quantizes, there are still quite a few ambiguities in the quantization process. This talk showed in the example of anisotropic universes, how imposing the residual symmetries and left after freezing most degrees of freedom, and demanding that the correct classical limit follow, allows to cut down on the number of ambiguities present. This increases the confidence in results previously obtained in loop quantum cosmology, some of which may have observable implications for the anisotropies of the cosmic microwave background radiation.

Monday, January 29, 2018

New dynamics for quantum gravity

Tuesday, Jan 23rd

Cong Zhang, Univ. Warsaw/Beijing
Title: Some analytical results about the Hamiltonian operator in LQG 
PDF of the talk (1.7M)
Audio+Slides [.mp4 10MB]

by Jorge Pullin, LSU

One of the central elements when building quantum theories using the approach known as "canonical" is to define a quantity known as the Hamiltonian. This quantity is responsible for the time evolution of the system under study. In general relativity, when one tries to construct such quantity one notices it vanishes. This is because in general relativity one can choose any arbitrary time variable and therefore there is not a uniquely selected evolution. One needs to make a choice. One such choice is to use matter to play the role of a clock. That leads to one having a non-vanishing Hamiltonian. In this work a detailed construction for the quantum operator associated with such Hamiltonian in loop quantum gravity was presented. The implementation presented differs from others done in the past. Among the attractive elements is that it can be shown in certain circumstances that the operator has the desirable mathematical property known as "self-adjointness". This property ensures that physical quantities in the theory are represented by real (as opposed to complex) numbers.

A discussion was also presented of how the operator acts on certain states that behave semi-classically known as "coherent states", in particular in the context of cosmological models. It was observed that it leads to an expanding universe.

Monday, January 15, 2018

Construction of Feynman diagrams for group field theory

Tuesday, Dec 5th

Marco Finocchiaro, Albert Einstein Institute
Title: Recursive graphical construction of GFT Feynman diagrams 
PDF of the talk (1M)
Audio+Slides [.mp4 24MB]

By Jorge Pullin, LSU.
A common technique for computing probability amplitudes in quantum field theory consists in expanding such objects as power series in term of the coupling constant of the theory. Each term in the expansion, usually involving complicated expressions, can be represented in a pictorial way by using diagrams. This graphical technique (known as "Feynman diagrams method") allows to write down and organize the terms in the perturbative series in a much easier way.

Group field theories (GFTs) are ordinary quantum field theories on group manifolds. Their Feynman amplitudes (i.e. amplitudes associated to Feynman graphs) correspond by construction to Quantum Gravity Spinfoam amplitudes. There exists an analogue situation in 1+1 dimensional theories known as matrix models, which are quantum field theories whose Feynman diagrams are related to the path integrals for gravity in 1+1 dimensions. From this point of view group field theories can be seen as a four dimensional generalization of matrix models.

The seminar, articulated in three parts, dealt with several aspects concerning the construction of GFT's Feynman diagrams and the evaluation of the corresponding amplitudes. In the first part a general introduction to group field theory was provided, stressing the importance of studying the divergences appearing in the amplitudes' computations. Indeed they can be used as tools to constraint and test the type of theories that can be built. In the second part the main methods to extract the amplitudes' divergences were briefly reviewed. Moreover a new GFT/Spinfoam model for Euclidean quantum gravity was presented. The last part was devoted to the seminar's main topic, namely the generation of Feynman graphs in group field theory. Beyond the leading order in the power series expansion this is often a difficult task. It was shown how to construct GFT's Feynman diagrams using recursive graphical relations that are suitable for implementations in computers. Future works will deal with making the computations parallelizable.

Entanglement in loop quantum gravity

Tuesday, Nov 7th

Eugenio Bianchi, PennState
Title: Entanglement in loop quantum gravity 
PDF of the talk (9M)
Audio+Slides [.mp4 19MB]

By Jorge Pullin, LSU

Entanglement is one of the most fascinating new concepts introduced in quantum mechanics. When quantum systems interact, the resulting systems properties cannot be described by considering the properties of the individual systems. One needs to consider global properties of the set of systems as a whole. Not only one cannot reconstruct the properties of the whole from the properties of the constituent parts. It turns out that the properties of the constituent parts cannot be determined if one does not know the properties of the whole. Entanglement entropy is a quantity that measures "how much entanglement" there is in a set of quantum systems. This seminar dealt with the application of this concept to the quantum states of loop quantum gravity. Here one tries to understand how different regions of space become entangled with each other in a quantum geometry and how the entanglement entropy measures such entanglement. 

This is not a mere theoretical development. Quantum theory plays an important role in cosmology. We now know that the fluctuations we see in the cosmic microwave background radiation are the product of the evolution of the vacuum state of the inflaton field during inflation. If one assumes that before inflation the field was in a vacuum state and evolves it, the state develops non-trivial correlations that are precisely the ones observed in the cosmic background radiation fluctuations. 
The cosmic microwave background fluctuations. Credit: NASA/WMAP team.

The vacuum state of a quantum field is a highly entangled state. Therefore the correlations one observes in the cosmic microwave background are directly related to entanglement. This seminar raises the mesmerizing possibility that the particular type of entanglement that occurs in the states of loop quantum gravity could leave an observable imprint in the cosmic microwave background radiation. This occurs through their evolution from the big bounce that loop quantum cosmology replaces the big bang with  up to the beginning of inflation influencing the type of vacuum the inflaton starts in. 

Wednesday, January 10, 2018

Black holes exploding into white hole fireworks

Tuesday, Oct 24th

Marios Christodoulou, Aix Marseille U/SUSTec Shenzen
Title: Geometry transition in covariant LQG: black to white 
PDF of the talk (3M)
Audio+Slides [.mp4 11MB]

By Jorge Pullin, LSU

Black holes are regions of space-time where gravity is so intense that nothing, including light, can escape, hence they are black. They are expected to form as stars exhaust their nuclear fuel and start to contract due to gravitational attraction. Eventually they become so dense that a black hole forms. According to classical general relativity, the star matter continues to contract inside the black hole until the density diverges. That is what is known as a "singularity". Obviously nothing can diverge in nature so it is believed that the singularities are an indication that one has pushed general relativity beyond its domain of validity. One expects that at high densities quantum effects should arise and a theory of quantum gravity is needed. There has been some progress in spherically symmetric loop quantum gravity that indicates that the singularity is replaced by a highly quantum region that eventually leads to another classical region of space-time beyond it. 

At the same time Hawking showed in the 70's that if one puts quantum fields to live on the classical background of a black hole, radiation is emitted as if the black hole behaved as a black body with a temperature inversely proportional to the black hole's mass. There is no contradiction with the black hole radiating because the radiation is produced by the quantum field outside the black hole. If the black hole radiates, then it should lose energy. Hawking's calculation cannot study this, because it assumes the quantum field lives in a fixed black hole background. It is expected that more precise calculations including the back-reaction of the field on the background should make the black hole shrink as it emits radiation. As the temperature increases as the black hole loses mass (it is inversely proportional to the mass) the black hole heats up and radiates more. Eventually it should evaporate completely. No detailed analysis of such evaporation is available at present. Such evaporation raises many questions, in particular what happened to the singularity inside the black hole (or the highly  quantum region that apparently replaces it). What happened to all the information of the matter that formed the black hole? Is it lost?

The work described in this seminar posits that the highly quantum region inside the black hole transitions into the future into a "white hole" (the time reverse of a black hole). A great explosion in which all the information that entered the black hole exits. This scenario is known as "fireworks". An important question is: does the explosion happen fast enough for it to make the loss of information through Hawking radiation irrelevant? In this seminar spin foams are used to try to address the question. The calculation at hand is to compute the probability of transition from a black hole to a white hole. There are many assumptions needed to make such calculation, so the results are at the moment tentative. However, the main conclusion seems to be that the explosion takes as long as the process of Hawking evaporation to take place. This may rule out the "fireworks" as candidates for fast radio bursts that have been observed by astronomers, but may keep in play other astrophysical predictions associated with them.