Power spectrum in effective theories for inflation

Tuesday, September 10th

Mauricio Gamonal San Martin, Penn State
Primordial power spectrum in effective theories for inflation>
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By Jorge Pullin, LSU.

The main achievement of inflationary cosmology is how it reproduces the inhomogeneities of the Universe using a relatively simple model. You put a quantum field in its simplest state -the vacuum-, evolve it through inflation (a period of exponential expansion of the Universe) and voila, the quantum state acquires non-trivial features that leave an imprint on the Universe that matches beautifully the inhomogeneities we observe in the cosmic microwave background (CMB). 

Beyond that simple story, people have proposed slightly different models for inflation to address several issues. In particular, if one considers quantum gravity further modifications are possible.While quantum gravity effects are typically too weak if inflation lasted too long, they could play a role in setting different initial conditions if a pre-inflationary epoch occurred, for example by preparing an excited vacuum state for the quantum fields. This is exciting because it means that quantum gravity effects could leave observable imprints in the observations of the CMB.

This talk presented a unified treatment of a large group of models of inflation and their potential observable imprints on the CMB, including those stemming from loop quantum gravity and spinfoams.

Localized energy of gravitational waves

Tuesday, Mar 5th 

Simone Speziale, Aix Marseille University
Localized energy of gravitational waves
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By Jorge Pullin (LSU)

The idea of associating a local energy density to a gravitational field has been problematic in general relativity. In electromagnetism, a region with an electric or magnetic field contains an energy whose density (energy per unit volume at a point) is proportional to the field squared. In gravity, however, things are more complicated. This is illustrated by a thought experiment first proposed by Einstein. Consider an observer in a windowless elevator and two situations: a) the elevator is in outer space, where gravity is negligible, but accelerating at a rate of 9.8 m/s2, the acceleration of gravity on Earth, and b) it is motionless on the surface of the Earth. In both cases if the observer releases a mass, it will fall to the floor with the same acceleration. No experiment carried out in the elevator can distinguish both situations. Therefore, one could not claim that one has an energy content and the other does not.

Over the years this has led to confusion and to attempts to create local energy densities that are problematic, namely, they are ambiguous and coordinate-dependent. For many years the issue of if gravitational waves carried an energy flux was contentious, eventually being settled in the1960's. The end result is that one cannot define a local energy density but must discuss energy considerations only considering complete regions of space-time and studying them from far away. Mathematically this requires treating fields at infinity. One can define energies and fluxes in an invariant way at infinity only.

This talk discussed some of the subtleties involved and presents a framework where infinity and other regions of interest, like the horizons that surround black holes, can be treated in a unified way. This may lead to insights into what are the true physical degrees of freedom that one should consider quantizing in a theory of quantum gravity.

Reviving Quantum Geometrodynamics

Tuesday, Nov. 14th
Susanne Schander, Perimeter Institute
Quantum Geometrodynamics
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By Jorge Pullin, LSU

Geometrodynamics is the name John Archibald Wheeler gave to the description of space-time completely in terms of geometry and its eventual quantization. The description of space-time is in terms of a metric of space that evolves in time. 

An approach to quantization that has been successful for the kind of theories that describe particle physics, like chromodynamics -which describes the strong interactions inside nuclei-, is the use of lattices. In it, one approximates the differential equations of the theory by finite differences. This has two upshots. On the one hand, infinities that tend to arise associated with the differential equations are eliminated. On the other hand, the resulting equations are amenable to be solved on a computer. The resulting approach is known as lattice gauge theory. Its application to the theory of strong interactions, lattice quantum chromodynamics, allows for instance to compute the mass of the proton.

Since the gauge theories of particle physics are typically represented in terms of a vectors like the potentials that appears in electromagnetism, attempts to apply lattice techniques to gravity have usually started from formulations of the theories in terms of potentials. The formulation used to set up loop quantum gravity would be an example. In this talk the use of lattices was explored with the traditional formulation of gravity used in geometrodynamics. Among the issues discussed was how to keep the metric of space yielding positive distances in the quantum theory. Moreover, a method to represent the symmetries of the theory on the lattice was given. Also the issue of the continuum limit, that is, how to retrieve from the discrete theory the continuum behavior we observe in space-time at large scales was addressed.

Quantum reference frames

Tuesday, March 7th
Flaminia Giacomini, ETH Zurich

Quantum reference frames
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By Jorge Pullin, LSU

It is generally accepted that the energies at which full quantum gravity effects will be relevant are so high that there is no chance of generating them in the laboratory. Full quantum gravity is only expected to be relevant in extreme environments like deep inside black holes or near the origin of the universe.

Nevertheless, there is interest is studying situations in which both quantum effects and gravity are important. Experiments can currently probe gravitational effects of masses as small as 90 milligrams, or quantum superpositions at scales of half a meter. These types of situations, though short of fully quantum gravitational in essence, can offer experimental guidance in a field that is notoriously short of it.

The talk focused on the issue of quantum reference frames. Reference frames are commonly used in physics and are treated as idealizations. In reality, any reference frame is a physical system and is subject to the laws of quantum mechanics like any other. Taking that into account leads to modifications in the form of the laws of physics from the one they take in idealized frames. In particular several important quantum properties like the "entanglement" that physical systems exhibit is a frame dependent phenomenon. Also the equivalence principle, the statement that all masses fall at the same acceleration in gravity, can be extended to be valid in quantum reference frames and in situations such as a massive object in a spatial quantum superposition.

The summary is that we do not currently know which experiments will prove definitively that gravity has quantum features, and probing regimes involving quantum mechanics and gravity can offer guidance on how to quantize gravity.

 Tuesday, November 8th

Mehdi Assanioussi, University of Warsaw

Matter in LQG
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by Jorge Pullin, LSU

Traditional quantum field theories are formulated using a mathematical framework called the Fock representation. In such mathematical framework physical elements like the notion of particles like photons and their properties have a well-defined mathematical counterpart. This framework is also used in quantum field theory in curved space-time, an approximation to full quantum gravity in which one treats gravity classically as a curved space-time and studies quantum fields that live on it. Quantum field theory in curved space-time has been extensively developed since the 1960’s and has led to major predictions like Hawking radiation or particle production in the early universe. If loop quantum gravity is to provide a good description of nature, one expects a connection of its framework with that of quantum field theory in curved space-time should emerge.

To this aim, Varadarajan, in the early years of this century, developed the r-Fock representation for quantum fields on flat and curved space-times. This representation has elements in common both with the loop representation used in loop quantum gravity and the Fock representation. At first it was only developed for Abelian quantum fields (like photons) and this was viewed as a limitation of the framework. Later, Ashtekar and Lewandowski presented a generalization to non-Abelian fields (like gluons), but it had some technical difficulties. The speaker, together with Lewandowski, has recently developed an alternative version of the r-Fock representation that bypasses the technical difficulties. The talk discussed this approach and outlined possibilities for it. Open questions include how to formulate the dynamics of loop quantum gravity in this representation and if it could help recover the continuum picture of classical space-time from the inherently discrete picture that loop quantum gravity yields at the quantum level.

The search for tabletop quantum gravity signatures

 Tuesday, Apr 5th

Marios Christodoulou, University of Vienna

The search for `table-top' quantum gravity signatures
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By Jorge Pullin, LSU

We know that the strong, weak and electromagnetic interactions require of quantum mechanics for their correct descriptions. This is in part because those three forces are important at the microscopic level and we know that at that level classical mechanics fails. Gravity is a bit different. At the microscopic level, its effects are negligible. For instance, the electric repulsion of two electrons (they have the same charge) is 10⁴⁴ (that is one followed by 44 zeros) times larger than their gravitational attraction. Gravity is important in the macroscopic world, where quantum effects are washed out due to the large presence of degrees of freedom. Do we need to quantize gravity, then? Conceptual reasons suggest it, we do not really know how to consistently couple classical and quantum theories.

Recently, advances in quantum technologies have allowed to study gravitational interactions among objects of ever shrinking sizes. This opens the possibility of revealing quantum phenomena. In particular a phenomenon called entanglement in which the properties of the two masses become intertwined. But do they include quantum aspects of gravity? The issue is hotly debated. The experiments involve tiny levitated masses that are at microscopic distances from each other. Usually dynamics becomes clearer when masses are far away from each other, since one can introduce notions like waves, photons and gravitons, that are more difficult to characterize close to their sources. This has led to several claims and counterclaims in the literature. The talk gave an overview of the issues and papers involved and suggested that experiments in the relatively near future could help clarify the situation and perhaps offer a conclusive probe of the quantum nature of gravity.

Clock dependence and unitarity in quantum cosmology

Tuesday, Mar 22nd
Lucía Menéndez-Pidal, Nottingham University

Clock dependence and unitarity in quantum cosmology
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By Jorge Pullin, LSU

In ordinary physics, time (and space) are given once and for all. They are "background" quantities that do not evolve. In theories of gravity like general relativity, where one describes gravitational effects not as the result of a force but as a deformation of space-time, things are different. To begin with, unless one considers a concrete gravitational configuration (a concrete space-time), time (and space) simply do not exist. Even after considering a given space-time, to interpret it as "an evolution" of space (and matter) as "a function of time", requires some care, especially when one is considering the quantum version of things. The most obvious procedure is to consider some variable of the problem, like the value of a matter field, and use it to "keep time". Some such choices can obviously be very bad. For instance, if one chooses the position of a rock that does not move as one's "time", the resulting "evolution" of what one is trying to study will not be something easily recognizable. Even if one makes "judicious" choices, it is not at all clear that the resulting evolutions can be considered physically equivalent. Difficulties are further compounded by details of how the Einstein equations operate.

This talk considered these questions in the simplified setting of homogeneous cosmologies, where spatial dependence is very simple, allowing to make calculations explicit and controlled. Even in this simplified setting, the talk showed there are several subtleties. One of the central properties of ordinary quantum systems, called unitarity, that essentially implies that information is not destroyed, is not automatically guaranteed. In loop quantum gravity applied to cosmology (loop quantum cosmology) the Big Bang singularity usually is eliminated and evolution is regular where in classical general relativity infinities appear. The talk showed that this feature is not guaranteed and depends on the choice of time made.

Polymerized black hole constraints from Hawking radiation

Tuesday February 8th 2022
Jeremy Auffinger, Univ. Lyon

Polymerized black hole constraints from Hawking radiation
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By Jorge Pullin, LSU

Black holes come in different kinds. The ones people are most familiar with are those that result when a star, with a mass a few times that of the Sun, collapses. Their mass is therefore a multiple of the mass of the Sun and are called "stellar sized" black holes. There are much larger black holes, with a mass a million to a billion times the mass of the Sun. These black holes are at the center of galaxies and presumably they formed by absorbing surrounding stars and other black holes. They are called supermassive black holes. A third class of black holes, which has not been observed directly yet, would consist of much smaller black holes. They are produced in the early universe from fluctuations in the density of matter. 

The way stars rotate around when they are in galaxies suggests that the latter contain more matter than what is visible. This is the origin of the conjectured "dark matter" present in them. There are various proposals for what could constitute dark matter, ranging from elementary particles of various kinds to primordial black holes. 

In the 1970's Hawking showed theoretically that black holes emit radiation much like a heated piece of metal does, with a characteristic temperature. The latter is inversely proportional to the black hole mass. For stellar-sized black holes, the temperature is very small, a millionth of a degree. As a result, the Hawking radiation from such black holes is unobservable in practice. Primordial black holes, as they are much smaller, would have a much higher temperature and therefore more Hawking radiation. This radiation has not been observed (yet) so it can be used to constrain the presence of these types of black holes. If one takes them as a candidate for dark matter, it helps put constraints on the resulting dark matter models.

Loop quantum gravity has been applied over the last decade to spherically symmetric situations, including black holes. Various different models have emerged, differing in the assumptions and provide a picture that differs in some details. But the main feature is they eliminate the infinities that appear in classical general relativity inside black holes and are known as the singularity. This was a long expected result of any successful approach to quantum gravity, as infinities do not exist in reality.

This talk analyzed the modifications to the calculations of Hawking radiation from primordial black holes, and consequently in dark matter models that involve them, if one considers the black holes that stem from loop quantum gravity. If the radiation from these black holes is ever observed it could therefore provide valuable experimental information about loop quantum gravity.

Imprints of black hole area quantization in gravitational waves

Tuesday, Jan 25th Adrián del Río, PennState

Imprints of black hole area quantization in gravitational waves
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By Jorge Pullin, LSU

One of the distinct places where quantum mechanics has an imprint on our everyday life is in atomic spectra. The theory says that atoms can only absorb and emit certain discrete quantities of energy (quanta) when they interact, for instance, with an electromagnetic field. Since the energy of photons is directly related with their frequency, this means that atoms emit light at specific frequencies. An example of this is easily seen by sprinkling table salt on an open flame. It will turn yellow, the color associated with the typical quanta of sodium. 

Quantum gravity theories predict that the mass (and therefore the area) of black holes is quantized. This means that when black holes interact with gravitational waves, the frequencies involved will be quantized. The situation is analogous to  that of atoms and electromagnetic radiation. This talk shows that this quantization can leave imprints in the types of gravitational waves that are currently being detected by interferometric gravitational wave observatories like LIGO or VIRGO. These waves come from collisions of black holes. The collisions perturb the holes and the latter "ring down" emitting gravitational waves, much like a bell rings down emitting sound waves (in fact, for Solar sized black holes the frequencies are similar, of the order of kiloHertz). This ring down would have imprints from the quantization of the area that appear as "echos", repetitive patterns in the waves emitted. 

The quantization of areas has long been expected in theories of quantum gravity. Usually people assumed that the quantization would be given by some integer multiple of the "fundamental" area given by the Planck length squared. The Planck length is the fundamental length one can construct using the gravitational constant G, the speed of light c and Planck's constant of the quantum theory known as "hbar". This talk showed that if areas are quantized in this way, then there are potentially observable consequences in gravitational waves detected from black hole collisions. Loop quantum gravity, on the other hand, has a more sophisticated prediction about the quantization of areas. In it, the quanta are not equally spaced, but quickly "bunch up" as one considers larger areas. This implies that for large black holes like the one LIGO can observe, the effects of the quantization are incredibly small. In a sense this can be viewed a positive aspect of the theory, since no deviations from the predictions of the classical theory have been actually observed in gravitational wave detections.

Quantization of the volume of the simplest grain of space

Tuesday, October 19th

Hal Haggard, Bard College

Quantization of the Volume of the Simplest Grain of Space
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By Jorge Pullin, LSU

There exists a concept in mathematics called "asymptotic resurgence" in which an infinite sum of terms exhibits a surprising behavior. The terms that appear late in the summation around one physically relevant point are exactly the same as the terms that appear early in the sum around another physically relevant point. The result is a rich connection between the physics at the two different extremes and has applications in many areas of physics, for instance in the calculations of intensities of rainbows.

This talk applies these ideas to the calculation of the volume in loop quantum gravity. The volume of a region of space is discrete in that theory and has a complicated expression depending on the details of the quantum state one is considering. The expressions are known but are difficult to interpret. Previous studies have dealt with them primarily through numerical methods. In this talk an approximate expression is derived that can be much more easily interpreted and studied. It applies it to the simplest "grain" of space, a tetrahedron. A neat illustration of the power of the insights that can be learned from having an easier to interpret expression is the following movie following tetrahedra of different shape but equal volume:

To quote the concluding slide: "Quantization of geometry provides a remarkable laboratory for understanding resurgent perturbative/non-perturbative relations and, due to the richness of its underlying quantum structure, may even require extensions of this formalism."

Complex critical points and curved geometries in Lorentzian EPRL spinfoam amplitude

 Tuesday, October 5th

Dongxue Qu, Florida Atlantic University

Complex critical points and curved geometries in Lorentzian EPRL spinfoam amplitude
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By Jorge Pullin, LSU

The states of quantum gravity in the loop representation are given by spin networks. These are multivalent graphs with a number associated with each line. Spin foams represent the transition from an initial spin network state to a final one, as show in the figure (credit: Alejandro Perez). The expanded picture on the right is what is known as a "vertex", where new lines in the spin network are created as it transitions forward in time (time is the vertical axis). These diagrammatics correspond to precise mathematical 

equations that embody the dynamics of general relativity at a quantum level. One of the proposals for the vertex is the "EPRL" one (after Engle, Pereira, Rovelli and Livine). There has been controversy over the years about if the vertex correctly encoded the dynamics of general relativity. That requires studying how it behaves in the classical limit, as one expects departures from classical general relativity in situations where quantum effects are important. Previous calculations, done within certain approximations, seemed to suggest that curved geometries were not properly captured by this construction. The talk was about recent numerical results that imply that indeed it does capture the dynamics of classical general relativity in appropriate situations. Connections were made with a discretization of classical general relativity proposed by Tullio Regge known as Regge calculus. This is a very encouraging result indicating that the dynamics of classical general relativity is properly being captured by the "EPRL vertex".

How the cosmological constant q-deforms symmetries in Loop Quantum Gravity

Tuesday, September 21st

Qiaoyin Pan, Perimeter Institute

How the cosmological constant q-deforms symmetries in LQG
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By Jorge Pullin, LSU

Ashtekar showed in 1986 how to rewrite general relativity in terms of variables that make it look like the Yang-Mills theories that describe particle physics. This was the cornerstone that allowed the introduction of loop variables by Rovelli and Smolin and led to the development of loop quantum gravity.

Yang-Mills theories are generalizations of Maxwell's electromagnetism which have several electric and magnetic fields. These theories have a symmetry through which multiple field values correspond to the same physical situations. The transformations among the fields that keep the physical situation invariant form a mathematical structure called a group. The particular group that arises in loop quantum gravity is called SU(2) and is similar to the one that appears in the theory of the weak interactions.

When a cosmological constant is present, things can be reconfigured in such a way that the group that arises is a mathematical structure called q-deformed group, with q a parameter related to the value of the cosmological constant. Observations indicate that our current universe indeed has a cosmological constant present that makes its expansion accelerate, therefore this is a situation of physical interest.

The talk described the mathematical structures that arise when one formulates loop quantum gravity in terms of the q-deformed structures, including the dynamics of the theory. It also points to connections with another mathematical structure known as quantum groups.

Vacuum state for LQC perturbations

 Tuesday, March 23rd

Rita Neves, Universidad Complutense

Vacuum state for LQC perturbations
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by Jorge Pullin

One of the main achievements of the model of cosmology known as Inflation, in which the universe after the Big Bang expands exponentially, is that it predicts the spectrum of cosmic microwave background radiation. This is radiation that comes to us directly from the earliest moments when the universe stopped being a primordial soup and became transparent to light. If one looks in different directions, the frequency of the radiation is not exactly the same. It differs in parts in a million. And the differences are not random. If one looks in a given direction and then looks at a circle in the sky centered in that direction and averages out the frequencies, if things were random, the result would be the same no matter what size the circle. It turns out it does, mathematically one says the signals are correlated. 

If one assumes one starts inflation with a quantum field present, and one assumes the simplest possible state for the quantum field (the vacuum) and evolves the quantum state through inflation, the state develops correlations that correspond precisely to the ones observed in the cosmic microwave radiation. This model is remarkable in its simplicity and efficacy. 

In traditional cosmology, where things start with a Big Bang where the whole universe is concentrated at a point, it appears natural to place the quantum state of the field in the vacuum at the beginning of inflation, as it is impossible to place it at the Big Bang as the theory breaks down there (densities and curvatures are infinite). But in loop quantum cosmology, the Big Bang is replaced by a Big Bounce where everything is finite and there is dynamics of the universe prior to it. Why would then place the state in a vacuum at the beginning of Inflation, as that instant in time does not have any privileged meaning. Perhaps one should place it at the Bounce (now this is possible as the space-time is regular there). Or somewhere else. All that means that at the beginning of Inflation, the quantum field will not be in the vacuum state anymore. This talk addressed these issues.

Supergravity in loop quantum gravity

Tuesday, March 9th

Konstantin Eder, FAU Erlangen

Supergravity in LQG
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By Jorge Pullin, LSU

Supersymmetry is a conjectured symmetry of nature in which to each particle corresponds a "superpartner" particle. The partners of bosons are fermions and vice-versa. So for instance, the electron (a fermion) has a boson superpartner known as the "selectron" and so on. No superpartner has ever been observed in reality so it is conjectured that this symmetry is broken in nature and can only be present at very high energies. Unfortunately, experiments at large accelerators like the Large Hadron Collider at CERN in Switzerland, are putting tighter and tighter bounds on supersymmetry. Supersymmetry is usually incorporated into string theory, hence the name superstrings. 

If one incorporates this symmetry into gravity, one obtains supergravity. This theory potentially has interesting properties. It could avoid the infinities one faces in usual perturbative quantum gravity, although this is not entirely clear yet.

This talk was about applying loop quantum gravity techniques to supergravity. It updated the treatment with modern techniques (older results referred to techniques that are not used anymore, in particular the use of complex variables) and further insights on how supersymmetry can manifest itself in the form of a gauge symmetry, the kind of symmetry that is the basis for the description of the other forces in nature. Among other aspects it explored the behavior of the theory in cosmology and how one could use supersymmetric matter as a "clock" to study the evolution in time. It also considered calculations of black hole entropy and how it could lead to connections with similar calculations in string theory.

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.