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.