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.