Implications of a dynamical cosmological constant

Tuesday, Mar 19th

Lee Smolin, Perimeter Institute
Title: Implications of a dynamical cosmological constant 
PDF of the talk (10M)
Audio+Slides of the talk (28M)

By Jorge Pullin, LSU

Experimental cosmologists have determined that 95% of the content of the universe is not made up of ordinary matter. The vast majority of the universe consists of strange forms of matter known as dark matter and dark energy. Some people believe that in reality there is no such matter, but a modification of Einstein's general relativity is needed to explain the universe in large scales. That is, just ordinary matter with a new theory of gravity.

The cosmological constant was a term Einstein added to his equations in 1917 in a futile attempt to make the universe static (at the time it was not known the universe expands). The extra terms it implies in the equations has a behavior similar to dark energy.

Cosmologists have proposed several generalizations of Einstein's theory involving extra fields and constants in order to attempt to explain dark energy and dark matter. However, more complex theories tend to depend on extra parameters that need to be determined, limiting their predictive power. Essentially one can adjust parameters to fit any observed behavior. Also, there is a high degree of arbitrariness in how one can modify Einstein's theory.

The aim of this talk is to introduce a basic principle for the creation of generalized theories that does not involve extra fields. To give more details we have to discuss some basic concepts. Most classical equations of motion, like those of general relativity, can be derived from what is known as an "action principle". The "action" is a function of the variables of the theory such that if one requires that it be a minimum (or a maximum), the equations of the theory follow. That is, the condition for minimization (or maximization) is that the equations of the theory hold. It turns out one can add to the action of a theory some terms such that the resulting equations of motion remain unchanged. Such terms (usually multiplied times a constant) are called "topological terms". The proposal of this talk is to add to the action such terms but allow the constant that multiplies them (called "cosmological constant" in the talk, generalizing the idea of Einstein) to change with time and even possibly space. So if the term were constant we would just recover the usual Einstein theory, but when it is not, one gets a new theory.

Three such theories are proposed in the talk, with various properties discussed. In particular, the geometry they imply is more general than that of Einstein's theory, in addition to a metric to describe space-time another quantity called torsion appears. This is still early days for these theories and various properties are being worked out. In particular, cosmological models have been studied. It appears that the one of the considered "cosmological constants" appears to be clumped around ordinary matter. This is just like dark matter behaves, it tends to clump around galaxies, modifying the orbits of outer stars (this is how dark matter was detected, the stars did not move as they were supposed to given the mass of the galaxy). More complex concepts, like black holes, are yet to be worked out in the new theories as well as several other properties, but some initial glimmers of interesting possibilities are emerging.

Towards loop quantum gravity effective dynamics

Tuesday, Feb. 19th

Andrea Dapor, LSU
Title: Toward LQG effective dynamics 
PDF of the talk (250K)
Audio+Slides of the talk (57M)

By Jorge Pullin, LSU

The dynamics of loop quantum gravity is quite complex. This is understandable, as it should reproduce in the classical limit the dynamics of general relativity which in itself is quite complex. This has led investigators to concentrate on situations with a lot of symmetry, in order to achieve simplifications. One of those simplifications is loop quantum cosmology, which studies homogeneous and isotropic spacetimes, i.e. spacetimes that are the same at all points and in all directions. This might seem like too drastic a simplification, but the dynamics of our universe at large scales is well approximated by it.

Imposing a symmetry in the quantum theory is not easy. One has to choose a subset of quantum states that are symmetric and study the action of quantum operators on them. All these operations take place in the full theory and therefore can potentially be as complex as dealing with it in generality. This led people to seek a further approximation: impose the symmetry in the classical theory and only then quantize. The problem is that when one imposes the symmetry at a classical level, general relativity simplifies too much and a lot of the techniques of loop quantum gravity are not applicable anymore. Nevertheless people proceeded by using techniques analogous to those of loop quantum gravity. The resulting construction is known as loop quantum cosmology and has been studied for over a decade.

This talk dealt with the first approach, namely choose a set ofsuitably symmetric states in the quantum theory and study the action of the quantum operators on them. Remarkably some portions of loop quantum cosmology can be retrieved from this approach, but not quite. Some of the quantum operators differ. The talk studied the resulting quantum cosmologies. The picture that emerges is rather different from traditional loop quantum cosmology. There one has that the Big Bang, the singularity that arises at the origin of the universe when all matter is concentrated at a point, is replaced by a Big Bounce in which there is high -but finite- density of matter. If one studies the evolution back in time one can go past the Bounce and one emerges into a previous universe that eventually becomes big and classical like the one we live in. So the picture that emerges is that our universe originated in a large classical universe like ours that contracted, increased in density, became highly quantum, bounced at a finite density, and started to expand eventually becoming classical again. The modified dynamics of the approach followed in the talk leads to a different picture. Our universe starts in a large but highly quantum universe that is highly symmetric (it is known as De Sitter spacetime), it eventually bounces and starts expanding until it becomes the classical universe we live in. The talk also explored the implications for the singularity inside black holes and showed that the modified dynamics leads to a transition in which the black hole explodes into a "white hole" where everything that went into the black hole comes out. This behavior had been suggested by other approaches, but the details differ. The whole approach relies on a conjecture about how the chosen symmetric states in the full theory behave. Proving the conjecture is a future challenge awaiting.