Spinfoam cosmology with the cosmological constant

by David Sloan, Institute for Theoretical Physics, Utrecht University, Netherlands.

• Francesca Vidotto, CNRS Marseille

Title: Spinfoam cosmology with the cosmological constant
PDF of the slides (3 MB)
Audio [.wav 26MB], Audio [.aif 2MB].

Current observations of the universe show that it appears to be expanding. This is observed through the red-shift - a cosmological Doppler effect - of supernovae at large distances. These giant explosions provide a 'standard candle', a fixed signal whose color indicates relative motion to an observer. Distant objects, therefore appear not only to be moving away from us, but accelerating as they do so. This acceleration cannot be accounted for in a universe filled with 'ordinary' matter such as dust or radiation. To provide acceleration there must be a form of matter which has negative pressure. The exact nature of this matter is unknown, and hence it is referred to as being 'dark energy'.

 An image of the remnants of the Tycho type Ia supernova as

recorded by NASA's Spitzer observatory and originally observed by

Tycho Brahe.

According to the standard model of cosmology, 73% of the matter content of the universe consists of dark energy. It is the dominant component of the observable universe, with dark matter making up most
of the remainder (ordinary matter that makes up stars, planets, and nebulae comprises just 4%). In cosmology the universe is assumed to be broadly homogeneous and isotropic, and therefore the types of matter
present are usually parametrized by the ratio (w) of their pressure to energy. Dark energy is unlike normal matter as it exhibits negative pressure. Indeed in observations recently made by Reiss et al. this ratio has been determined to be -1.08 ± 0.1. There are several models which attempt to explain the nature of dark energy. Among them are Quintessence which consists of a scalar field whose pressure varies with time, and void (or Swiss-cheese) models which seek to explain the apparent expansion as an effect of large scale inhomogeneities.However, the currently favored model for dark energy is that of the cosmological constant, for which w=-1.

The cosmological constant has an interesting history as a concept in general relativity (GR). Originally introduced by Einstein, who noted there was the freedom to introduce it in the equations of the theory,  it was an attempt to counteract the expansion of the universe that appeared in general relativistic cosmology. It should be remembered that at that time it was thought the universe was static. The cosmological constant was quickly shown to be insufficient to lead to a stable, static universe. Worse, later observations showed the universe did expand as general relativistic cosmology seemed to suggest. However, the freedom to introduce this new parameter into the field equations of GR remained of theoretical interest, its cosmological solutions yielding (anti) DeSitter universes which can have a different topology to the flat cases. The long-term fate of the universe is generally determined by the cosmological constant - for large enough positive values the universe will expand indefinitely, accelerating as it does so. For negative values the universe will eventually recollapse, leading to a future 'big crunch' singularity. Recently through supernovae observations the value of the cosmological constant has been determined to be small yet positive. In natural (Planck) units, its value is 10^(-120), a number so incredibly tiny that it appears unlikely to have occurred by
chance. This 'smallness' or 'fine tuning' problem has elicited a number of tentative explanations ranging from anthropic arguments (since much higher values would make life impossible) to virtual wormholes, however as yet there is no well accepted answer.

The role of the cosmological constant can be understood in two separate ways - it can be considered either as a piece of the geometry or matter components of the field equations. As a geometrical entity it can be considered just as one more factor in the complicated way that geometry couples to matter, but as matter it can be associated with a 'vacuum' energy of the universe: energy associated with empty space. It is this dual nature that makes the cosmological constant an ideal test candidate for the introduction of matter into fundamental theories of gravity. The work of Bianchi, Krajevski, Rovelli and Vidotto, discussed in the ILQG seminar, concerns the addition of this term into the spin-foam cosmological models. Francesca describes how
one can introduce a term which yields this effect into the transition amplitudes (a method of calculating dynamics) of spin-foam models. This new ingredient allows Francesca to cook up a new model of cosmology within the spin-foam cosmology framework. When added to the usual recipe of a dipole graph, vertex expansions, and coherent states, the results described indeed appear to match well with the description
of our universe on large scales. The inclusion of this new factor brings insight from quantum deformed groups, which have been proposed as a way of making the theory finite.

This is an exciting development, as the spin-foam program is  'bottom-up' approach to the problem of quantum gravity. Rather than beginning with GR as we know it, and making perturbations around solutions, the spin-foam program starts with networks representing the fundamental gravitational fields and calculates dynamics through a foam of graphs interpolating between two networks. As such, recovering known physics is not a sure thing ahead of time. The results discussed in Francesca's seminar provide a firmer footing for understanding the cosmological implications of the spin-foam models and take these closer to observable physics.