LQG and the begining of the universe

the bigbang or "time zero" singularity of GR is a failure of the theory-----a limit to its applicability

as you take GR back towards time zero the numbers begin to diverge and the theory stops being able to compute

People have been trying to QUANTIZE general relativity since at least 1960 and it has always been expected that when GR
was quantized the singularity (i.e. the breakdown of the theory at time zero) would go away

This is what happened when the classical theory of the hydrogen atom was quantized----the classical theory had a failure and predicted an absurd result, then when the theory was quantized by Nils Bohr the glitch went away. Sometimes quantizing a theory
gets rid of notorious glitches. So the people working on quantizing GR expect that the big bang divergence (infinite density infinite curvature----i.e. failure to compute) would go away.

Happily enough the singularity DOES go away when LQG is used.
Also the LQG model matches the Friedmann equations away from time zero and includes matter etc. It is nicely behaved.
The most authoritative word on this is a paper by
Ashtekar, Bojowald, Lewandowski
"Mathematical Structure of Loop Quantum Cosmology"
http://arxiv.org/gr-qc/0304074 [Broken]
much of the paper is technical
for a less technical discussion see Ashtekars more popularly written
"Quantum Geometry in Action: Big Bang and Black Holes"
http://arxiv.org/math-ph/0202008 [Broken]

The discovery that LQG eliminated the singularity at time zero,
thus fixing a failure of the classical GR theory, was made by
Martin Bojowald, a postdoc at Penn State
I have lost count of how many papers have now appeared referencing Bojowald's work and rederiving his results
and extending them and so on. This has been an active research
line for the past two years---since sometime in 2001 when Bojowald's paper came out about getting rid of the singularity.

 

first notice that LQG is an attempt in progress to quantize GR.
(preserving the non-perturbative background-independent character of classical GR, in which the geometry is not pre-selected but is a dynamic variable)

this attempt is still in development and will be modified as it is experimentally tested---there will be elaborations of the theory which we cannot foresee

the only reason that people can now get concrete results for cosmology is that cosmology involves a radical simplification

the classical Friedmann equations which are the core equations of cosmology are simple equations derived from the more complex Einstein equation by making radical assumptions of
uniformity----isotropy, homogeneity, the idea that the universe is rather uniform at large scale.

These equations turn out to be not so hard to quantize with LQG and result in something that is nicely behaved and compatible with the classical model (away from places where the classical model breaks down)

when the Loop Quantum Cosmology model is run backwards it does not break down at time zero, so there is a wavefunction calculated at before time zero. I cannot say how to interpret this.

It appears that there was a CONTRACTING phase that led up to the expanding phase we are now in. But one should not push this too far. Perhaps it should be thought of as a way of presenting the initial conditions. for now I think one can just be
hopeful because the timezero glitch seems to be fixed and one can just wait to see what more comes out of this about very early times. Several papers have discovered that LQG predicts an early inflationary epoch (after time zero but only a little bit after).
Probably inflation is the right thing to be interested in now, instead of what the theory says about before time zero. But that is just my view of it--keep an open mind and an eye out for new papers.