1. Backreaction The effect of clumpiness in cosmology
Syksy Räsänen
University of Geneva
Leopoldina Dark Energy Conference, Munich, October 9, 2008

2. A factor of 2
Observed distances in the late universe are a factor of 2 longer than predicted in homogeneous and isotropic models with ordinary matter and gravity.
There are three possibilities:
1) There is matter with negative pressure.
2) General relativity does not hold.
3) The universe is not homogeneous and isotropic.
The coincidence problem: structure formation could explain it. But that is a philosophical issue, while the absence of the effect of structure formation is a matter of a physical effect being present in reality and missing in the model.
Leopoldina Dark Energy Conference, Munich, October 9, 2008

3. Our clumpy universe
The early universe is exactly homogeneous and isotropic, up to linear perturbations.
At late times, the universe is only statistically homogeneous and isotropic, on scales > 100 Mpc.
The average evolution of an inhomogeneous and/or anisotropic spacetime is not the same as the evolution of the corresponding smooth spacetime.
Describing the average behaviour of a clumpy universe was termed the fitting problem by George Ellis in 1983.
Clumpiness affects the expansion rate, light propagation and their relationship.
Leopoldina Dark Energy Conference, Munich, October 9, 2008

4. A scanner lightly
Since most observations probe the expansion rate only via the distance scale, it could be possible to explain the data without accelerated expansion.
The effect of clumpiness on light propagation was first studied by Zel’dovich and Feynman in 1964.
Since then, numerous papers with various conclusions have appeared.
To summarise(arXiv: ):
It appears that the effect of clumpiness on light propagation is small for realistically sized, randomly distributed structures, assuming that the average expansion rate does not change.
Leopoldina Dark Energy Conference, Munich, October 9, 2008

5. Love in a void
Speculative large structures can have a significant effect on light propagation.
The old idea that we are located in a large (100 Mpc-1 Gpc) underdense region has been recently studied with the Lemaître-Tolman-Bondi (LTB) model.
It is possible to fit the SNIa, CMB and BAO data, as well as the age of the universe and Hubble parameter(arXiv: ).
However, we have to be near the center (within ∼10 Mpc) to avoid a large CMB dipole(astro-ph/ ).
There are also constraints from spectral distortion, the kinetic SZ effect and the difference between radial and angular expansion from BAO(arXiv: , arXiv: , arXiv: ).
Void models good from two points of view: they show that inhomogeneities can have a large effect on light propagation, and they have led to observational checks of the Copernican principle (i.e. homogeneity).
Leopoldina Dark Energy Conference, Munich, October 9, 2008

6. Going faster
The average expansion can differ from the FRW model, as shown by Buchert in 1999(gr-qc/ ), even when the universe is statistically homogeneous and isotropic and structures are small.
The average expansion rate can accelerate because the fraction of volume occupied by faster expanding regions grows(astro-ph/ ).
Acceleration has been demonstrated in the LTB model(astro-ph/ , gr-qc/ , astro-ph/ ).
In a simple model with a realistic distribution of structures, Ht grows by 10-30% around 10 billion years(arXiv: ).
There is no fully realistic calculation yet.
The connection to light propagation needs more work.
Leopoldina Dark Energy Conference, Munich, October 9, 2008

7. Summary
Observations of the late universe are inconsistent with a homogeneous and isotropic model with ordinary matter and gravity.
FRW models do not include the effect of non-linear structures.
The effect on light propagation is likely to be small unless there is a speculative large structure or the expansion rate changes.
Local void models are under pressure, but not ruled out.
The effect on the expansion rate can be large.
The correct order of magnitude and timescale emerge from a simple model of structures.
Before concluding that new physics is needed, it is necessary to quantify the effect of non-linear structures.
Leopoldina Dark Energy Conference, Munich, October 9, 2008