Tag Archives: backreaction

Acceleration paper published

Hooray! The acceleration paper was published in Phys. Rev. D a couple of days ago.

I was quite pleased with how this one turned out – it’s a nice clarification, I think. Tim had the idea of using the blueshift in collapsing regions to mimic acceleration in the Hubble diagram, which is pretty cool in itself. It was also good to find a concrete example of the link between acceleration of the average and acceleration in the Hubble diagram that Syksy Rasanen has discussed in a couple of papers (see our discussion for references).

Of course, we’re not claiming that “dark energy is backreaction” or anything nearly as strong as that, but I think it does extend the backreaction debate a little. The papers by Ishibashi, Green, and Wald, which seem to show that inhomogeneities on small scales don’t affect the background evolution much, suggest that backreaction effects can’t have any bearing on dark energy. I suppose our paper responds to theirs by saying “yes, perhaps they can’t dynamically, but what about non-linear optical effects?”


Philip Bull, Timothy Clifton (2012). Local and non-local measures of acceleration in cosmology. Phys. Rev. D: 10.1103/PhysRevD.85.103512


Buchert deceleration parameter doesn’t care about the sign of the expansion rate

This week’s task: debugging some code that calculates the Buchert spatial average in LTB models. It’s a Python code, using my homebrew LTB background solver (also in Python). I’m using the results reported in a few papers to help debug my code, but I’ve run into problems with reproducing one model in particular (model 8 from Bolejko and Andersson 2008, an overdensity surrounded by vacuum). Hmmm.

I’ll spare the gory details, but one potential problem was that I might have used the wrong sign for the transverse Hubble rate. The model, as specified in the paper, gives no clue as to the sign of the Hubble rates (i.e. whether the overdense region is in a collapsing or expanding phase), only specifying a density and spatial curvature profile. In the process of constructing the model, you need to take the square root of the LTB “Friedmann” equation,¬†and of course there is a freedom in which sign of the root you take. Out of force of habit with LTB models, I was choosing the positive sign. So would choosing the negative sign solve the discrepancy I was seeing between my code and the Bolejko and Larsson paper?

As it turns out: No. I’ll have to keep trying. But it did lead to what I thought was an interesting little result: the Buchert averaged hypersurface deceleration parameter, usually written q_\mathcal{D}, is invariant under \Theta \mapsto - \Theta, where \Theta is the expansion scalar for the dust congruence. This means that it doesn’t care whether your structures are collapsing or expanding, as long as the density profile and variance of the Hubble rates are the same. This is pretty trivial by inspection of the general form of the expression for q_\mathcal{D}, but it hadn’t crossed my mind before.