# Tag Archives: buchert

## Code release: LTB in Python, spherical collapse, and Buchert averaging

The release of our next paper is imminent (yay!), and so it’s time for another code release. I try to make all of my code, or at least a substantial fraction of it, publicly available. This enables other people to reproduce and check my work if they want to. It also allows them to build off my code and do cool new things, rather than having to spend months solving problems that, well, have already been solved. That’s the theory, anyway – I only know of a couple of people who’ve actually poked around in the code, or tried to use it for something. But hey, you’ve got to start somewhere. For posterity, I’ve posted the closest thing I have to release notes below.

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.