Set certain perturbations to zero

[Harry Ye]

Hi everyone, I'm doing a research project on cosmological perturbations. For my purpose, I only need to keep first order tensor perturbation (1)E_ab in my expansion. However, I do need to expand the Einstein tensor to second order (involving terms like E_ab*E_cd). I used the Newton gauge, but as you can see in the picture, there are those second order perturbations (green stuff) I don't want. Is there a easy way to set them to zero? In other words, I want to use background field method.

Also, as you can see, there are also first order scalar perturbations \phi and \psi that I don't want. I set them to zero by adding the rules manually, which is cumbersome. One big problem is that it takes my computer a long time to consider all these perturbations even if I don't actually need them. How can I set them to zero beforehand so that the computation can be done faster?

Thanks a lot!!!

[Cyril Pitrou]

Hi,

First you can use the option

BackgroundFieldMethod = True

to turn off all second order perturbations

Then if you want to get rid of scalar first order perturbations there are several ways of doing it.

The dirty way is to go directly into xPand.nb and look at the function 'SplitMetric'.

You should see where the Newton Gauge is defined in it. Just erase all occurences of scalars there.

Then if you save the xPand.nb file, it should regenerate a xPand.m file (It might be a Mathematica option to ensure this is the case)

and now scalars will not appear in the Newton gauge.

A cleaner way is to avoid using the SplitMetric function which is hidden in MyToxPand. This require to determine by yourself the splitting rule for the metric perturbations.

In the example folder, you can look at the 7th example. There you see that a custom rule for splitting the metric perturbation is built in the variable

RulesProjectedComponents

which is then used after

SplitPerturbations[MyR, RulesProjectedComponents, h]

So in your case, this would require to put only tensors in the perturbations of your first order metric. That is your custom rule would be like

RulesProjectedComponents = { dg[LI[n_], i1_, i2_],  2 Eth[LI[n], LI[0], i1, i2] }

Regards,

Cyril Pitrou

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