define the perturbation to the metric as g_ {ab} = n_ {ab} + {ab} H_ alpha phi -alpha n_ {ab}

[arest...@gmail.com]

Hi, I'm new using this powerful tool, and emerged me a doubt, the problem is I need to define the perturbation to the metric  as,

g_ {ab} = n_ {ab} + {ab} H_ alpha phi -alpha n_ {ab}

where alpha is a constant and phi corresponds to a scalar field. I have been reading and I have not found how to define the perturbation to the metric in this way.

Thank you

[arest...@gmail.com]

Sorry the correct metric is

g_ {ab} = n_ {ab} +  alpha h_ {ab} - alpha phi n_ {ab}

Thank you

[Sergio González]

Supposing that n is your metric, this should work

expansion=Perturbationn[LI[1], a_, b_] :> alpha a[a, b] - alpha phi n[a, b];

SetOptions[ExtraRules->expansion];