SynchronousGage perturbations of continuity equations

[Hengameh Bagherian]

Hello, 

I am brand new to xAct. I tried using xPand to write the continuity equation of the stress energy tensor in synchronous gauge, but I cannot get the results in terms of \eta and h which are the standard cosmological synchronous gauge variables. 

I am attaching my notebook here and any help would be appreciated. 

[Hengameh Bagherian]

P.S. 

Just to be clear, \eta and h are Fourier space scalar perturbations of the metric in synchronous gauge.