content_image/349545.jpg content_image/349546.jpg content_image/349548.jpg content_image/349550.jpg content_image/349551.jpg
We may write this more compactly as 

where 

<img src='content_image/349545.jpg'>

<img src='content_image/349546.jpg'>

<img src='content_image/349548.jpg'>

If we suppress the discrete indices in equations (A21) and (A22) they take an even simpler form 

<img src='content_image/349550.jpg'>

<img src='content_image/349551.jpg'>

This is the generic form that the scalar perturbation equations of motion take for N − 1 coupled scalar fields and a graviscalar. 

