xAct - Terms (2)^E_ab How do I interpret them as?

[mariaco...@gmail.com]

Hi, I work with gravitational waves (tensor sector only),  I am perturbing the metric tensor to second and third order, and I get these terms  (2)^E_ab. I do not know how interpret them algebraically. For example, to second order in metric perturbations the inverse metric reads g^ab=\bar{g}^ab - h^ab +h^ac h_cb, where \bar{g}^ab is the background metric and  h^ab the tensor perturbation and xAct will usually represent it as (1)^E_ab . Is there supposed to be an extra term there, like a "pure" tensor perturbation of the form  (2)^E_ab? Can you help me understand what this object is? 

Thank you! 

Maria