Density coefficients

Displayed formulas in this passage

• X-E-ST@1#eq:densities · line 341

  $$\begin{array}{rlrl}{a_1}^{\mu \nu }[h]& =\frac{1}{2}H{\eta }^{\mu \nu }-h^{\mu \nu },& b_1[h]& =\frac{1}{2}H,\\ b_2[h]& =\frac{1}{8}{H}^2-\frac{1}{4}{h}_{\alpha \beta }{h}^{\alpha \beta },& & \\ {a_2}^{\mu \nu }[h]& =h^{\mu }{}_{\lambda }{h}^{\lambda \nu }-\frac{1}{2}H{h}^{\mu \nu }+b_2[h]{\eta }^{\mu \nu },& & \\ A^{\mu \nu }[h,k]& ={a_1}^{\mu \nu }[k]+{a_2}^{\mu \nu }[h],& B[h,k]& =b_1[k]+b_2[h].\end{array}$$

• unlabeled · line 356

  $$J_q{q}^{\mu \nu }={\eta }^{\mu \nu }+\kappa {a_1}^{\mu \nu }[h]+{\kappa }^2{A}^{\mu \nu }[h,k]+O({\kappa }^3),J_q=1+\kappa b_1[h]+{\kappa }^{2}B[h,k]+O({\kappa }^3).$$