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Stress Energy Tensor

The stress energy tensor can be broken up into fluid (f) contributions and seed (s) contributions (see e.g. [18]). The latter is distinguished by the fact that the net effect can be viewed as a perturbation to the background. Specifically $T_{\mu\nu} = \bar T_{\mu\nu} + 
\delta T_{\mu\nu}$ where $\bar T^0_{\hphantom{0}0} = -\rho_f$,$\bar T^0_{\hphantom{0}i} = \bar T_0^{\hphantom{i}i} =0$and $\bar T^i_{\hphantom{i}j} = p_f \delta^i {}_j$is given by the fluid alone. The fluctuations can be decomposed into the normal modes of §IIC as  
\delta T^0_{\hphantom{0}0} &=&
 - [\rho_...{i}j} \vphantom{\displaystyle{\dot a \over a}}\, .\end{array}\end{displaymath} (31)
for the scalar components,  
 \delta T^i_{\hphantom{0}0} & = & -[(\rh...
 ...tom{i}j}\vphantom{\displaystyle{\dot a \over a}}\, ,\end{array}\end{displaymath} (32)
for the vector components, and  
\delta T^i_{\hphantom{0}j} = [p_f\pi_f^{{(2)}} + \pi_s^{(2)}] \,
 Q^{(2)}{}^i_{\hphantom{i}j} \, ,\end{displaymath} (33)
for the tensor components.

Wayne Hu