Covariant derivate problem (christoffel symbols)

[Fisica]

Homework Statement

I need to calculate $$\square A_\mu + R_{\mu \nu} A^\nu$$ if $$\square = \nabla_\alpha \nabla^\alpha$$, and is the covariant derivate

SEE THIS PDF arXiv:0807.2528v1 i want to get the equation (5) from (3)

Homework Equations

$$A^{i}_{{;}{\alpha}} = \frac{{\partial}{A^{i}}}{{\partial}{x^{\alpha}}} + \Gamma^{i}_{{j}{\alpha}} A^{j}$$

Lool arXiv:hep-th/0504052v2 for the conections and christoffel symbols o ricci tensor components

The Attempt at a Solution

for example The 00 component for Ruv is

$$R_{\mu \nu} = -3(\dot{H}+H^2)$$

see the links for more compoents

 

[bloby]

Do you see why only one equation remains?
How $\square$ is expressed with low index nabla's only?
Do you know the expression for $A_{{\alpha}{;}{\beta}}$ ?

(I use latin indices for space components and greek indices for space-time components)

note: if you past an url it becomes clickable, for inline latex wrap it with ##.

http://arxiv.org/pdf/0807.2528v1

eq (8)
http://arxiv.org/pdf/hep-th/0504052v2