B Why do we use expanding metric?

[Ibix]

also $g_{\mu\nu}=0$ for $\mu\neq\nu$ in the FLRW metric in the Cartesian coordinates.

Not in co-moving coordinates.

 

[stoper]

In that case I also want to know whether these off-diagonal components will be decreasing or increasing with time due to $a=a(t)$.