# Scalar curvature

1. Jul 27, 2013

### Elliptic

1. The problem statement, all variables and given/known data

Find the equation of scalar curvature for homogenous and isotropic space with FLRV metric.

2. Relevant equations

$R=6(\frac{\ddot{a}}{a}+\left( \frac{\dot{a}}{a}\right )^2+\frac{k}{a^2})$

3. The attempt at a solution
$G_{AB}=R_{AB}-\frac{1}{2}Rg_{AB}$

2. Jul 27, 2013

### WannabeNewton

That's not really much of an attempt to be honest :p

What did you get when you calculated the Ricci curvature for the FLRW metric? Just plug the metric into the formulas.

3. Jul 29, 2013

### Elliptic

If I strart from this point:
$B_{\mu\nu}+\lambda g_{\mu\nu}B=0 / \cdot g^{\mu\nu} \\ R(1+4\lambda)=0$
what next?

4. Jul 29, 2013

### Elliptic

Any help?

5. Jul 29, 2013

### WannabeNewton

I can't really understand your notation. Why not just calculate it directly? $R = g^{\mu\nu}R_{\mu\nu} = g^{\mu\nu}R^{\alpha}{}{}_{\mu\alpha\nu}$. The FLRW metric is diagonal and extremely simply in the usual form so the computation shouldn't be so bad.

6. Jul 30, 2013

### tia89

With the FLRW metric actually you should be able to use directly the definition of $R_{\mu\nu}$ and then take out the scalar as here above.
Anyway try and look in any GR book (e.g. Carroll or others). It is done quite everywhere.