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Mod note: OP warned about not using the homework template.

I have read that 'a(t)

I'm trying to see this from what I know, but I'm struggling...

## dt^{2}+a^{2}(t) ds^{2}, where ds^{2}=g_{ij}x^{i}x^{j}##, and ##g_{ij}## is the isotropic and homogenous spatial metric.

##R_{abcd}=\frac{1}{6}R(g_{ac}g_{bd}-g_{ad}g_{bc})##

I have no idea how I can tie these together , or use anything I know to show that 'a(t) determines the value of the constant spatial curvature'

I have read that 'a(t)

**determines the value of the constant spatial curvature'..***Where a(t) is the scale factor, and we must have constant spatial curvature - this can be deduced from the isotropic at every point assumption.*I'm trying to see this from what I know, but I'm struggling...

**Here's what I know:**__The FRW metric takes the form:__## dt^{2}+a^{2}(t) ds^{2}, where ds^{2}=g_{ij}x^{i}x^{j}##, and ##g_{ij}## is the isotropic and homogenous spatial metric.

__The Riemann tensor and metric are related via:__##R_{abcd}=\frac{1}{6}R(g_{ac}g_{bd}-g_{ad}g_{bc})##

I have no idea how I can tie these together , or use anything I know to show that 'a(t) determines the value of the constant spatial curvature'

**Any hints or links to sources etc really , really appreciated, ta.**
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