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GR: FRW Metric relation between the scale factor & curvature

  1. Dec 18, 2014 #1
    Mod note: OP warned about not using the homework template.
    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.
     
    Last edited by a moderator: Dec 18, 2014
  2. jcsd
  3. Dec 23, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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