Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wave equation given a cosmological inflationary metric

  1. Mar 10, 2015 #1
    Hi everybody!
    Can you explain me how I can obtain wave equation given a metric? For example, if I have this metric $$g_{μν}=diag(−e^{2a(t)},e^{2b(t)},e^{2b(t)},e^{2b(t)})$$, how can derive the relation $$\frac{1}{\sqrt{g}}\partial _t(g^{00}\sqrt{g}\partial _t \phi)+\frac{1}{\sqrt{g}}g^{ii}\partial ^2 \phi$$ where ##\phi=\phi (t)## is a scalar field? Moreover, from this equation the professor has derived a Bessel's equation in the form u¨+ταu=0. I don't understand... Thanks
     
  2. jcsd
  3. Mar 10, 2015 #2

    Chalnoth

    User Avatar
    Science Advisor

    You'd need to use Einstein's equations with the stress-energy tensor of the scalar field on the right hand side.
     
  4. Mar 11, 2015 #3
    And then, to obtain that relation?
     
  5. Mar 11, 2015 #4

    bapowell

    User Avatar
    Science Advisor

    That will give you the relation you've written down in your post. To get the Bessel equation, simply substitute in the metric you've been provided.
     
  6. Mar 11, 2015 #5
    OK, thanks :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Wave equation given a cosmological inflationary metric
Loading...