Newtonian theory of cosmological perturbations

  • #1
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Main Question or Discussion Point

In the Newtonian theory of cosmological perturbations, a density excess ##\delta\rho## in a localised region of spacetime leads to the equation of motion ##\ddot{\delta\rho} \sim G\delta\rho##. I can see that this follows directly from Newton's gravitational law.

Why does this equation lead to an exponential instability of flat spacetime to the development of fluctuations?
 

Answers and Replies

  • #2
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Just solve the differential equation?
 
  • #3
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Well, I get ##\delta\rho = A\ e^{\sqrt{G}x} + B\ e^{-\sqrt{G}x}##.

I can see that this is the sum of an exponential growth and an exponential decay of the initial density fluctuation in a localised region of spacetime.

Does the exponential instability of flat space-time to the development of fluctuations refer to exponential growth or exponential decay?
 
  • #4
34,493
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Does the exponential instability of flat space-time to the development of fluctuations refer to exponential growth or exponential decay?
It is called instability...
 
  • #5
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Thanks!

I was also wondering why it is inconsistent in General Relativity to consider density fluctuations in a non-expanding background.

Why can't Einstein's field equations be used to analyse density fluctuations (in the early universe) in a non-expanding universe?
 
  • #6
Chalnoth
Science Advisor
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Why can't Einstein's field equations be used to analyse density fluctuations (in the early universe) in a non-expanding universe?
I'm pretty sure it's just because it's not stable. There is no static solution to the Einstein field equations that both contains matter and is stable.
 
  • #7
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Got it!

Thanks!
 

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