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Definition of Energy in Friedmann equations?

  1. Nov 13, 2015 #1
    The first Friedmann equation for a flat Universe is given by:

    $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$

    The energy density ##\rho(t)## is given by:

    $$\rho(t) \propto \frac{E(t)}{a(t)^3}$$

    where ##E(t)## is the energy of the cosmological fluid in a co-moving volume.

    Is the energy ##E## the energy measured by a local observer at time ##t## or is it the energy measured with respect to a (global) reference observer at the present time ##t_0## where ##a(t_0)=1##?
     
  2. jcsd
  3. Nov 13, 2015 #2

    PeterDonis

    Staff: Mentor

    No, you have it backwards. The energy density ##\rho(t)## is a direct observable (it is the energy density measured by a comoving observer); it isn't derived from anything. If you want to try to define a "total energy" ##E(t)##, then you could do it along the lines of ##E(t) \propto \rho(t) a(t)^3##. But the physical meaning, if any, of such an ##E(t)## would be an interesting question.
     
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