0

I'm curious as to the equations necessary for finding a total energy of 0 (or, I suppose, the energy density of empty space due to quantum fluctuations) in a flat Friedmann universe such as ours.

The FLRW metric is as follows:
$ \mathrm{d}\mathbf{\Sigma}^2 = \frac{\mathrm{d}r^2}{1-k r^2} + r^2 \mathrm{d}\mathbf{\Omega}^2 $

And solving the formula the formula: $$\mathrm{d}\mathbf{\Sigma}^2 = \mathrm{d}r^2 + S_k(r)^2 \, \mathrm{d}\mathbf{\Omega}^2$$ For a $S_k(r)$ where $k=0$ gives us $r$. Adding in the scale factor, we get a simplified equation: $$d^2(t) = a^2(t)(x^2 + y^2 + z^2)$$ But this has nothing to do with the energy of the system, only the curverature and the distance between points at a given time $t$. I'd like to understand why a flat universe has a cumulative energy of zero in a mathematical equation. I understand that the gravitational potential energy is the counteractive energy to matter, but I'm looking for a mathematical equation that shows this and I'm wondering if it is truly absolute zero, since the $\text{Uncertainty Principle}$ tells us zero is impossible for an oscillating system: $$ \Delta E\cdot \Delta t \ge {\hbar\over 2} $$

Qmechanic
  • 201,751
Goodies
  • 1,140
  • 1
    to get a vacuum density different than zero you need either a cosmological constant or some quantum field equivalent to it (but we do not have a quantum theory of gravitation yet). –  Oct 14 '14 at 23:37
  • Ahh, thank you. However, I'm looking for an equation (unfinished or currently unsolvable is perfectly fine) that would seemingly describe our Universe's total energy for a $K$ value of $0$. – Goodies Oct 14 '14 at 23:41
  • I am not sure to understand if you want the energy density of the vacuum or the total energy density, which includes the matter/energy present in the universe. –  Oct 15 '14 at 00:08
  • 1
    both are actually parameters of the Friedman equations, so you do not "calculate" them, you give them values to solve your model (see http://en.wikipedia.org/wiki/Friedmann_equations) –  Oct 15 '14 at 00:12
  • both values determine if the solution results in an expanding, static, or expanding universe –  Oct 15 '14 at 00:15
  • I'm talking of the total energy density of the universe. – Goodies Oct 15 '14 at 00:17
  • you do not calculate either of them, as I said (they could have any values given by you on the Friedman equations), please check the link. –  Oct 15 '14 at 00:21

1 Answers1

4

The total energy of the universe is a vexed issue since different commentators have different views about what the concept means. See the question Total energy of the Universe for a sampling of the various viewpoints. If you Google for zero energy universe you'll find several papers purporting to show that the total energy is zero. However since their results depend on the assumptions they make at the start treat their conclusions with care - because a paper appears on the Arxiv does not necessarily make it authoritative.

You might want to read Phil Gibbs' views on the subject, though note that another prominent member of this site, Luboš Motl, heartily disagrees.

Community
  • 1
John Rennie
  • 355,118