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First, I asked myself the question: Is there any gravitational waveform, however fantastical, that could explain dark energy.

I suppose for a ubiquitous gravitational wave to be an explanation for dark energy, then it would have to have the same effect: Dark energy effectively stretches space itself at every point in the universe. What kind of primordial gravitational 'wave' could effectively produce such an effect in the universe?

Please point out any absurdity in this thought experiment:

********************** Begin Edit June 27 2017 **************************

Imagine a 2-D model of our universe before inflation as an arbitrarily tiny patch of space on that drumhead.

A drumstick strikes anywhere on that drumhead, initiating a wave that stretches the drumhead equally in all directions.

  • Now inflationary epoch begins.
  • The drumhead grows at least 10^26 bigger in O(10^-33) seconds.
  • Inflationary epoch ends

What is the state of the initial drumhit waveform now?

Very much like the CMB, it would effectively still be propagating as a very nearly uniform wave coming from all directions.

Now lets make some big assumptions and work backwards.

Extrapolate the 2-D universe to 3-D, and the drumhit to gravitational waves (GWs).

The drum-hit would need to be a collection of interfering GWs, such that:

  • GWs stretch our tiny patch of space equally in 3 dimensions. The drumhead analogy falls apart here, and dreaming up a set of cancelling GWs is non-trivial. Is cancellation of gravitational waves possible?

    * begin edit June 28th It appears that it is not possible for any combination of GWs to stretch space equally in 3 dimensions. As a GW passes a given volume of space, the volume contained cannot change. Any stretching in one dimension must be counterbalanced by a compression in the other dimension(s). end edit June 28th *

  • their wavelength(s) have now been stretched to O(Hubble length).
  • period has also been stretched to O(Hubble age).
  • amplitude is O(lambda Cosmological constant)

If you were to work backwards, could you come up with plausible initial conditions for the GWs before inflation started? Certainly someone has attempted this math in the past? ********************** End Edit June 27 2017 ****************************

Original thought experiment (2016):

  • a gravitational wave must propagate at the speed of light
  • if the wave was/is produced by the big bang itself, the source of the gravitational wave comes from every direction, and is nearly uniform in every direction.
  • I’m thinking along the lines of a single giant, long period gravitational wave, amplitude of up to 10^N meters (the size of the universe), and a wavelength of ~ 8 billion years.
  • a wavelength of ~ 8 billion years doesn’t really make sense, unless you say that due to the inflationary epoch, its wavelength is being stretched out.
  • gravitational waves are complex 3 dimensional waves... however:
    • because it comes from every direction for any observer, the ‘stretching’ of spacetime happens evenly in every direction radially. I'm thinking of a polar coordinate system.
    • stretching in the other polar dimensions are cancelled out from any observer’s point of view, again since the wave is coming from every direction radially.
    • Maybe there is a flaw here... would the wave also cancel out in the radial dimension itself?
  • Since it was/is produced by the big bang itself, its ’source’ is ~380,000 years beyond the observable universe’s event horizon (i.e. 380,000 years beyond the cosmic background radiation). Again, its wavelength stretched out because of inflation.
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  • $\begingroup$ This is a reasonable question. Down voters, could you please back up with reasoning. "Primordial gravitational wave" can make more sense than totally made up thing called "dark energy". For one, the wave fluctuates, means it goes high and low. It is known that universe has gone through cycles of accelerated, and slowed down expansion. Last switch/fluctuation from slowed down expansion to accelerated expansion is supposed to have taken place 5 billion years ago. We know big bang started with acceleration. Therefore there must have been at least one more fluctuation before the last one. $\endgroup$ – kpv Jul 20 '16 at 2:45
  • $\begingroup$ It may be a wave with ~5 billion year period. $\endgroup$ – kpv Jul 20 '16 at 2:48
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    $\begingroup$ Thank you for acknowledging my question. I think I found a problem with my thought experiment. The Higgs field didn't exist during inflation, so no gravitational wave could be generated during the inflationary epoch: physics.stackexchange.com/q/207970 $\endgroup$ – Keith Knauber Jul 20 '16 at 16:07
  • $\begingroup$ Actually the Higgs field and/or a Higgs-like field is present during inflation in most inflationary models, according to this paper: iopscience.iop.org/article/10.1088/1742-6596/840/1/012030/pdf This paper summarizes several theories of "Dark energy due to effective quantum field theory" sciencedirect.com/science/article/pii/S0370269308003845#bib002 Although very different from my thought experiment, with a better understanding of the equations laid out in that paper, this could be formulated into a theory, or ruled out. $\endgroup$ – Keith Knauber Jun 27 '17 at 17:43

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