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So photons have momentum right? And stars are constantly expelling light on all directions, which eventually hits any object on its way and transfers a small amount of momentum. So wouldn't this constant 360°x360° transfer of momentum from all existing starts work as a constant expansion wave? Like constant explosions pushing everything around them away? I reckon it would be a very small amount of momentum transferred per star, but it would be almost constant, and it would come from every observable star, which could amount for enough momentum to cause the acceleration.

So, wouldn't the momentum transfer from the spherical expanding light of a star be causing the negative pressure we've been calling dark energy?

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    $\begingroup$ But starlight arrives equally from all directions. So where is the net force? $\endgroup$ – Rob Jeffries Apr 26 '17 at 22:46
  • $\begingroup$ That's a god point. I guess it would depend on whether the light expelled from a star is greater than the amount of light that hits the star from all directions. $\endgroup$ – Sergio Cárdenas Reyes Apr 26 '17 at 22:58
  • $\begingroup$ You are not that far about apparently tiny amounts of energy becoming huge at large scales. It does not answer your question , but you might find this interesting en.wikipedia.org/wiki/Olbers%27s_paradox $\endgroup$ – user126422 Apr 27 '17 at 0:37
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No. What you're thinking about is the radiation density pressure on objects accelerating the expansion of space. First, the effects of radiation pressure are already accounted for in the Friedmann equations that describe how the universe expands. Second, the radiation of the universe, both in number of photons and energy content, are dominated by the cosmic microwave background left over from when the universe first became transparent. It is a nearly perfect black body spectrum at a temperature of $2.725\,\mathrm{K}$. This gives the photons an energy density that is about $9\times 10^{-5}$ times the critical density of the universe, too small to account for dark energy's effects by a factor between $1,000$ and $10,000$.

There is also the problem of the sign of the effect. The pressure exerted by a radiation field slows down the expansion of space, it doesn't speed it up. What makes dark energy special is that it has a negative pressure (see the description in the Friedmann equations article on mixtures). Ordinary blackbody radiation, as described by Wikipedia's photon gas article, have a pressure equal to $\frac{1}{3}$ it's energy density. Dark energy, as nearly as we can tell, has a pressure equal to $-1$ times its energy density.

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In summary no
1) If light (or anything else) were applying a repelling force throughout the universe the speed of expansion would be increasing rather than constant. Indeed it is, this point is just like a minor correction to the question.
2) At the scale of universal expansion, light including CMB intensity reaching objects in our region is pretty directionally uniform, and the momentum from it would cancel out on average. You would need starlight from one direction (the center of the universe, presumably) to be more intense than from another. This is not the case.
3) The rate of expansion of the universe exceeds the speed of light. Indeed but no thing is exceeding c, in theory space is itself being created according to the Hubble constant. This means that there is a large but limited sphere called the observable universe, we don't receive light from beyond that sphere. It also means that at least part of the cause of expansion must be due to a mechanism that creates new space. The impact of light on objects doesn't satisfy this criteria, tellings us is could only ever account for a portion of the expansion that was non-relativistic.
4) One could go on and compare the magntiude of light pressure to the rate of acceleration of expansion of the universe, but I'm not sure that's necessary given 1-3.

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