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As I understand it, dark matter and dark energy are used as an 'explanation' for how universe expansion is accelerating; because without it gravity would be expected to cause a long term shrinking.

Why, when extremely distant objects have such tiny gravitational effects upon each other, is it not considered that the radiation emit by all objects in the universe, causing radiation pressure, might be the cause?

Has the effect of radiation pressure been considered at all? Or is that far smaller than the tiny gravitational pull such that it can be ignored completely?

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  • $\begingroup$ a) yes, it is orders of magnitude weaker than you might anticipate, and b) that doesn't account for the fact that the recession is proportional to distance. Radiation-pressure-based recession would decrease in magnitude with distance. $\endgroup$
    – controlgroup
    Commented Jun 6 at 0:55
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    $\begingroup$ Hi @Claud. Welcome to Phys.SE. Did you try to do a back-of-an-envelope estimate? $\endgroup$
    – Qmechanic ♦
    Commented Jun 6 at 7:02
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    $\begingroup$ I'm uncertain about this, so not leaving it as an answer, but unless we happened to be at the center of such a universe from which the radiation shines outward, wouldn't any outward pressure from our perspective be balanced by an equal but opposite inward pressure, since the universe is isotropic? There is just as much universe out the other side of some distant galaxy/bit of space pushing it back toward us after all. $\endgroup$
    – Jason Patterson
    Commented Jun 6 at 10:20

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Radiation pressure, both from the cosmic microwave background and all the stars of all the galaxies is so far, far, FAR smaller than the gravitational pull of the galaxies that it can completely, absolutely (and many more adverbs) be ignored.

Since radiation pressure and gravitational pull from a star both decrease as the square of the distance, compare the radiative pressure of sunlight to the gravitation of the Sun that keeps Earth in an orbit around the Sun.

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    $\begingroup$ it should be mentioned that in the early days of the universe, radiation did indeed dominate the cosmic evolution, but arguably, that was because nothing else existed. Shortly after the formation of matter, the influence of radiation diminished. $\endgroup$
    – paulina
    Commented Jun 5 at 22:27
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    $\begingroup$ Another point is that radiation on cosmological scales should be isotropic, so it couldn't create a net force in any direction, so wouldn't be useful for explaining expansion. $\endgroup$
    – Andrew
    Commented Jun 5 at 22:29
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    $\begingroup$ @paulina You are absolutely right. I was answering for now, not for the time very near the Big Bang $\endgroup$
    – Alfred
    Commented Jun 5 at 22:30
  • $\begingroup$ @Alfred of course. My point was rather to illustrate that radiation is "weak" in the sense that immediately after the appearance of matter, it lost its dominance. $\endgroup$
    – paulina
    Commented Jun 5 at 22:33
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    $\begingroup$ @paulina the matter is expected to have formed before the first second but only came to dominate over radiation around 50000 years $\endgroup$
    – Sten
    Commented Jun 6 at 1:38
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Positive pressure like that of radiation has attractive gravity, not repulsive. If the universe was radiation dominated the Hubble parameter would go like

$$\rm H(a)=\frac{H_0}{a^2} \to H(t)=\frac{1}{2 t}$$

so as you can see it shrinks to the square by the growing scale factor $\rm a$ or linear by the cosmic time $\rm t$, while in our accelerating universe the Hubble parameter will asymptotically converge to the constant value of $\rm H(\infty)=H_0 \sqrt{\Omega_{\Lambda}}$.

You can also see it in the 2nd Friedmann equation for the acceleration $\rm \ddot{a}/a$, if you plug in the density and pressure for radiation it is decelerating, so you need dark energy with the proper equation of state.

In a radiation dominated universe the Hubble radius would coincide with the particle horizon and they would grow with constant $\rm 2 c$, so there would be no event horizon. The corresponding spacetime diagram would look like this:

radiation domination

With dark energy the event horizon converges to the Hubble radius like it will in our ΛCDM universe:

ΛCDM universe

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    $\begingroup$ This answer, I think, gets at the OP's confusion the most directly. They seem think that a positive pressure of a perfect fluid would cause space to expand (which seems like an intuitive way that things could behave.) But in fact a positive pressure acts the same way as a positive mass-energy density, causing deceleration of the expansion. $\endgroup$
    – Michael Seifert
    Commented Jun 6 at 15:28
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Here's an article illustrating the relative magnitudes of radiation pressure vs. gravitational attraction of the Earth and the Sun.

So, if we want to know how hard the Sun pushes on the Earth, we need to know how many photons are hitting the Earth per second. This is a really huge number, that we can roughly estimate by taking the total power of sunlight reaching the Earth-- about $10^{17}$ watts, where a watt is one joule of energy delivered per second-- and dividing by the energy of a single photon. Using $500\ \mathrm{nm}$ as a sort of average wavelength, this comes out to around $5 \times 10^{35}$ photons per second. Multiply that by the momentum per photon, and you get the total force, which is something like $6.6 \times 10^8 N$.

These are absurdly big numbers, but roughly speaking, that's about the weight of an object with a mass of 70,000 metric tons. That's five-and-a-bit times the mass of the CMS detector at the Large Hadron Collider, so even a superhero would strain to hold it up.

This is not, however, a significant force when you start talking about the interaction between the Earth and the Sun. For one thing, even if this were the only force acting on the Earth, the resulting acceleration would be ridiculously small-- around $10^{-16}\ \mathrm{m/s^2}$. If you let that force push on the Earth for the entire age of the universe from the Big Bang to today, the Earth would be moving at maybe $50\ \mathrm{m/s}$.

Of course, that's not the only force acting between the Earth and the Sun. The gravitational force of the Sun on the Earth is about $1\times10^{23}\ \mathrm{N}$, which is a bit more than a hundred trillion times the radiation pressure force. So, while the Sun does, in fact, push on the Earth pretty hard by (super)human standards, it's not anything you need to worry about when thinking about the motion of planets in the Solar System.

The gravitational attraction of the Sun on the Earth is roughly 15 orders of magnitude larger than radiation pressure of the Sun on the Earth. It's true that the Sun is far closer to the Earth compared to the extragalactic distances you're thinking of, but the Sun is also much brighter (as seen from the Earth) than these other galaxies. At cosmological distances, gravitational forces still dominate.

That said: there was a period in the very early universe where radiation dominated the universe's expansion. It ended early, however, since radiation's energy density decreases faster than matter's (which in turn decreases faster than dark energy's - it is why dark energy is dominating expansion currently).

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Radiation pressure forces are relevant in cosmology, but only at the level of studying localized perturbations in the density. This is because you only get a net force if there is a gradient in the pressure (so something is pushed more on one side than the other). The overall pressure exerts no net force.

(This is separate from the matter of pressure being a source of gravity, which is what another answer is discussing.)

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