Exploring Intergalactic Space Expansion Using Light Propulsion

[stoomart]

Hello all,

Is electromagnetic radiation considered a driving factor of intergalactic space expansion similar to directed energy propulsion? I assume every point in space has countless photons passing through it from every direction at all times.

 

[PeterDonis]

Is electromagnetic radiation considered a driving factor of intergalactic space expansion

Not at present, no. The energy density in EM radiation is much too small to matter in the universe at present. In the early universe, the energy density in radiation was much larger relative to other energy densities; then it did have a significant effect on the dynamics of the expansion.

similar to directed energy propulsion?

I'm not sure what you're referring to here.

 

[Orodruin]

Not at present, no. The energy density in EM radiation is much too small to matter in the universe at present. In the early universe, the energy density in radiation was much larger relative to other energy densities; then it did have a significant effect on the dynamics of the expansion.
I'm not sure what you're referring to here.

To expand (haha) on this a bit in relation to the OP

electromagnetic radiation considered a driving factor of intergalactic space expansion

In a radiation dominated flat universe the expansion is decelerating as $a\propto \sqrt t$. In that sense, radiation never drives expansion.

 

[stoomart]

Thanks guys, that answers my question.

I'm not sure what you're referring to here.

https://en.m.wikipedia.org/wiki/Beam-powered_propulsion

 

[PeterDonis]

https://en.m.wikipedia.org/wiki/Beam-powered_propulsion

Ah, ok. Then the answer to that part of your question is that beam powered propulsion has nothing to do with the effect (if any) that radiation energy density has on the dynamics of the universe's expansion. Beam powered propulsion means radiation is pushing against some part of a spacecraft or other object. There is no sense in which radiation is pushing against the universe to expand it.

 

[stoomart]

In a radiation dominated flat universe the expansion is decelerating as $a\propto \sqrt t$.

In the early universe, the energy density in radiation was much larger relative to other energy densities; then it did have a significant effect on the dynamics of the expansion.

I want to learn the meaning of these types of equations but it's been years since I've done any algebra, let alone anything related to physics. Are there any comprehensive reference guides for variables used in astrophysics online?

Is this equation correct to calculate the current radiant energy density of the first photons emanated from the big bang:

w_e = Q_e / ctH

Or in case I used the wrong variables: radiant energy density = radiant energy / (speed of light x time x Hubble expansion rate)

 

[PeterDonis]

Is this equation correct to calculate the current radiant energy density of the first photons emanated from the big bang:

w_e = Q_e / ctH

No. First, the units aren't right; the denominator on the right doesn't have units of volume (length cubed). Second, the "radiant energy" $Q_e$ is not a meaningful quantity; according to our best current models, the universe is spatially infinite, so there is no finite "total energy" contained in photons (or anything else). And if you try to just count the photons in our observable universe, that doesn't give you a meaningful "total energy" either, since photons can move into and out of our observable universe so you aren't counting a constant number of photons. (The same goes for any other particles.)

The energy density of various kinds of substances is actually the fundamental variable in cosmology. What distinguishes the dfifferent kinds of substances in cosmology ("matter", "radiation", "dark energy" are the three main ones) is how their energy density behaves as the universe expands. "Matter" has an energy density that decreases as the cube of the scale factor; "radiation" (like photons) has an energy density that decreases as the fourth power of the scale factor; and "dark energy" has a constant energy density (at least as far as we can tell), it doesn't change as the universe expands.

 

[stoomart]

Thank Peter, this gives me a lot to chew on.

The energy density of various kinds of substances is actually the fundamental variable in cosmology. What distinguishes the dfifferent kinds of substances in cosmology ("matter", "radiation", "dark energy" are the three main ones) is how their energy density behaves as the universe expands. "Matter" has an energy density that decreases as the cube of the scale factor; "radiation" (like photons) has an energy density that decreases as the fourth power of the scale factor; and "dark energy" has a constant energy density (at least as far as we can tell), it doesn't change as the universe expands.

Do these variables apply equally to substances in the protective orbit of a galaxy as they do substances in intergalactic space?

 

[PeterDonis]

Do these variables apply equally to substances in the protective orbit of a galaxy as they do substances in intergalactic space?

The "substances" I was referring to are not individual objects like stars or planets or people. They are averaged distributions of energy density over very large distance scales, hundreds of megaparsecs and larger. The dynamics of the universe as a whole is driven by these average energy densities; the corrections due to the fact that the universe is not actually filled with a continuous fluid but instead with galaxies, stars, etc. separated by mostly empty space are too small to matter for most purposes.

 

[stoomart]

The "substances" I was referring to are not individual objects like stars or planets or people. They are averaged distributions of energy density over very large distance scales, hundreds of megaparsecs and larger. The dynamics of the universe as a whole is driven by these average energy densities; the corrections due to the fact that the universe is not actually filled with a continuous fluid but instead with galaxies, stars, etc. separated by mostly empty space are too small to matter for most purposes.

Gotcha, that makes sense. Is it accurate to say every point in this empty space has a very large number of electromagnetic waves of varying energies passing through it from nearly all directions?

 

[PeterDonis]

Is it accurate to say every point in this empty space has a very large number of electromagnetic waves of varying energies passing through it from nearly all directions?

Sure, since the empty space will contain radiation from various stars and other light-emitting objects, and also the CMBR.

 

[stoomart]

I think the equation I was looking for in post #6 can be derived from the standard Doppler effect, to determine the spaghettification of infant EM waves from the big bang.

f_o = fc / ct

where

• f_o is the observed frequency
• f is the emitted frequency

 

[stoomart]

If this equation is correct, we should be able to calculate the original frequency of CMBR by:

f = f_oc²(t₀ - t_e)

where

• t₀ is the age of the universe
• t_e is the age of the universe emitting CMBR

 

[PeterDonis]

If this equation is correct

Which equation?

we should be able to calculate the original frequency of CMBR by:

f = f_o c²(t₀ - t_e)

This equation doesn't even have the correct units. The correct equation is

$$
1 + \frac{f_0}{f} = 1 + z = \frac{a}{a_0}
$$

where $a$ is the scale factor of the universe now and $a_0$ is the scale factor at the time of emission of the CMB. This equation is actually used in reverse, since we can directly observe the redshift $z$ of the CMB, to calculate $a_0$. Relating the ratio $a / a_0$ to the time (in FRW coordinates) from CMB emission to now is a little complicated since the universe has switched from radiation dominated to matter dominated to dark energy dominated during that time, so the relationship between the scale factor and time has not been the same all along.

 

[stoomart]

Nice thanks Peter, wasn't sure if accounting for redshift was necessary, makes sense though.

Which equation?

I posted another equation in post #12.

 

[PeterDonis]

I posted another equation in post #12.

Ok. That one isn't correct either (and the units aren't right).

 

[russ_watters]

Beam powered propulsion means radiation is pushing against some part of a spacecraft or other object. There is no sense in which radiation is pushing against the universe to expand it.

2. The EM radiation in the universe is traveling in all directions, so even if it was pushing on "space", it would be pushing in all directions and thus cancel itself out.

 

[stoomart]

Sean Carroll's Dark Energy FAQ calculates its leading candidate "vacuum energy" to be "a fixed amount of energy attached to every tiny region of space, unchanging from place to place or time to time. About one hundred-millionth of an erg per cubic centimeter", or 10^-9 joules (10^-2 ergs) per cubic meter (10¹¹³ joules per cubic meter per QFT).

http://www.preposterousuniverse.com/blog/2011/10/04/dark-energy-faq/

Is the ratio between EMR and dark energy in a region of spacetime calculated, or even possible to calculate at this time?

[Moderator's note: personal speculation deleted.]

 

[PeterDonis]

Is the ratio between EMR and dark energy in a region of spacetime calculated

There is no fixed ratio of these two energy densities. The two types of energy densities behave differently as the universe expands, so the ratio changes with time. At present, IIRC the energy density in EM radiation (the major component of which is the CMBR) is about 4 orders of magnitude smaller than the energy density of dark energy. I'll try to find a reference.

 

[PeterDonis]

@stoomart, I have deleted the part of your latest post that you flagged with a "layman crackpot warning". If you feel the need to put something like that in front of something you intend to post, it means you shouldn't be posting it in the first place. Please bear in mind the PF rules on personal theory/speculation.

 

[stoomart]

@stoomart, I have deleted the part of your latest post that you flagged with a "layman crackpot warning". If you feel the need to put something like that in front of something you intend to post, it means you shouldn't be posting it in the first place. Please bear in mind the PF rules on personal theory/speculation.

Agreed, was trying to provide some context for my line of questioning. So far almost all my preconceived notions about cosmology and physics have been corrected/debunked since I joined the forum on Monday, so I'd say it's been a productive (sometimes depressing) week!

 

[GeorgeDishman]

Is the ratio between EMR and dark energy in a region of spacetime calculated, or even possible to calculate at this time?

There are two competing parts to that, new radiation is being produced by stars and other sources all the time but that is a lesser effect, the main one is that the universe is expanding. The effect of that can easily be calculated, as distances increase in line with the scale fact $a$, volumes increase as $a^3$ which reduces densities by $a^{-3}$. The redshifting of the radiation adds a further factor of $a$ through Planck and Einstein's relation to energy so overall the energy density falls as $a^{-4}$.

I'll try to find a reference.

I find the diagram in this appendix to a lecture useful but I'd like to know if you consider it a reliable source

http://www.nicadd.niu.edu/~bterzic/PHYS652/Appendix_09.pdf

 

[PeterDonis]

I find the diagram in this appendix to a lecture useful but I'd like to know if you consider it a reliable source

It looks OK to me.

 

[stoomart]

http://www.nicadd.niu.edu/~bterzic/PHYS652/Appendix_09.pdf

So to verify I'm understanding this diagram correctly, is it accurate to say the universe has been dark-energy dominated for the last 4.05 billion years? Is this the timeframe we consider expansion to be accelerating?

 

[GeorgeDishman]

Almost. I'll say what I think and hope an expert will correct it if I'm wrong, I think my explanation might be somewhat contentious. Dark energy contributes to expansion two ways, through the energy content and through pressure both of which appear in the stress-energy tensor. Now some cosmologists say the pressure is negative (but some don't like that way of putting it) but overall you get $+1$ from the energy and $-3$ from the pressure (since there are three spatial dimensions) giving a total of $-2$, so for that to exactly cancel the matter (and lesser radiation) contribution, the matter density needs to be twice the dark energy density. That happened about 6 billion years ago. On the graph which shows $log_{10} \Omega$, a factor of 2 is $+0.3$ on the vertical scale.

 

[PeterDonis]

some cosmologists say the pressure is negative (but some don't like that way of putting it)

What references can you give for cosmologists not "liking" describing dark energy as having negative pressure? AFAIK that's not at all contentious, and if you model dark energy as a perfect fluid the fact that it has negative pressure is necessary to get the physics right.

 

[GeorgeDishman]

My comment was cautionary, based on this from Sean Carroll:

http://www.preposterousuniverse.com...oes-dark-energy-make-the-universe-accelerate/

However, in a FAQ from two years earlier he said:

"Does that mean that dark energy has negative pressure?
Yes indeed. Negative pressure is what happens when a substance pulls rather than pushes ..."

http://www.preposterousuniverse.com/blog/2011/10/04/dark-energy-faq/

 

[PeterDonis]

My comment was cautionary, based on this from Sean Carroll:

He's not saying that dark energy doesn't have negative pressure or that that's a bad way of describing dark energy in general; he's just saying that certain "naive" or "fast talking" explanations of how the negative pressure causes accelerated expansion are not correct.

Notice that the article doesn't talk at all about how you determine when the universe transitions from matter dominated to dark energy dominated; that is a different question from the question of how dark energy causes accelerated expansion when it's dominant. To determine the transition point, you do have to take into account the negative pressure of dark energy, just as you did in your post. If you left that out, you would get the wrong answer for the transition point.

(Notice also that what Carroll says is the "right way" to explain accelerated expansion depends crucially on the fact that dark energy does not dilute as the universe expands. What he doesn't go into--not surprisingly, since it's a layman's article and not a peer-reviewed paper--is what the requirements are for anything, dark energy or otherwise, to not dilute as the universe expands. That requirement is that the stress-energy tensor of any such substance must be proportional to the metric. And any such stress-energy tensor, if we assume it has positive energy density, must have negative pressure--the easiest way to see this is to look at the SET in a local inertial frame, where the metric tensor is the Minkowski metric $\text{diag}(1, -1, -1, -1)$. So negative pressure is in fact a requirement even if we use Carroll's "right way" of explaining accelerated expansion.)

 

[GeorgeDishman]

Thanks for that, I'll read it through again. I'm a bit paranoid about not spreading disinformation or pseudo-science but being just an amateur, it's hard to keep comments like that in perspective. Your comment in parentheses explains the connection, thanks for that.

 

[PeterDonis]

Your comment in parentheses explains the connection

Another way of seeing the connection is to look at the second Friedmann equation given the assumption that $\ddot{H} = 0$ (which is implied by $H = \text{constant}$, as Carroll describes the effect of dark energy). That equation is

$$
\frac{\ddot{a}}{a} = \dot{H} + H^2 = - \frac{4 \pi}{3} \left( \rho + 3 p \right)
$$

If we take $\ddot{H} = 0$ and substitute $H^2 = 8 \pi \rho / 3$ from the first Friedmann equation, we obtain, after rearranging terms and cancelling common factors, the simple relationship $p = - \rho$. So positive $\rho$ necessarily means negative $p$ for this case.

 

[GeorgeDishman]

I follow that, thanks. Although I am vaguely familiar with the equations, I need to get better at manipulating them that way so thanks for the tutorial :-)