# 3 questions on Physical Cosmology

1. Sep 3, 2008

### WCOLtd

First question:

According to Hubble's Law, the redshift observed by distant galaxies are proportional to their distance.

This is what I already know: It says on wikipedia that Hubble observed cepheid variable stars in a spiral nebulae to calculate their distance, cepheid variable stars are cosmological candles, meaning they emit a consistent light signature.

Q: How did Hubble calculate distances using cephied stars in spiral nebulae?

Last edited: Sep 3, 2008
2. Sep 3, 2008

### Kurdt

Staff Emeritus
Cepheids have a relationship between their period and luminosity. So basically you have to measure the period of the Cepheid and the luminosity. You can use the period -luminosity relation to tell you what the luminosity should be and the inverse square law of light to calculate the distance.

3. Sep 3, 2008

### WCOLtd

Thanks Kurdt,
I see, the star is emitting light homogeneously in all directions, so since the total luminosity (the luminosity emitted in all directions) is exclusively determined by the relation to the Cepheid's period, then you can treat the total luminosity of the star a known quantity and thereby calculate the distance by the observed luminosity, because the observed luminosity is a proportion of how large the telescope's surface area is to the area of the spherical shell (with radius r) around the Cepheid.

What I know; according to Hubble's Law Red-shift is a function of distance.

The Doppler Effect is the phenominon in which wave-emitting bodies which are moving toward an observer will be percieved by that observer to be of a lower frequency (a function of the relative velocity) and wave emitting bodies which are moving away will have a lower frequency

According to the Expanding Space Paradigm, this observed red-shift as a function of distance is the result of the stars moving away from us.

Q2:So by this, is it right to assume that stars are moving away from each other at an exponential rate with time?

(because after a time period has elapsed the space in between will be greater and therefore the redshift will be greater and therefore the recession velocity will too.)

4. Sep 4, 2008

### Kurdt

Staff Emeritus
I'm not really sure under what circumstances (if any) it would be safe to assume exponential rate of recession. The difficulty arises because the Hubble parameter is a function of time. A resident cosmologist will be able to provide a more in depth answer.

5. Sep 4, 2008

### neutralseer

WCOLtd,

I'm more of an astrophysicist, but here's my answer anyway.

How fast things are moving away from each other (due to expansion of space) depends on a variety of properties of the mass-energy density in the universe. As it turns out, we think the universe is accelerating due to some energy density in the universe (dark energy) that somehow remains constant in time (it might change, but not nearly as fast as the energy density of matter). As this dark energy begins to dominate, then the stars (unless they are gravitationally bound in a galaxy or group of galaxies) will be moving away from each other exponentially.

You do get exponential expansion if the Hubble constant were really constant, which is probably why you asked that question. In reality, the proportionality constant between proper distance and recessional velocity is not a constant. This "not a constant" is known as the Hubble parameter and is written as H(t). The Hubble parameter evaluated now, at t ~ 14 Gyr is known as the Hubble constant $H_0$. However, in a dark energy dominated universe, the Hubble parameter will be constant in time, giving us exponential expansion. (Incidentally, during inflation the universe underwent exponential expansion also.)

6. Sep 5, 2008

### WCOLtd

Neutralseer,

Thank you for that post, albeit I am a little confused.
Let me rephrase, the Hubble constant is a measure of the recession velocity as a function of distance.
Gravity works in the opposite direction, it's the measure of directed velocity as a function of mass and distance.

So, the distribution of mass effects the observed expansion.

However, I would think that this would lead to clusterings of mass, beyond a certain distance, the recession velocity by Dark Energy will exceed the directed velocity by gravity. Once bodies of mass move beyond this threshold, they begin to move apart from eachother, so the larger the distances, the more the recession velocity should approach the value predicted by the Hubble constant, because the Gravitational effects will become negligable at greater distances.

Am I correct so far?

7. Sep 5, 2008

### neutralseer

WCOLtd,

Your close to being on the right track here. Gravity does work against the expansion of the universe (partially described the Hubble constant). However, remember that gravity is a directed force (which causes directed acceleration), not a directed velocity.

Yes, you're right, but you have to keep in mind an extremely important fact about cosmology. All our cosmological theories and observations are only about the universe on cosmological length scales which are ~10 000 times the diameter of our galaxy. On these scales you can pretend that all the stars and galaxies are smoothly spread out, like in a room full of jello or water. It is only on these scales that we observe the universe to expanding.

You're also on the right track here, but still need a few corrections. Your absolutely right that at some point, gravity will win over expansion and there will be clusterings of mass. These clusterings of mass include (from smallest to biggest): stars, clouds of hydrogen, globular clusters, galaxies, groups of galaxies, clusters, superclusters. When gravity has won over expansion and each of the object's own velocities, the resulting structure is described as being gravitationally bound. The expansion of the universe will not stretch these bound structures (there's some subtleties here, but for the most part that's true).

It's not that Dark Energy will take over at some point, just expansion will take over. Dark energy is just one of the things that affects expansion in certain ways. If there were no Dark Energy, expansion would still take over at some point.

Yep, except gravitational effects never become negligible. The way the expansion of the universe changes with time is intimately connected with average energy density of the universe (remember that mass and energy are the same via $E=mc^2$). The theory that connects the energy density with the expansion of the universe is gravity (General Relativity). So, although the individual gravitational effects of two masses moving far away from each other may become negligible, the collective gravitational effects of all mass/energy in the universe never becomes negligible.

8. Sep 6, 2008

### WCOLtd

..Alright, I will.

I was walking one day a few months ago and I was thinking about a car and skydiving, I was thinking about how certain cars can accelerate at rates comparable to free fall. Yet when a skydiver falls relative to the ground at the acceleration as the car driver, the skydiver feels no force. (F=ma?) But the car driver does when he is not even accelerating, (through weight) so I thought maybe it was like the ground was accelerating upwards or something. I know that it probably won't make any sense because than the world would be expanding at an accelerated rate, and quickly expand into the sun, but then I thought maybe the space around mass is growing and accelerating inwards at the same time, so that all volumetric proportions of mass remain constant. (it's probably just a crazy idea, but it was a very convincing thought, while it may be crazy, I am incredibly stubborn about it.)

I was describing it in terms of inertia of the body in free fall, I felt as though it was more correct to say it is a directed velocity than a directed force. Because body does not experience a force when it's in free fall or freely passing through a gravitational field, it experiences a change in velocity over time. It is as if the body is moving at a constant velocity in space and the space it's moving in is being sucked up by the mass. Kind of like a stick in a whirlpool or something.

How about beyond those scales? Let me guess, at that distance the recession velocity is so great that you have to start taking into account time dilation, so the galaxies would appear to the observer to be clustered, or moving away at a slower rate from each other than the stars preceding it (closer to you).

Which makes me wonder - because at some distance that has to be true - is there an edge to our observable universe? do stars ever fade away completely from our view or do they dim asymptotically?

This question makes me wonder about light, and whether, by Hubble's constant, is only capable of traveling a certain distance until it becomes entirely red-shifted. What would that mean?

Expansion and Dark Energy are two different things?!?! my view was that dark energy was this mysterious thing that is completely homogeneously distributed in the universe. This Dark energy leads to more space - thus more dark energy, but you're telling me that even without any dark energy, there would still be an expansion? Didn't Steve Hawking say something like "The expansion of the universe is a function of the amount of dark energy"

I'll concede that gravity does not become negligible, that makes sense, it should be true that approaches a certain proportion (or lessening proportion) to the expansion.

I wonder if dark energy should even be considered energy, because if it's constantly growing, wouldn't that violate conservation? Does dark energy contain with it any observational signatures other than the expansion itself? Why not just say it's an attribute of 'empty' space rather than calling it energy? What does the term "energy" signify in the case of dark energy?

Last edited: Sep 6, 2008
9. Sep 6, 2008

### neutralseer

WCOLtd,

Once again, let me warn you, I'm neither a cosmologist nor a general relativity expert. I do astrophysics which (in my case) only requires me to have a peripheral knowledge of such fields.

You're thinking has certain similarities to Einstein's as he was developing his theory of gravity, general relativity. When I was speaking of gravity before, I was referring to Newtonian gravity (F=ma=-GMm/r^2), which is only approximately correct. Your questions go to the heart of Einstein's insights, namely the equivalence principle. Check out this link to learn about why a sky diver (who doesn't feel any air resistance) doesn't feel any force.

I don't think your right about the earth expanding, etc. Also, about the directed velocity: in general relativity a light object--say a satellite-- moving under Earth's influence is actually just moving in a straight line, it's just the mass of the Earth is warping space-time, which means that the straight line for the satellite is straight in the curved space-time. This produces what appears to us to be Newton's law of gravitation in a flat space-time.

You don't have to take special relativity into account here. Special relativity only applies on very small scales in the universe, in a static (i.e. not expanding) flat space. Thus, having galaxies moving faster than the speed of light presents no problems. There is time dilation, but it's not due to special relativity. A burst of photons from a supernova that lasts for a week, will last for 3 weeks by the time it gets to us if the supernova is at a certain cosmological (meaning ~billions of light years) distance. This dilation is only because space expansion stretched the "train" of photons, not due to special relativity.

Not an edge like a wall. Current observations (and theory) suggest our universe is infinite. If it were finite, there still wouldn't be a wall. Imagine we aren't 3-D creatures but 2-D creatures living in flatland, except flatland exists as the surface of a sphere. Then you could keep going and going in flatland and never reach the edge. Furthermore, if you kept going in a straight line, you'd eventually circumnavigate the universe! This type of universe is clearly finite and has a radius of curvature. If such a finite universe were the 3-D analog of the 2D surface of a sphere, then the radius of curvature would simply be the radius of the sphere.

You're right. Light from distant galaxies is not just appearing redder due to expansion, but it's apparent brightness decreases because of expansion too. So, a light source far away enough will be redshifted so much we won't be able to see it.

Yep. We don't know what initially caused the universe to start expanding, but once it started we can use general relativity to tell us how the expansion is slowing down or speeding up. For must of the universe's history, expansion was slowing down due to the mass in the universe. Only recently (in the last 4 billion yrs or so) has dark energy caused the expansion to start accelerating. This is because the most important thing in cosmology is the energy density of stuff. The energy density of matter is decreasing with time, since the volume of space between galaxies is increasing, but the amount of matter isn't. Thus the matter energy density has been decreasing all this time, while dark energy density has remained constant (maybe). About 4 billion yrs ago the matter density finally decreased enough so that it was equal with the dark energy density, and the expansion of space started accelerating. Stephen Hawking is right, but expansion is also a function of the amount of matter and radiation too! (As time progresses and the matter and radiation energy densities get diluted to zero, dark energy will be the only thing affecting expansion)

Don't think about the total amount of dark energy since space is (probably) infinite, in this case talking about the total amount of anything doesn't make much sense. It's all about energy densities (Amount of energy per volume of space). In fact, in general relativity, talking about energy conservation in the universe is a very tricky business.

Very astute observation. Once again, energy conservation in the universe is a tricky business so I'll avoid that question, but moving on... Dark energy does have other observational signatures but they are more indirect. Namely, we've pinned down the total energy density of the universe, and we can only "see" about 30% of this total energy density, we're missing 70% of it! As it turns out, the acceleration of expansion is the only direct evidence of the missing 70%. The observations this is all predicated on related certain statistical properties of the CMB and the distribution of galaxies and stuff in the cosmos.

You're right that people could call dark energy an attribute of space itself. Sometimes people just call it the cosmological constant or vacuum energy (vacuum refers to empty space). The term energy in this case, just refers to fact that, in the absence of this stuff/thing/property-of-space, the motion of galaxies wouldn't be accelerating. In general relativity, only energy can affect space time (in this case causing the expansion of space to accelerate).

Great questions.

10. Sep 8, 2008

### WCOLtd

To Neutralseer,
I appreciate all your answers, I can say that I have learned more than I ever thought I would.

Yeah, I think there are some serious issues with my idea

I don't know if there is any observational difference between the two cases, an opposing velocity, and one which there's an expanding wavelength

I heard that analogy before, in Steven Hawkings "A Brief History of Time" and in Lisa Randall's "Warped Passages"

Does light going around the event horizon of a black hole red-shift with time just as if it were traveling across the universe?

Empty space has properties like "dark energy" but does it posess any form of comparable properties? Meaning, does there exist an energy to (expanding) distance equivalency? For instance, if you have a mass of 10 kg and you were able to convert all that rest-mass energy into pure distance, what volume of empty space would it constitute? I thought that maybe entirely red-shifted light (light of zero frequency) actually contains energy. Is that what "dark energy" is insinuating?

11. Sep 10, 2008

### WCOLtd

Imagine two circles seperated by a distance of r, according to one theory, the distance between the two circles measured in terms of the size of the circle increases with time.
That would be analgous to saying that the distance r remains constant and the sizes of the circles shrink with time.

Could that same concept be applyed to the universal expansion model to explain the expansion of the universe? in terms of a relative shrinkage of the observers?

is light only an interaction between masses? Or does it travel into the depths of space indefinitely? In other words, does baryonic matter in the universe decrease with time as a function of emitted light? (Since that light is ultimately being created by the rest-mass energy of the star and since that light never gets re-absorbed into rest-mass?)