Red Shifts and the expanding universe

[Mike2]

In a denser past the universe was also homogeneous and isotropic on large scales and therefore the photons were not forced to climb out of any potential wells against any special direction. Local inhomogeneities, however, may lead to a redshift or blueshift of photons emitted beyond them.

Yes, I think we're talking about the Sachs-wolfe effect described at:

http://en.wikipedia.org/wiki/Integrated_Sachs_Wolfe_effect

I'm not so sure. Wouldn't a photon climbing out of a less dense region be redshifted less than one climbing out from near the surface of a black hole with the same mass? So if the redshift depends on density, than wouldn't the expansion cause a less of redshift with time? If a photon looses energy because by the time it leaves a galaxy cluster that cluster has become more compact, then wouldn't there be a similar effect from the average density decreasing with time?

As an after thought, is it because the galaxies are not gravitationally bound their increasing distance does not have gravitational effects of tranversing photons?

 

[hellfire]

I'm not so sure. Wouldn't a photon climbing out of a less dense region be redshifted less than one climbing out from near the surface of a black hole with the same mass?

Yes, the amount of gravitational redshift depends not only on the mass but also on the distance (to the mass) from which the photon is emitted.

If a photon looses energy because by the time it leaves a galaxy cluster that cluster has become more compact, then wouldn't there be a similar effect from the average density decreasing with time?

No, as far as I know. Both scenarios are different. For gravitational redshift to take place there must be a potential well. The photon climbs out of it to the region where the gravitational interaction is weaker getting redshifted. In a perfectly homogeneous and isotropic universe there is no such a situation.

 

[Mike2]

Yes, the amount of gravitational redshift depends not only on the mass but also on the distance (to the mass) from which the photon is emitted.


No, as far as I know. Both scenarios are different. For gravitational redshift to take place there must be a potential well. The photon climbs out of it to the region where the gravitational interaction is weaker getting redshifted. In a perfectly homogeneous and isotropic universe there is no such a situation.

What I guess I'm wondering about is doesn't the gravitational well get deeper for more dense homogeneous isotropic distributions? Isn't a photon in the middle of a very dense distribution of dust in a deeper well then such a fine distribution of dust? What exactly is the equation for the gravitational well for an even distribution, and how does it change with lighter density?

 

[Mike2]

What I guess I'm wondering about is doesn't the gravitational well get deeper for more dense homogeneous isotropic distributions? Isn't a photon in the middle of a very dense distribution of dust in a deeper well then such a fine distribution of dust? What exactly is the equation for the gravitational well for an even distribution, and how does it change with lighter density?

The gravitational potential, U, can be calculated at any point, \[<br /> {\rm{\vec r}}<br /> \], for a mass density distribution, \[<br /> {\rm{\rho (r)}}<br /> \], using the formula:

\[<br /> {\rm{U = - }}\int_{{\rm{all space}}} {G\frac{{{\rm{\rho }}({\rm{\vec r&#039;)}}}}{{\left| {{\rm{ \vec r - \vec r&#039; }}} \right|}}} \,\,\,d^3 {\rm{r&#039;}}<br /> \].

See:
http://scienceworld.wolfram.com/physics/GravitationalPotential.html

Integrating over the same region with a lesser fixed desity means the potential is less. And photons would be blue shifted as the density is decreased. But since things are not static, galaxies are moving apart, I wonder how that would affect the calculation. I suppose you'd have to integrate over time as well from when the photon was emitted to when it was received. Perhaps the region of integration would increase with expansion, or maybe the region remains out to the event horizon for a given time. But since even the most distant galaxies are still within our view, I suppose we would have to feel their gravity as well.

 

[hellfire]

My understanding of gravitational redshift is based on the derivation that is usually done based on the Schwarzschild geometry, so I may be missing something in your argument. But even the SW and ISW effects are derived in this way, making use of the Newtonian approximation. This means that for (this kind of) redshift to take place you have always a inhomogeneous distribution of energy density in the line of sight. Consider a photon emitted from x_0 and traveling on a direction x in an homogeneous and isostropic expanding space. There will be never an inhomogeneous distribution of energy density in the line of sight and thus it is not possible to find any region so that the photon may "feel" any kind of attraction during its journey from x_0, along x to the observer. It seams to me that you claim that the photon "feels" the attraction of the energy density that existed in past, but I fail to make any sense of this.

 

[Mike2]

My understanding of gravitational redshift is based on the derivation that is usually done based on the Schwarzschild geometry, so I may be missing something in your argument. But even the SW and ISW effects are derived in this way, making use of the Newtonian approximation. This means that for (this kind of) redshift to take place you have always a inhomogeneous distribution of energy density in the line of sight. Consider a photon emitted from x_0 and traveling on a direction x in an homogeneous and isostropic expanding space. There will be never an inhomogeneous distribution of energy density in the line of sight and thus it is not possible to find any region so that the photon may "feel" any kind of attraction during its journey from x_0, along x to the observer. It seams to me that you claim that the photon "feels" the attraction of the energy density that existed in past, but I fail to make any sense of this.

I don't know. It seems obvious to me. Given a potential


\[<br /> {\rm{U = - }}\int_{{\rm{all space}}} {G\frac{{{\rm{\rho }}({\rm{\vec r&#039;)}}}}{{\left| {{\rm{ \vec r - \vec r&#039; }}} \right|}}} \,\,\,d^3 {\vec{r&#039;}}<br /> \].

if the density decreases so does the potential. A homogeneous, isotropic universe only means that rho is constant over space. But if rho decreases with time, then the potential that a test particle (or photon) would feel will also decrease with time. And a photon feeling less of a potential will be blueshifted compared to the prior potential that it felt. There might be some complications when trying to apply this to an expanding universe, but I think just this much would indicate that it should be considered, right?

I think that the usual GR derivation assumes a none interacting dust, but I'm asking what happens if the dust has a gravitation interation.

 

[hellfire]

A homogeneous, isotropic universe only means that rho is constant over space. But if rho decreases with time, then the potential that a test particle (or photon) would feel will also decrease with time.

It does not "feel" any potential because it is immersed in a homogeneous and isotropic distribution of matter.

 

[Mike2]

It does not "feel" any potential because it is immersed in a homogeneous and isotropic distribution of matter.

I suppose my question is: why does the integral in post 36 not apply? Or why is it constant for temperal change in the spatially invariant mass density? If this is a new consideration that has not been mathematically proven irrelevant, then it has the potential to remove the cosmological constant from the supernova data. For a correction of redshift due to changing potential energy might offset the acceleration we see in the supernova data.

 

[Mad_Morlock]

Big questions.

1. Why is Virgo the only cluster of galaxies massively blue-shifted?

2. Why are galaxies in the Draco cluster supermassively redshifted?

3. Does the metric expansion of space imply a decrease or implosion across a 4th dimension?

 

[Chris Hillman]

Milne universe distinct from Minkowski vacuum?

Hi, spacetiger,

I am also puzzled by your assertion that "the Milne cosmology is an actual model of the universe, not just a different coordinate system", probably because I don't fully understand what you have in mind when you say "model of the universe".

My own view (which is the mainstream view, at least in classical gravitation) is that a cosmological model is a spacetime model (Lorentzian manifold) together with some tensor fields (spinor fields, whatever) describing some nongravitational physics. Strictly speaking, such a model should in some sense should be consistent with the idea that it is describing very large scale physical phenomena, possibly in a highly idealized fashion.

To fix ideas: a familar example of a cosmological model in gtr, in the sense I have in mind, would be the FRW dust solution with E^3 hyperslices orthogonal to the world lines of the dust particle (in MTW, a marginally open matter-dominated zero Lambda FRW model), which is a Lorentzian universe equipped with a tensor field describing a (pressureless) perfect fluid. But as this example illustrates, in fact it often suffices to give the metric tensor in some coordinate chart, adding only that we consider this spacetime model a perfect fluid solution in gtr, since the stress-energy tensor of our perfect fluid and the world lines of the fluid particles can then be obtained from the EFE, by computing the Einstein tensor directly from the given metric (which also shows that the pressure measured by observers flowing with the fluid is zero).

In more complicated situations, of course, simply specifying that we consider a given Lorentzian manifold to be a solution in gtr of a given type (e.g., perfect fluid plus Lambda plus source-free EM field plus a minimally coupled massless scalar field) might not be quite enough to deduce the intended nongravitational physics from the EFE alone. In any case, whatever deductions are possible are most conveneniently discovered by employing an appropriate frame field (called an "anholonomic basis" in MTW).

From this viewpoint, it seems to me, it is natural to consider the Milne model to be nothing but a certain vacuum solution (the Minkowski vacuum) equipped with a timelike congruence (which can be naturally if not quite uniquely extended to a frame field corresponding to a family of inertial non-spinning observers) which we consider to model the world lines of galaxies. But in this cosmological model, galaxies are treated (in gtr) as test particles, unlike the FRW models and more interesting models, in which they produce a nonvanishing gravitational field. If you drop the somewhat dubious assertion that a particular family of test particles (timelike congruence) is distinguished, in gtr the Milne model does then reduce to the "Milne chart" for the Minkowksi vacuum solution.

Maybe the distinguished timelike congruence is the additional structure you had in mind?

 

[Chronos]

But isn't the Milne model an oversimplification designed to test other hypotheses? In my mind, Milne is the poor man's null hypothesis in an N simulation.

 

[SpaceTiger]

From this viewpoint, it seems to me, it is natural to consider the Milne model to be nothing but a certain vacuum solution (the Minkowski vacuum) equipped with a timelike congruence (which can be naturally if not quite uniquely extended to a frame field corresponding to a family of inertial non-spinning observers) which we consider to model the world lines of galaxies. But in this cosmological model, galaxies are treated (in gtr) as test particles, unlike the FRW models and more interesting models, in which they produce a nonvanishing gravitational field.

All I'm saying is that you can't simply take an FRW model and change the coordinate system to get the Milne cosmology and, thus, cannot interpret redshift as a doppler shift. A Minkowski vacuum with timelike congruence is not consistent with the data. Even further, to treat the galaxies as non-gravitating test particles requires new physics (or, at least, the rejection of old physics), since these galaxies have been independently measured to have cosmologically significant masses.

 

[heusdens]

I hope I didn´t misinterpret you, but I think the stretching of the photon due to the cosmic expansion is the only possible explanation for such enormous redshifts.

There are of course other possible candidates for explaining redshift-distance correlation. For instance, the light on it's long way (billions of years) could interact with interstellar atoms, ions, molecules, dust or other particles/material objects, and get redshifted because of that.
That none of these have turned out to be right is another question.

 

[Pavel]

Hi, sorry to bring this thread back, but this is a very interesting topic. I read some references and I think ended up more confused than enlightened. So, if you could answer just one simple thought-experiment question to me, I'll be clear and grateful.

So, I have a star and the Earth in the same reference frame - no motion relative to each other. The star emits a photon in the direction of the Earth. The photon has frequency x. ( I assume a single photon has frequency. After all, its energy level is defined by e=hv, right?) Now, some time during its journey to the earth, space between the star and the Earth starts expanding. Then the expansion stops while the photon is still travelling! Now the star and the Earth in the same frame again. The photon finally reaches the Earth. My question is, does the photon have the same frequency x when it arrived or did it get redshifted because there was a period of expansion on its journey.

If the answer is the same x, things would get pretty hot right now if the expansion of the universe stops (despite the fact that radiation got deluded), wouldn't they?

In advance, thanks!

Pavel

 

[Mike2]

So, I have a star and the Earth in the same reference frame - no motion relative to each other. The star emits a photon in the direction of the Earth. The photon has frequency x. ( I assume a single photon has frequency. After all, its energy level is defined by e=hv, right?) Now, some time during its journey to the earth, space between the star and the Earth starts expanding. Then the expansion stops while the photon is still travelling! Now the star and the Earth in the same frame again. The photon finally reaches the Earth. My question is, does the photon have the same frequency x when it arrived or did it get redshifted because there was a period of expansion on its journey.

The photon frequency would not change. The change in frequency is due to the Dopler effect, due to the preceived velocity. With initially no recession velocity, then some, then none again, by the time the photon got here, the stretching due to velocity would be compensated for. It would be as though the photon was first accelerated away from us, and then accelerated towards us. The final distance to the star would have changed, but not its velocity at the time of reception.

If the answer is the same x, things would get pretty hot right now if the expansion of the universe stops (despite the fact that radiation got deluded), wouldn't they?

I don't think things would get hotter because the density has been reduced quite a lot since it initial start of expansion.

 

[Pavel]

I don't think things would get hotter because the density has been reduced quite a lot since it initial start of expansion.

Well, if the frequency of the photon is the same when emitted and received, then it follows that all the light that we receive today would be of higher energy, some much higher, if the Universe would stop expanding today. What would happen to the CMBR? Also, what about Olbers's Paradox? Isn't [pretty much] the only solution to the paradox the expansion of the Universe? If the expansion stops, the sky would be lit, wouldn't it?

That's what makes me think things would get hot indeed. But I'll go with the experts' opinions.

Pavel.

 

[hellfire]

Cosmological redshift is not due to Doppler effect (relative motions), but due to stretching of space (change of geometry). I think that the photon in your Gedankenexperiment would get redshifted.

 

[Jorrie]

We won't fry

Well, if the frequency of the photon is the same when emitted and received, then it follows that all the light that we receive today would be of higher energy, some much higher, if the Universe would stop expanding today.
Pavel.

I think Hellfire has effectively answered the questions indirectly, but to make it clearer, think about cosmological redshift as equivalent to the ratio (or factor) that the universe has expanded by between the time the photon has left the source and the time the photon reaches the observer. The wavelength of the photon has been stretched and stays stretched. Hence, if the universe would hypothetically stop expanding, the redshifts we measure will not change, neither will we fry.

Actually, loosely speaking, one can say that the cosmological redshift on its own does not really show that the universe is expanding, only that it has expanded!

Jorrie