Understanding Astrophysics: The Hubble Distance and Beyond

[marlon]

You know, there are many things in astrophysics, that i do not understand

For example, this thing of the Hubble distance. At distances that exceed the Hubble distance the universe is expanding with velocities that are bigger then the speed of light. Suppose that in this region a star emits light, then we would never be able to see that light because this star moves away from us with a velocity that is bigger then the velocity with which the EM-radiation is propagating towards us. But i heard this statement is wrong because as time passes by this Hubble distance gets bigger and bigger. So at some time, the Hubble distance will be bigger then the distance between us and the star and we would indeed be able to see the cosmological redshifted emitted light. Is this correct, SpaceTiger ? How was this discovered in General relativity ?

regards
marlon

 

[dextercioby]

And if we did see that radiation,what would make us think it's a purely (general) relativistic effect,and not a quantum one,similar in a way to the Hawking radiation...?

Smart question,Marlon. Mine is not bad,either.

Daniel.

 

[marlon]

Ha, i think we are going to have to wait awhile because SpaceTiger is very busy writing a post in the "A conceptual problem regarding work" thread...mmm

marlon

ps dexter, is it my imagination or do we indeed get along better since i started doing physics in Leuven ? :)

 

[dextercioby]

Your imagination is flying ...

We've never had an argument,remember (i asked Greg to delete the posts,but keep the postcount,so you wouldn't find out ) ?

We've always gotten along just fine...

Daniel.

 

[hellfire]

The Hubble sphere (with radius = c / H) is not an horizon. In case of a de-Sitter expansion (exponential expansion due to an empty universe but with a cosmological constant), the Hubble parameter is constant through time and the event horizon (limit of objects whose light will never reach us in future) is actually located at the Hubble sphere. Otherwise, for an universe with matter content the event horizon, if it exists, is always greater than the Hubble sphere. Objects beyond the Hubble sphere but inside the event horizon emit photons towards us which are overtaken by the recession of the Hubble sphere (the Hubble parameter decreases with time in an universe with matter content). Photons emitted by objects beyond the event horizon will be never overtaken by the Hubble sphere and will never reach us. May be this paper helps: http://arxiv.org/astro-ph/0310808 .

 

[SpaceTiger]

Horizons are calculated by examining the motion of a light ray in comoving coordinates. Why comoving? Because we want to know how the light moves relative the galaxies, which are expanding. The Friedmann-Robertson Walker metric for a flat, homogeneous and isotropic universe is

$$ds^2=dt^2-a(t)^2dr^2-a(t)^2r^2d\psi^2$$

where I've set c=1. If we're following a photon moving radially, we have ds=0 and $$d\psi=0$$, so it simplifies to:

$$dt=adr$$

So if we want to see how far it goes from t=0 (the big bang) to some later time, we get

$$r=\int_0^{t_0} \frac{dt}{a(t)}$$

This is the particle horizon. Likewise, we can define an event horizon as the comoving distance it travels from t=t₀ to infinity:

$$r=\int_{t_0}^{\infty} \frac{dt}{a(t)}$$

The fate of the photon depends on the model of the universe that you're using. The current universe is a bit complicated, but we can examine the limiting cases. Until recently, the universe was well described by a flat, matter-dominated model. This gives a scale factor dependence of

$$a(t)=a_0t^{2/3}$$

Putting this into the equation for the particle horizon, we get

$$r_p \propto t^{1/3}$$

That is, people observing the universe at later times can see more of it. Notice also that the event horizon diverges, meaning that a light ray emitted from the Earth will eventually explore the whole universe.

This is not the universe that we live in, however. We currently think that the late-time expansion of the universe will be dominated by a "cosmological constant", a field with constant energy density that pervades the universe. By the Friedmann equation in a flat universe:

$$H^2=\frac{8\pi G\rho}{3}$$

a constant energy/mass density will mean a constant Hubble constant. What does that mean for the scale factor?

$$H=\frac{\dot{a}}{a}$$

$$a=a_0e^{Ht}$$

This is exponential expansion. Finally, we can plug this into the equation for the event horizon and get:

$$r_e=\frac{1}{a_0H}e^{-Ht_0}$$

A finite value! This means that, with our current understanding of the universe, we don't think that we, or anyone else, will ever be able to see or communicate with the whole thing. I wouldn't put a lot of faith in our current models, though, so think of this instead as one possibility.

Note 1: Hellfire is right that none of the things we're concerned about here are called the "Hubble horizon", but I just assumed you meant the particle and event horizons.

Note 2: Please feel free to ask me to explain any of this further, I was a bit liberal with the math and terminology this time around.

 

[Nereid]

Daniel and marlon: have you taken the time to read through Ned Wright's Cosmology tutorial? It contains links to his full set of lecture notes for two university courses on cosmology ... if you do take a gander, would you mind letting us know if you find the material useful? interesting??

 

[marlon]

Thanks SpaceTiger for the text and thanks Nereid for the link...Give me some time to check it out

regards

marlon

 

[Haelfix]

Hellfire is 100% correct.

We can in principle (with an open-expanding universe) see objects that are receding at faster than light, this has caused a lot of confusion and is often badly explained in textbooks.

To wit, our particle horizons is LARGER than our event horizons. So while we will never see an actual event in a galaxy that has passed our event horizon, we can still see the galaxy as it was from long ago, from a time when it was within our event horizon.

The other related confusion is how people note Inflation is superluminal expansion, whereas standard cosmology is not. This is misleading, and may or may not be correct. All objects that satisfy Hubbles law have superluminal expansion if they are sufficiently distant from an observer. The only difference is in inflation the Hubble constant is much larger than after it is over. Really to fully justify calling Inflation 'pure superluminal expansion' you would want all distances, down to the Planck scale to be receding faster than light, or in other words some huge value of Hubbles constant (and it is probably never that large)

 

[Andrew Mason]

You know, there are many things in astrophysics, that i do not understand

For example, this thing of the Hubble distance. At distances that exceed the Hubble distance the universe is expanding with velocities that are bigger then the speed of light. Suppose that in this region a star emits light, then we would never be able to see that light because this star moves away from us with a velocity that is bigger then the velocity with which the EM-radiation is propagating towards us. But i heard this statement is wrong because as time passes by this Hubble distance gets bigger and bigger. So at some time, the Hubble distance will be bigger then the distance between us and the star and we would indeed be able to see the cosmological redshifted emitted light. Is this correct, SpaceTiger ? How was this discovered in General relativity ?

I share a similar sense of bewilderment about the theories of astrophysics. I have never really understood why a period of superluminal expansion is thought to be needed to explain the post-big bang universe.

I don't think it has ever been established that the universe exists at distances greater than C/H. Absent some superluminal 'expansion', C/H represents the maximum radius of the universe.

As you point out, H is not really a constant. H represents inverse time... so as time passes, H decreases. Also H is frame dependent. I think C/H will always exceed the width of the universe in every frame of reference (as H is measured in that frame).

AM

 

[yogi]

AM - I would agree - I like to envision the Hubble Sphere as a closed two dimensional universe - every observer at any point on the surface of this expanding bubble can see all other observers - the observers are not aware of the curvature, so all other points appear to be moving away in a plane tangent to the surface of the sphere at the observers location (a two dimensional radial divergence). In other words, all observers share the same space and each can see light that is emitted from any point on said surface if they wait long enough, but each views the same universe from his own perspective.

Open Universes lead to many questions that don't get easily answered - similarly, inflation also creates problems which might be easer solved by assuming an exponental spaciotemporal scale - e.g., expansion may be driven by an exponential function as are many other naturally occurring process. One of the nice results of these musings is that there no longer has to be a beginning in the spatial or temporal sense.

 

[pervect]

I share a similar sense of bewilderment about the theories of astrophysics. I have never really understood why a period of superluminal expansion is thought to be needed to explain the post-big bang universe.

Have you read about "The Horizon Problem" in GR?

http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/HorizonProblem.html

also (you have to skip down a lot)

http://www.astro.ucla.edu/~wright/cosmo_03.htm

 

[Andrew Mason]

Have you read about "The Horizon Problem" in GR?

http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/HorizonProblem.html

also (you have to skip down a lot)

http://www.astro.ucla.edu/~wright/cosmo_03.htm

The horizon problem seems to be the result of a disparity between the age of the universe and the size of the universe. But neither of these are values have been reliably established. Until they are, it seems rather premature to get worked up about 'contradictions' and the need to invent fancy explanations for them.

AM

 

[pervect]

The horizon problem is related to the issue that the big bang is not a point, but has a causal structure. The causal structure is such that we wouldn't expect the microwave background radiation to be isotropic without some mechanism such as inflation.

 

[Andrew Mason]

The horizon problem is related to the issue that the big bang is not a point, but has a causal structure. The causal structure is such that we wouldn't expect the microwave background radiation to be isotropic without some mechanism such as inflation.

Why?
If the big bang produced a uniform isotropic explosion of whatever it was that exploded out of it (and which later formed into quarks, electrons, nuclueons atoms photons etc, let's call it big bang stuff) presumably the big bang stuff would all behave in the same way in all directions.

The stuff on the outer edge of the expanding universe would be traveling at something very close to the speed of light (very large gamma) so the radiation it emitted would be doppler shifted into the microwave range. The isotropic nature of that radiation is simply the result of the stuff on the outer edge of the universe having been created at the same time and having the same speed.

In other words, and I may be missing something, the causal connection seems to me to be with the common origin of the stuff on the outer edge of the exploding universe.

AM

 

[pervect]

The common idea of the big bang is a more-or-less single cause that occurs at a single point that caused the universe.

Not only is this the common idea, it's the idea that the isotropy of the microwave background radiation supports. The temperature of the universe is nearly the same in all directions, suggestion that all of the microwave background radiation came from some sort of single cause, this cause set the temperature that we observe.

There is only one small problem with this idea, and that is that the solutions of GR wihtout inflation say that the events that we see on the "left side" of the universe do not and never did have any common history with the events we see on the "right side" of the universe.

But nonetheless we see that these events have almost exactly the same temperature.

Inflation solves this dilema, by providing a means whereby past history can affect both events.

I'd suggest going back and reading the links I quoted - not only can the authors write in more depth than I can in a post, they can include diagrams.

 

[Garth]

The horizon problem is caused by the deceleration of the universe's expansion - an inevitable feature in Friedmann cosmology of a non-empty universe. However we do not live in a Friedmann universe, apparently the universe is accelerating, and this would reverse the horizon problem - everything could be in causal contact with the earliest space-like surface of the observable universe. However recent (distant SN Ia)acceleration is switched on and off and as a result cannot itself resolve the horizon problem. That is why the enormous acceleration of the inflation epoch is required.

However if the universe is not decelerating in the first place e.g. in the “Freely Coasting” model then the horizon problem does not exist in the first place, neither do the smoothness and density problems, and inflation is not required. Occam's razor anybody?

Garth

 

[DrChinese]

Why?
If the big bang produced a uniform isotropic explosion of whatever it was that exploded out of it (and which later formed into quarks, electrons, nuclueons atoms photons etc, let's call it big bang stuff) presumably the big bang stuff would all behave in the same way in all directions.

The stuff on the outer edge of the expanding universe would be traveling at something very close to the speed of light (very large gamma) so the radiation it emitted would be doppler shifted into the microwave range. The isotropic nature of that radiation is simply the result of the stuff on the outer edge of the universe having been created at the same time and having the same speed.

In other words, and I may be missing something, the causal connection seems to me to be with the common origin of the stuff on the outer edge of the exploding universe.

AM

I believe that your explanation inevitably leads to the prediction of shock waves in the CMBR which aren't seen by WMAP. The accelerating expansion models don't suffer from this feature.

 

[Andrew Mason]

The common idea of the big bang is a more-or-less single cause that occurs at a single point that caused the universe.

Not only is this the common idea, it's the idea that the isotropy of the microwave background radiation supports. The temperature of the universe is nearly the same in all directions, suggestion that all of the microwave background radiation came from some sort of single cause, this cause set the temperature that we observe.

There is only one small problem with this idea, and that is that the solutions of GR wihtout inflation say that the events that we see on the "left side" of the universe do not and never did have any common history with the events we see on the "right side" of the universe.

But nonetheless we see that these events have almost exactly the same temperature.

Do you mean "common history" or "causal interaction"? The events on the far left side of the universe may have had no interaction with those on the far right side. But they may well have had a common history.

The light cones of these events may not intersect at any time after the big bang. But that does not mean they lack a common origin and history.

Inflation solves this dilema, by providing a means whereby past history can affect both events.

I guess one has to see it as a dilemma first. It seems a bit like pulling a rabbit out of a hat. I don't see any evidence for it.

Hyperphysics has a pretty good explanation of some of these issues.
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/inflat.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/cosmo.html#c5
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/wmap.html#c1

AM

 

[pervect]

The horizon problem is caused by the deceleration of the universe's expansion - an inevitable feature in Friedmann cosmology of a non-empty universe.

Let me see if I can clear something up - if we look at Ned Wright's conformal diagram at the end of

http://www.astro.ucla.edu/~wright/cosmo_03.htm

are you saying that conformal time extends backwards indefinitely in the freely coasting model, instead of stopping at the bottom of the page, so that the yellow triangles do overlap (?).

 

[pervect]

Do you mean "common history" or "causal interaction"? The events on the far left side of the universe may have had no interaction with those on the far right side. But they may well have had a common history.

I mean common history. Take a look at the figure I mentioned at the bottom of Ned Wright's cosmology page. You really need to look at the pages I'm referencing, I'm giving the links for a reason. If you can't look at them all, you

*really*

still need to look at the one on Ned's page!

To actually draw Ned's diagram for yourself to gain a deeper understanding, you need to know how light-like geodesics are calculated, plus the notion of "conformal time"

One way of getting the equations for lightlike geodesics has been discussed in another thread

https://www.physicsforums.com/showthread.php?t=77636

This is the straightforwards but stupid way, using the Geodesic equations

http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/GeodesicDeviation.htm

If you take the metric

ds^2 = a(t)^2 (dx^2 + dy^2 + dz^2) - dt^2

The geodesic equations x = x(lambda), t=t(lambda) below, where the prime mark represents differentiation with respect to lambda. These are computed from the Christoffel symbols for the metric above

x'' + 2 [da/dt / a] x' t' = 0
t'' + a da/dt (x')^2 = 0

The first equation reduces to a^2(t)*x' = constant, i.e.

$$\frac{d}{d \lambda} \, [ a(t)^2 \frac{dx}{d \lambda} ]= 0$$

The constant above is a conserved momentum-like quantity, which exists for spacelike, timelike, and light-like geodesics. A more sophisticated explanation for the existence of this constant is that it is the consequence of the spatial symmetry of the metric above - space translation invariance gives rise to a conserved momentum.

If you don't have tensor analysis, you can just take this single equation as a given for now. It's the only thing you'll need to assume other than fairly straightforwards calculus. There is a fair amount of calc. required to derive the final results, though.

The second equation can be greatly simplified too. For lightlike geodesics it becomes

a^2(t)*(x')^2 - (t')^2 = 0

It's just saying that the Lorentz interval of a light-like geodesic is zero. This should be obvious.

It's difficult to see the cause and effect relationships, the light cones, until one introduces 'conformal time'

http://www.physics.louisville.edu/astro/students/590/sdss/node8.html

Conformal time eta has the property that

$$d \eta = \frac{dt}{a(t)}$$

In conformal time, the equations for light-like geodesics are simple

$$x = \eta + k$$ or $$-\eta + k$$

(it is assumed that we are using geometric units for time and distance).
The rest is just a matter of drawing the light-like geodesics on a diagram, which is simple because they are straight lines. The valid values for eta are those which corresponds to times t > 0, as the big bang is a singularity at which the laws break down.

 

[Garth]

Let me see if I can clear something up - if we look at Ned Wright's conformal diagram at the end of

http://www.astro.ucla.edu/~wright/cosmo_03.htm

are you saying that conformal time extends backwards indefinitely in the freely coasting model, instead of stopping at the bottom of the page, so that the yellow triangles do overlap (?).

More or less. Those yellow triangles in NW's diagram aren't triangles even in a Friedmann model, the inner edges bend in towards the centre but still leaving a gap between them. They should be distorted in the same way that the sixth diagram distorts the geometry when seen from A's point of view.
Remember the vertical world-lines actually are converging as t -> 0.

In the R = t model the inner edges of the yellow triangles overlap.

Garth

 

[pervect]

More or less. Those yellow triangles in NW's diagram aren't triangles even in a Friedmann model, the inner edges bend in towards the centre but still leaving a gap between them.

I think you may be misinterpreting what the diagaram is a diagram of. The vertical lines represent galaxies which have a constant co-moving spatial coordinate. The time on the diagram, however, is scaled such that light cones *ARE* exactly triangles, as per the text. This means that horizontal lines on the diagram are at a constant cosmological time coordinate 't', but that the distance between horizontal lines is not scaled linearly. Alternatively, we can say that the time on the diagram is linear in some "conformal time" $$\eta$$.

What's important to the horizon problem is the realationship between conformal time and cosmological time.

If we let $$\eta$$ be the conformal time in which the diagram is plotted, and t be cosmological time (the proper time of a co-moving observer), I get

$$t = \frac{1}{4}\eta^2$$
for the Friedman model and

$$t = e^{\eta H}$$

for the freely-coasting model. Since I worked these out for myself on the back of a (computerized) envelope, there is some possibility for error in the expressions :-(.

We can see that the valid range for conformal time is zero to infinity for the Friedmann model, but it's minus infinity to plus infinity for the freely coasting model.

[add1]
What's important to solving the Horizon problem is the relative interval in _conformal time_, between now and the point where the universe became transparant, vs the interval in conformal time between when the universe became transparent and the big bang.

In the Friedman model, the first interval is very large, and the second very short, so there is a definite horizon problem.

In the freely-coasting model, I'm getting the result that the second interval is _infinite_, so assuming this is correct there is no problem.

[add2]
Anyway, assuming this is all correct, it appears to me that the freely coasting model does indeed solve the horizon problem as advocated. I looked up some of the papers on nucleosynthesis - I can't really follow the details but it looks like the advocates of the theory have addressed this obvious point, and feel that it agrees with experiment. (I don't know what the critics think).

So the biggest question at this point is recovering from the damage that the theory does to Einstein's field equations, which predict a(t) = sqrt(t) for the early universe and not a(t)=t as the theory demands.

In other words, can the theory be made consistent with gravity?

 

[Garth]

I think you may be misinterpreting what the diagaram is a diagram of. The vertical lines represent galaxies which have a constant co-moving spatial coordinate. The time on the diagram, however, is scaled such that light cones *ARE* exactly triangles, as per the text. This means that horizontal lines on the diagram are at a constant cosmological time coordinate 't', but that the distance between horizontal lines is not scaled linearly.

I realize that - the geometry at the edge of this last diagram is not as straight forward as NW has made out - try plotting the inflation period during which the scaling of conformal time is reversed, i.e. the horizontal lines of arrowheads get closer together in the t->0 direction. How does that make the yellow areas overlap as it should? They should be skewed so their bottom edges reaches towards the centre line.

Alternatively, we can say that the time on the diagram is linear in some "conformal time" $$\eta$$.

What's important to the horizon problem is the realationship between conformal time and cosmological time.

If we let $$\eta$$ be the conformal time in which the diagram is plotted, and t be cosmological time (the proper time of a co-moving observer), I get

$$t = \frac{1}{4}\eta^2$$
for the Friedman model and

$$t = e^{\eta H}$$

for the freely-coasting model. Since I worked these out for myself on the back of a (computerized) envelope, there is some possibility for error in the expressions :-(.

That is quite correct

We can see that the valid range for conformal time is zero to infinity for the Friedmann model, but it's minus infinity to plus infinity for the freely coasting model.

So in NW's diagram the bottom line is projected downwards 'to infinity' and the yellow triangles overlap, skew or no skew, as you originally suggested.

[add1]
What's important to solving the Horizon problem is the relative interval in _conformal time_, between now and the point where the universe became transparant, vs the interval in conformal time between when the universe became transparent and the big bang.


In the Friedman model, the first interval is very large, and the second very short, so there is a definite horizon problem.

In the freely-coasting model, I'm getting the result that the second interval is _infinite_, so assuming this is correct there is no problem.

[add2]
Anyway, assuming this is all correct, it appears to me that the freely coasting model does indeed solve the horizon problem as advocated. I looked up some of the papers on nucleosynthesis - I can't really follow the details but it looks like the advocates of the theory have addressed this obvious point, and feel that it agrees with experiment. (I don't know what the critics think).

So the biggest question at this point is recovering from the damage that the theory does to Einstein's field equations, which predict a(t) = sqrt(t) for the early universe and not a(t)=t as the theory demands.

In other words, can the theory be made consistent with gravity?

The freely coasting model is an empirical model that works but requires a mechanism to deliver a(t)=t. Self Creation Cosmology provides that mechanism in the form of a non-minimally connected Machian (Brans Dicke) scalar field. Your equation for conformal time above, $$t = e^{\eta H}$$
is equation 68 in that SCC paper. The theory is highly falsifiable and it is being tested at the moment by Gravity Probe B, so the matter should be resolved, one way or the other, in less than a year.

Garth

 

[pervect]

I realize that - the geometry at the edge of this last diagram is not as straight forward as NW has made out - try plotting the inflation period during which the scaling of conformal time is reversed, i.e. the horizontal lines of arrowheads get closer together in the t->0 direction. How does that make the yellow areas overlap as it should? They should be skewed so their bottom edges reaches towards the centre line.

I don't think the diagram is meant to represent the universe with inflation, but the universe without inflation - which illustrates why the horizon problem exists with the standard Friedmann model in which a(t) = sqrt(t).

I don't quite follow the mental leap you are making to allow the bends - from my POV the whole point of the diagram is to keep the lines straight. But if we both accept that the diagram is drawn represents a non-inflationary universe, I'm not sure we need to go into any more detail on what the inflationary case would look like. I'm fairly happy with the "hand-waving" explanations of why inflation solves the horizon problem at this point (the point of updating the diagram would be to explain why inflation solves the horizon problem).

I can see the appeal of the rather elegant coasting model, the current model requires an inflationary phase, a radiation dominated phase, a matter dominated phase, and a cosmological constant dominated phase, whereas the coasting model has none of this, just a uniform expansion.

How does it (the freely coasting model) fare with regards to the supernova brightness results?

[add]
The other thing that inflation explains is the apparent spatial flatness of the universe - how does the freely coasting model fare in that regard?

 

[Garth]

I don't think the diagram is meant to represent the universe with inflation, but the universe without inflation - which illustrates why the horizon problem exists with the standard Friedmann model in which a(t) = sqrt(t).

I don't quite follow the mental leap you are making to allow the bends - from my POV the whole point of the diagram is to keep the lines straight. But if we both accept that the diagram is drawn represents a non-inflationary universe, I'm not sure we need to go into any more detail on what the inflationary case would look like. I'm fairly happy with the "hand-waving" explanations of why inflation solves the horizon problem at this point (the point of updating the diagram would be to explain why inflation solves the horizon problem).

There is no reason why that diagram cannot be drawn for various, indeed varying, a(t) = f(t). The geodesics converging radially onto the observer at top centre are straight, all others are 'skewed''

I can see the appeal of the rather elegant coasting model, the current model requires an inflationary phase, a radiation dominated phase, a matter dominated phase, and a cosmological constant dominated phase, whereas the coasting model has none of this, just a uniform expansion.

How does it (the freely coasting model) fare with regards to the supernova brightness results?

From A Concordant “Freely Coasting” Cosmology

Linear coasting is as accommodating for more recent high red-shift objects as the standard nonminimal inflationary model. The concordance of linear coasting with SNe1a data finds a passing mention in the analysis of Perlmutter [13] who noted that the curve for
Omega_lambda = Omega_M = 0 (for which the scale factor would have a linear evolution) is “practically identical to best fit plot for an unconstrained cosmology”. We display this “practical coincidence” in figure I that includes the more recent high redshift objects.

Note: That figure is at the end of that paper.

[add]
The other thing that inflation explains is the apparent spatial flatness of the universe - how does the freely coasting model fare in that regard?

From that same paper as above

The main point we make in this article is that in spite of a significantly different evolution, the recombination history of a linearly coasting cosmology can be expected to give the location of the primary acoustic peaks in the same range of angles as that given in Standard Cosmology. Given that none of the alternative anisotropy formation scenarios provide a compelling ab initio model [39] , it is perhaps best to keep an open mind to all possibilities. As the large scale structure and CMB anisotropy data continue to accumulate, one could explore the general principles for an open coasting cosmology to aid in the empirical reconstruction of a consistent model for structure formation.

The SCC model is subtlety different from their model in that it is closed; yet it is linearly expanding in its Einstein conformal frame and static in its Jordan conformal frame. These models are a cone and cylinder (Einstein's original model) respectively. Both are conformally flat. As the WMAP data is angular in nature, and angles are preserved by conformal transformations, conformally flat models appear spatially flat in the WMAP data. They are also spatially finite thus predicting that the largest fluctuations should be missing, as indeed they are in the WMAP, BALLOON and COBE data.


Garth

 

[Garth]

pervect

They should be skewed so their bottom edges reaches towards the centre line.

Obviously this poster did not know what they were talking about! In that final conformal diagram of NW's the null-geodesics are all straight lines. I was thinking about copying onto that diagram the early epoch when the rate of expansion is different. In fact in the radiation dominated era a(t) ~ t^1/2 the yellow light cones would be turned inwards if plotted on the same diagram, which would make the horizon problem worse. The outward skewed yellow triangle, which I was referring to, was that of inflation plotted on the same diagram.

A more consistent and less confusing way of comparing these different expansion rates would be to alter the time conformal transformation, as you suggested in the first place!

Having said that the argument holds firm: Friedmann models suffer from a horizon problem that can either be fixed by inflation, or that does not exist in the first place in a freely coasting model.

Garth

 

[pervect]

The SCC model is subtlety different from their model in that it is closed; yet it is linearly expanding in its Einstein conformal frame and static in its Jordan conformal frame.

Garth

This brings up another couple of questions, one of which is stability. One of the problems with Einstein's model was that his cosmology wasn't stable.

So is a linear expansion a(t) = t a stable solution for your SCC theory? (You've previously said it's a solution - is the solution stable?).

A related question refers to the required initial conditions. How probable is it that the initial conditions will be such that a(t)=t? Do two or more parameters have to have a specific ratio to get a(t)=t, or is it impossible to get any solution other than a(t)=t no matter what parameters you chose?

 

[Garth]

This brings up another couple of questions, one of which is stability. One of the problems with Einstein's model was that his cosmology wasn't stable.

So is a linear expansion a(t) = t a stable solution for your SCC theory? (You've previously said it's a solution - is the solution stable?).

A related question refers to the required initial conditions. How probable is it that the initial conditions will be such that a(t)=t? Do two or more parameters have to have a specific ratio to get a(t)=t, or is it impossible to get any solution other than a(t)=t no matter what parameters you chose?

The last option, the theory is highly determined; the presence of the scalar field decouples the gravitational field from cosmological dynamics. The solution is therefore also stable.

In SCC the Jordan conformal frame has to be used to calculate gravitational fields and cosmological expansion. In this frame energy is locally conserved particle masses vary with gravitational potential energy and photons have constant frequency as measured between co-moving frames. Measuring the cosmos in this frame is achieved using a photon sampled from the CMB (at its peak intensity) as a standard - its frequency inverted is the measure of time, and therefore distance with c constant = 1, and its energy a measure of mass, the universe is static and eternal. This time is your conformal time above. Photons expand with the universe in SCC as in GR.

However in order to do nuclear physics, and to be in a more usual frame of measurement, it is necessary to transform into the Einstein conformal frame in which particle masses are constant. This time is that determined by atomic clocks and length measured by metal rulers. In this frame, in which BBN is readily calculated, the universe is strictly linearly expanding.

Garth

 

[pervect]

Very interesting, I must admit - thanks for the explanation. I don't suppose SCC can explain the galactic rotation curves / dark matter problem any better than GR can (or can it?).

 

[Garth]

Very interesting, I must admit - thanks for the explanation. I don't suppose SCC can explain the galactic rotation curves / dark matter problem any better than GR can (or can it?).

No, not yet - its a problem that has been discussed on the GA&C forum.

In SCC there is no need for DE and the total matter density is 22% closure. However SCC BBN requires ~20% baryonic closure density to obtain the correct amount of helium. In other words there is no need for exotic non-baryonic DM either.
However the question that leaves is where is all this baryonic matter?
There is no clear answer to this and as such there is just as much a problem with SCC as there is in GR, which leaves the non-baryonic DM unidentified.
One leading contender though is that the majority of the DM in SCC could be in the form of IMBHs of about 10² - 10³ solar masses. These would have formed as the end product of PopIII stars of about the same mass range. A few SMBHs would also form that could become proto-galactic nuclei, some of the IMBHs would be gravitationally bound to them and attract uncondensed gas that formed ordinary stars, planets and ISM. The presence of many PopIII stars going SN at an early stage would ionise the IGM and provide early metallicity. The primordial hydrogen and helium is also seeded with relatively high metallicity in freely coasting BBN and that allows PopIII stars of that mass range to form - metallicity is necessary to radiate the heat away.
Well that's my 'hand waving' scenario! Shoot it down if you want!

Garth