# Accelerating universe question

1. Oct 3, 2012

### Deeviant

It is well accepted that the universe is expanding at an increasing rate. Looking at the evidence, I certainly accept the universe is expanding as well, but is it expanding at an increasing rate?

I also understand it as an expansion of fabric of space, no simply a trait of motion between galaxies, so correct me if I am wrong.

My question is this, could the rate of expansion be constant? My reasoning is this: wouldn't the rate of expansion between two points be dependent on not only the rate of expansion of the universe, but also the distances between them, as the further they are from each other, the more space there is that is expanding between them. So even with a constant rate of expansion through the entire universe, it would appear to be faster the further you are away from that point.

I guess it is a rather simple point, but I hadn't seen it mentions elsewhere.

2. Oct 3, 2012

### bapowell

Yes, this is precisely Hubble's law! Hubble's law states that the recession velocity of a distant object is proportional to its distance from us: $v = Hr$. But this just tells you about the speed of the expansion (more precisely we should look at the Hubble parameter defined in terms of the scale factor: $H = \dot{a}/a$). In any case, the assertion that the universe is accelerating is given in terms of the 2nd derivative of the scale factor, $\ddot{a} > 0$: not only do more distant objects recede at a faster rate, this rate itself is growing in time!

3. Oct 3, 2012

### marcus

That's quite right, and as Brian Powell points out it is just what the conventional Hubble law says.
At least the rate of expansion, as a small percentage growth rate of distances, is ALMOST constant.
At the present it is estimated to be about 1/139 of one percent per million years. Doesn't sound like much but if you are looking at a vast distance then even a tiny percentage increase can amount to a lot of miles or lightyears.

Another way to remember it is that the present estimated growth rate means that it takes 139 million years for a distance to increase by 1%.

You know that if you leave money in a bank account at a fixed interest rate the actual yearly increase in dollar terms will grow as the principal grows. So there is a kind of acceleration (if you watch a particular initial sum grow.) even if the interest rate is being reduces there will still be acceleration if the bank is reducing the rate of interest slow enough. To have acceleration all you need is for the interest rate to be APPROXIMATELY constant.

Well the percentage growth rate of distance in our universe is slowly declining. Now 1/139 (percent per million years) but slated to very very slowing settle down to 1/163. that's the message we get from the standard cosmological model, which checks pretty well with data.

It doesn't conflict with the fact that if you watch some particular definite (cosmological scale) distance grow it will accelerate in the sense I mentioned. Add an increasing amount of length with each passing unit of time.

4. Oct 4, 2012

### Jorrie

Another way to put it: we cannot measure this "increasing amount of length", because of the small magnitude of change over human timescales; but we can look at things like distant supernovae today and check if their brightness correlate with a decelerating expansion. It turns out not to be the case - at certain distances they are quite a bit dimmer than what they should have been. They seem to be too far from us for a non-accelerating expansion model to work.

As an example, if one plug the value z=1.6 (or S = 2.6) into a cosmological calculator with standard flat, accelerating expansion values, the distance_then (or angular diameter distance) comes out as about 5.8 billion light years. Do the same with flat, decelerating expansion (matter-only) values, and the distance_then comes out as only 4 billion light years.

5. Oct 4, 2012

### Deeviant

Thank you for your replies. It seems my general understanding of the matter is at least somewhat close to the currently accepted knowledge.

I think my confusion comes from talk of the acceleration of the expansion, particularly in the idea of the "Big Rip". If the rate is constant and only the apparent rate accelerates proportional to distance, why would the effect grow in a local region in a manner not proportional to distance?

Last edited: Oct 4, 2012
6. Oct 4, 2012

### marcus

I remember there was some talk of "Big Rip" earlier (mostly I think 2002-2005?) but it depended on some special assumptions about the cosmological constant which have not been confirmed by subsequent observation.

In the popular media and public outreach channels a dramatic idea like that will not readily die down because it gets reader's attention, even if it dwindles to insignificance in the professional research literature. Wouldn't worry about it, at least not enough to cause a sense of confusion.

7. Oct 4, 2012

### bapowell

If I recall correctly, the initial impetus for considering big rip scenarios arose from the fact that observational constraints on $w = p/\rho$ favored $w<-1$. I'm not sure what the current constraints are, but in any case, this kind of energy -- phantom energy -- is badly behaved and leads to all sorts of pathologies. It would take some very decisive observational evidence for most cosmologists to take it seriously.

8. Oct 4, 2012

### bcrowell

Staff Emeritus
This seems to be the current state of the art, combining info from both supernovae and lensing: http://arxiv.org/abs/arXiv:1105.0946 . It seems like everything is still consistent with w<-1, so we can't rule out a Big Rip scenario, but we also don't have affirmative evidence for it.

Last edited: Oct 4, 2012
9. Oct 4, 2012

### cepheid

Staff Emeritus
The rate is NOT constant. The thing that has been mentioned, but not emphasized, is that the "H" in the equation v = Hr, is not a constant. It varies with time. H is called the Hubble parameter. The value of the Hubble parameter today is called the Hubble constant H0. So if you plug in H0 into the formula, it tells you how fast a galaxy at distance r is receding away from you NOW. It does not tell you how fast that galaxy was receding away from you in the past (answer: more slowly than now).

The expansion IS accelerating, meaning that the rate at which the distance between any two points grows is increasing. Those two points are currently separating at a faster rate than they did in the past, and in the future, they will separate at an even faster rate than they are now.

The dynamics of the expansion (i.e. what determines how H changes with time) are determined by the mass-energy content of the universe. In particular, the mass density affects the rate of expansion. For more information, look up the "Friedmann equations", which come directly from Einstein equations of General Relativity.

How to measure the rate of expansion? Bapowell indicated this already. The idea is, take the distance between any two objects (it doesn't matter which) at time t, and divide that by their distance today. This dimensionless ratio, 'a', is called the scale factor, because it is the factor by which you have to scale present-day separations between objects in order to get their separations at time t (either in the past or in the future). So, at the present day, a = 1, for t in the past, a < 1, and for t in the future, a > 1. The goal of the Friedmann equation is to solve for how a varies with time, thus giving you the expansion history of the universe. The rate of expansion is the rate of increase of a with time, which is denoted by $\dot{a}$. (I'm not sure if you know calculus, but this is the first derivative of a with respect to time). The rate of increase of $\dot{a}$ is the acceleration of the expansion (i.e. is the universe expanding at an increasing rate, or a decreasing rate)? This is denoted by $\ddot{a}$ (the second derivative of a with respect to time). As bapowell already said, $\ddot{a} > 0$ meaning that the rate of expansion is itself increasing with time. The expansion of the universe is accelerating. This is what observations show.

10. Oct 5, 2012

### Bandersnatch

I'm somewhat confused here. It's probably just me being dense in the morning, but what I read here is that marcus says that the rate of expansion is decelerating(asymptotically approaching 1/163 percent per million years), while both bapowell and cepheid both say it's accelerating.
Can you help me reconcile these two statements?

11. Oct 5, 2012

### Jorrie

I think Marcus and the others are talking about different things and the closeness of the terminology is confusing you. Marcus referred to the recession rate of galaxies at a specific distance from us. (H has the unit of speed per unit distance). This value is decreasing from the present value of around 70 and will settle at around 60 km/s per Mpc.

Both bapowell and cepheid referred to the expansion rate, which is essentially the recession rate of a specific galaxy as it moves away from us (not galaxies at at some unit distance). Since recession rate v = H x D (D is proper distance), there can be four cases, as measured per unit time:

(i) if H proportionally decreases more than what D increases, the recession rate drops (decelerating expansion);
(ii) if H proportionally decreases the same as what D increases, the recession rate is constant (coasting expansion) and
(iii) if H proportionally decreases less than what D increases, the recession rate increases (accelerating expansion).

Our universe seems to have gone from (i) through (ii) to (iii) at present. Eventually it will reach:

(iv) H is constant and D increases, meaning ever accelerating expansion.

Does this clear up some of the confusion?

Last edited: Oct 5, 2012
12. Oct 5, 2012

### Bandersnatch

Oh, yes. That's actually very helpful.
Cheers.

13. Oct 5, 2012

### johne1618

Here is a possible simple argument against an accelerating expansion.

The Universe is assumed to be homogeneous and isotropic.

Imagine a snapshot of the Universe at an instant of cosmic time.

All around particle A the Universe is isotropic.

Thus particle A experiences no net gravitational force from the rest of the Universe.

Thus particle A has zero acceleration relative to the rest of the Universe.

Now consider particle B at some distance from particle A.

Again all around particle B the Universe is isotropic.

Thus particle B experiences no net gravitational force from the rest of the Universe.

Thus particle B has zero acceleration relative to the rest of the Universe.

Therefore particle A has zero acceleration relative to particle B.

This result is inconsistent with an accelerating Universal expansion.

Last edited: Oct 5, 2012
14. Oct 5, 2012

### Jorrie

Incorrect logic. In all viable isotropic cosmic models, co-moving particles experience no net gravitational force from the rest of the Universe, whether expansion accelerates or not. Presently, the distance between galaxy clusters are increasing at an accelerating rate; this we know from observation, so what is the point arguing against it?

15. Oct 5, 2012

### johne1618

The argument I gave is "Newtonian" cosmology.

One might hope that Newtonian and Einsteinian cosmology would be consistent for the late Universe where gravitational fields are weak and spacetime is not too curved.

I think a linear cosmology as espoused by Fulvio Melia and others explains a lot from simple assumptions. I think it is worth thinking about even if current observations seem to go against it.

16. Oct 5, 2012

### RUTA

Well, acceleration is not what is actually measured. Luminosity and redshift are measured. From luminosity one computes a distance (luminosity and/or proper) that is correlated with redshift per some cosmology model. Then one finds the cosmology model that best fits the data and infers kinematics from that model. In fact, it is possible to fit the Union2 Compilation supernova data with a homogeneous, isotropic, spatially flat, decelerating model (yes, that's Einstein-deSitter) as well as the concordance model (Einstein-deSitter plus a cosmological constant) by modifying proper distance as a function of luminosity distance. See the following papers:

Stuckey, W.M., McDevitt, T. & Silberstein, M. (2012a). Modified Regge Calculus as an Explanation of Dark Energy. Classical and Quantum Gravity 29, 055015 doi: 10.1088/0264-9381/29/5/055015. http://arxiv.org/abs/1110.3973.

Stuckey, W.M., McDevitt, T. & Silberstein, M. (2012b). Explaining the Supernova Data without Accelerating Expansion. Honorable Mention in the Gravity Research Foundation 2012 Awards for Essays on Gravitation. To appear in International Journal of Modern Physics D. http://users.etown.edu/s/STUCKEYM/GRFessay2012.pdf

17. Oct 7, 2012

### Jorrie

I can see how Stuckey et. al fitted the supernove data to a flat Einstein-de Sitter (EdS) matter only model, but AFAIK, there are many WMAP observations that do not fit the EdS model. They all fit the LCDM model rather well.

Apart from that, only some 5% of the normal matter required for flatness are observed and there is no indication that dark matter can make up the other 95%. So how do they arrive at a flat EdS model?

18. Oct 7, 2012

### RUTA

LCDM is just EdS + Lambda and Lambda has very little effect in the early universe, so the MORC (modified Regge calculus) model should be consistent with WMAP.

MORC is merely a correction to Regge calculus EdS based on Relational Blockworld (RBW). A discussion of RBW has no place in this thread, so I'll have to point you to some papers thereupon:

Silberstein, M., Stuckey, W.M. & McDevitt, T. (2012). Being, Becoming and the Undivided Universe: A Dialogue between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory. To appear in Foundations of Physics, Online First: 4 May 2012. http://arxiv.org/abs/1108.2261.

Stuckey, W.M., Silberstein, M. & Cifone, M. (2008). Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox. Foundations of Physics 38, #4, 348-383. http://arxiv.org/abs/quant-ph/0510090.

An easy, short read based on these publications is in the FQXi essay contest:
http://www.fqxi.org/community/forum/topic/1393

The bottom line is that RBW will likely solve the dark matter problem exactly as it solved the dark energy problem, i.e., by changing the kinematics and removing a need for it.

Thanks for your interest, but we best not continue a discussion of RBW here. I was just trying to point out a popular misconception about what is actually measured and what is inferred concerning the accelerating expansion of the universe. There are definitely theoretical assumptions required to turn data into accelerating expansion and those assumptions may not survive physics on the horizon. That is all I wanted to point out