Dark energy might be modif'n of GR different from cosmo constant.

[marcus]

Sean Carroll has an excellent account of a new paper by Rachel Bean. I don't always share Carroll's attitudes or appreciate his reporting, but here's a case where I thought his post was top notch. You may have already read his posting

and if not I hope you will. Meanwhile let's take a cue from Sean and look at the original paper: http://arxiv.org/abs/0909.3853
==quote from Rachel Bean==
The COSMOS data gives the first indication that dark energy might be a modification to GR, rather than Λ.
It will be extremely interesting to see if this signature is seen in other lensing datasets...
==endquote==

She has two functions psi and phi:

"ψ and φ are the two Newtonian potentials respectively describing temporal and spatial perturbations to the metric."

As time goes on (or equivalently as the scalefactor a increases) the geometry of the universe gets more wrinkly/bumpy and warty. This is called "structure formation". Things curdle, condense, gather together in structure. So the geometry gets locally less smooth.
So there are these local perturbations---both to psi (curvature in timelike directions) and phi (curvature in spacelike).

Slow things like planets are more affected by temporal curvature (because their worldlines move a lot more in time than they do in space).
But fast stuff like light is equally affected by both curvatures, and both kinds of bumpiness, both psi and phi.

Rachel looks at the ratio ETA = spatial/temporal = phi/psi
If General Relativity is obeyed the two should be equal and ETA = 1.

She plots 1/ETA = temporal/spatial = psi/phi, as derived from her data, and it has a peak at around 3 or 4. Somehow temporal curvature, the kind of thing that orbiting planets and other slow bodies are more responsive to, has more structure formation than does spatial curvature.

Look at her figure 1, something of a shocker.

Sean points out that anomalies like this usually go away----some flaw in the analysis shows up, or more data comes in and contradicts the finding. He wisely cautions against jumping to conclusions. At this stage we still bet on GR being right. But figure 1 says that this analysis of this batch of data "disfavors GR at 98% significance level."

You can read more of what Sean Carroll has to say about it here:
http://blogs.discovermagazine.com/cosmicvariance/2009/10/12/a-new-challenge-to-einstein/
His headline is "A new challenge to Einstein?"

 

[dilletante]

You can read more of what Sean Carroll has to say about it here:
http://blogs.discovermagazine.com/cosmicvariance/2009/10/12/a-new-challenge-to-einstein/
His headline is "A new challenge to Einstein?"

The comments are worth reading also. Rachel Bean responds several times to some observations and criticisms.

Am I understanding this correctly, that a modification to GR could replace dark energy?

 

[Chalnoth]

The comments are worth reading also. Rachel Bean responds several times to some observations and criticisms.

Am I understanding this correctly, that a modification to GR could replace dark energy?

Yes, it is definitely within reason that a modification of GR could be the solution to why the expansion of the universe is accelerating. However, nobody has yet found a suitable modification (it turns out to be very difficult to modify Gravity on large scales). We shall see if Rachel's result pans out or not. I suspect, like Sean, that it will go away when we understand our data sets better. But we'll see.

 

[Wallace]

Just to clarify, this result does not actually pertain directly to dark energy at this point. There are separate threads of inquiry that attempt to explain the data by a different gravity theory instead of dark energy, but as Sean alludes to in his post, this is actually quite tricky to do given the constraints on gravity that we have. That being said there are ways it could be done.

Now, the result under discussion is not a cosmological modified gravity model. If you look at the details, the background cosmology being used is still LCDM, albeit with a parametrised growth history alteration. If the result was confirmed, we would still lack a theory that explains why you would get anisotropic stress AND also gives as LCDM like expansion history. These two things are not directly related, and it is non-trivial to link them together in a self-consistent physical theory.

If this result was confirmed we would have a clear detection that GR is not the full story of gravity, but whether or not dark energy exists would still be a separate question. That is to say, it is possible that we have dark energy AND gravity is not GR. This result tests the self consistancy of one aspect of GR, but it doesn't present a full cosmological model for an alternative model without dark energy (not that I mean this as a criticism, such a thing is very difficult!).

I believe there are some models of gravity, in the family of TeVeS (Tensor Vector Scalar..) theories that both predict anisotropic stress and an effective expansion history that mimics LCDM. These (and any others that could claim to do a similair job) would obviously get more attention if this results was confirmed, but then you would need to test the self-consistancy of these models to ensure yoou could simultaneously fit the background expansion and the growth history.

Fortunately, there is plenty of new data coming in the next few years, so we should get some answers either way soon enough!

 

[oldman]

She plots 1/ETA = temporal/spatial = psi/phi, as derived from her data, and it has a peak at around 3 or 4.

What is the ordinate L/Lmax in her Fig 1? (simply, please!) Can't find L or Lmax defined in Rachel Bean's interesting letter -- my apologies for such an elementary question.

 

[Chalnoth]

What is the ordinate L/Lmax in her Fig 1? (simply, please!) Can't find L or Lmax defined in Rachel Bean's interesting letter -- my apologies for such an elementary question.

That's the likelihood divided by the maximum likelihood. So you see the curve peaks at the value of 1.

 

[Wallace]

Figure 1 is a plot of the normalised likelyhood (L=likelyhood). You can see that this is unity the peak likelyhood (by definition) and very low at a value of 1/\eta corresponding to the GR value.

Essentially the way to interpret the plot is the higher the likelyhood for a given 1/\eta value the more that value is favoured by the data.

Edit: ninjad by Chalnoth :)

 

[twofish-quant]

Question: Is there a good review paper on modified gravities models and dark energy? Every time I go to a journal club I feel a little out of place because people have some background that I don't.

 

[Chalnoth]

Question: Is there a good review paper on modified gravities models and dark energy? Every time I go to a journal club I feel a little out of place because people have some background that I don't.

Hmmm. I'm not sure that anybody has done a review of the various models that people have put forward here. I mean, none of the models put forth have been in any way compelling as yet.

Here, however, is a general review of the subject:
http://arxiv.org/abs/astro-ph/0207347

I'm not sure it's what you're looking for, but there it is.

 

[twofish-quant]

As far as what I'm looking for... I was at a astrophysics lunch and they were talking about the latest experiment results, and I asked whether or not you could explain something with modified Newtonian gravity, and the response was that basically that those models are known to have certain properties X, Y, and Z. The trouble was that everyone else at the lunch seemed to know this common knowledge, and I didn't want to stop the discussion to explain what seems to be pretty basic knowledge.

By the time people do come up with a consensus on what works and what doesn't, then all of the fun stuff will have disappeared :-( :-( :-(

 

[Wallace]

The problem is that when you say 'modified gravity' it really depends on what regime you are talking about. You could be referring to efforts to modify gravity in order to formulate a coherent quantum gravity theory and remove the troublesome singularities in GR.

You could also be referring to MOND (Modified Newtonian Dynamics) which is relevant for talking about galaxies and clusters but is not a theory that can be applied to cosmology (althougth there are theories such as TeVeS that reduce to MOND in a Newtonian like limit). The 'goal' of a theory like MOND is to do away with the need for dark matter, or at least enough of it such that the rest could plausibly be baryons in a hard to seem form (cold clouds, or cold compact objects).

On the other hand, you could be talking about cosmological modified gravity models that leave dark matter in the theory but do away with the need for dark energy. In general these are quite different to MOND like theories. Some popular theories (put these into ADS to get more papers than you could poke a stick at) are DGP braneworlds and the general framework know as f(R) gravity (although there are many many more).

Judging from your post, it looks like people were talking about MOND, which is not something that would explain Rachel Bean's results (if they were confirmed). I know it's confusing, the problem is that people tend to use terminology in silos in astronomy/astrophysics so even if a different sub-field has already established a particular meaning for a term, it doesn't stop a different area of research developing a different meaning for the same term. Once you know that context it's okay, but it can be very confusing at first!

My advice would be to speak up and ask questions if you don't understand, especially as a student. There is almost certainly someone else in the room who also doesn't understand and being inquisitive looks far better than just nodding along hoping to find out later what the hell everyone was talking about! Plus people in academia love explaining stuff that they understand to people, otherwise they wouldn't be in the job ;)

 

[friend]

What about those efforts that add higher order terms of curvature to the Hilbert-Einstein action? What are they called and why are they used? Thanks.

 

[Chalnoth]

What about those efforts that add higher order terms of curvature to the Hilbert-Einstein action? What are they called and why are they used? Thanks.

That's called f(R) gravity. The motivation here is that the reason why the curvature R appears in the Hilbert-Einstein action is that it's the only scalar which can appear there (I forget the specific arguments). But there's no fundamental limit upon how many powers of R you can have, so this theoretical argument, in principle, means that the Hilbert-Einstein action could contain any function of R you want.

 

[friend]

That's called f(R) gravity. The motivation here is that the reason why the curvature R appears in the Hilbert-Einstein action is that it's the only scalar which can appear there (I forget the specific arguments). But there's no fundamental limit upon how many powers of R you can have, so this theoretical argument, in principle, means that the Hilbert-Einstein action could contain any function of R you want.

I'd like to learn a little more about these theories. Do you have any links to a general discussion of f(R) theories? Do these inclued higher derivatives of R? How do they change considerations about dark energy or dark matter? Thanks.

 

[Chalnoth]

I'd like to learn a little more about these theories. Do you have any links to a general discussion of f(R) theories? Do these inclued higher derivatives of R? How do they change considerations about dark energy or dark matter? Thanks.

I'm sorry, I'm not aware of any good resources on this subject. However, I can say that f(R) gravity basically can't have anything to do with dark matter, because of observations like the Bullet Cluster that pretty much conclusively demonstrate dark matter's existence.

 

[friend]

I found this reference:

http://arxiv.org/abs/0909.4672

It looks like f(R) theories are used to explain both dark energy and dary matter.

 

[Chalnoth]

I found this reference:

http://arxiv.org/abs/0909.4672

It looks like f(R) theories are used to explain both dark energy and dary matter.

Well, they have been. But with the demonstrated existence of dark matter, most people think it highly unlikely that modified gravity has much to say about the dark matter issue.

 

[oldman]

This is an most interesting thread about a fascinating analysis of observed data by Rachel Bean. From a kinematic and observational perspective my uninformed take on her letter is this:

A fundamental observation in cosmology is that (1) there is a cosmological redshift and (2) it is to a first approximation spatially isotropic and (3) it obeys Hubble's linear law, apart from late accelerations. For historical reasons and in full accord with the dynamics mandated by GR, this observation is described with a time-dependant variation in the spatial metric coefficient (a.k.a. the scale factor) as distinct from the Pythagorean metric of SR. (In the metric of SR both the spatial scale factor --- and the temporal metric coefficient, as distinct from the unit conversion factor c --- are everywhere eternally unity.)

In Rachel Bean’s letter this restriction of change to the spatial metric coefficient --- which for some time I’ve thought to be an unjustified straightjacket for theorists, --- is relaxed, as described in the context of the FLRW metric, using the conformal Newtonian gauge. It is assumed that both the spatial and temporal coefficients of the FLRW metric are perturbed in a way dictated by the analysis of satellite observations. This analysis of observations, assuming it to be correct, is said to be evidence that the ratio : time metric perturbation /space metric perturbation, as calculated from observations, is not consistent with GR. Disturbing.

To account for the redshift in the LCDM model (I think) GR requires that there be change only in the ratio of the metric coefficients. Are not the coefficients themselves free to change individually and kinematically, subject to the constraint of the observed (and predicted) run of the redshift with distance? Or does GR itself, rather than the FLRW model, really mandate that the potentials psi and chi be set equal?

The underlying dynamical reasons for the differing perturbations to both metric coefficients that are deduced from observations seems still mysterious. But are such observations truly inconsistent with GR? And if so, can someone simply explain why this is so?

 

[Chalnoth]

The most likely answer is just that there are some systematic errors in the data set that are not properly accounted for. This will be borne out by examining this data set in greater detail, and by comparing against other data sets (different data sets rarely have the same systematic errors, and thus if it is just a systematic, the effect will likely be very different in different data sets).

 

[Wallace]

The underlying dynamical reasons for the differing perturbations to both metric coefficients that are deduced from observations seems still mysterious. But are such observations truly inconsistent with GR? And if so, can someone simply explain why this is so?

Yes, it fundamentally violates GR for these potentials to be different. I think it violates the equivalance principle and possibly Lorentz invariance at some level, but don't quote me on that.

As Chalnoth said though, the inference that the data is saying these two potentials differ relies on certain systematic errors being well controlled, and it is quite likely that this is not true for the data set in question.

 

[oldman]

Yes, it fundamentally violates GR for these potentials to be different. I think it violates the equivalance principle and possibly Lorentz invariance at some level ...

Thanks, Wallace. Does this mean that Rachel Bean's choice of possibly different potential fuctions in the metric she uses (eqn 1), rather than the same function (as allowed by the inherent gauge freedom of GR --- e.g. see Peacock's Cosmological Physics p.41) --- is where violation is introduced into the picture?

Could perturbations to the metric caused by structure superimposed on the homogeneous isotropy of the FLRW model be described more simply as perturbations to both the scale factor and to the time metric coefficient, without violating GR? Or would this be a clumsy impossibility?

 

[Wallace]

I'm not quite understanding what you propose? The conventional way to write down a metric for our Universe which includes the perturbation from the perfect FRW model is the following metric:

d\tau^2 = dt^2(1-2\Phi) - (1+2\Phi)a^2(t)[dr^2 + d^2\Omega]

if you look at is you will see that a(t) is unchanged by the presence of perturbations, and in the case that a(t) = constant you get back a perturbed Minkowski metric (which is the flat space weak field metric).

Now, the test that Rachel Bean did is effectively to look at whether the two \Phi values are in fact equal, which is required in GR (in the weak field limit). I think what you are asking (correct me if I'm wrong) is whether you could instead write the perturbed FRW metric as something like

d\tau^2 = dt^2(1-2\Phi) - (a(t)-\delta a)^2[dr^2 + d^2\Omega]

where \delta a is some local perturbation. I don't think this would really help you, since in order for this metric to satisfy GR, there would be some complex relationship between the local potential and the local variation in a(t) such that it would be easier to simply use the first metric.

As a completely tangential note, no one has yet actually managed to demonstrate that the metric I wrote down is actually an appropriate solution for our Universe. It's possible that the perturbations actually alter the average expansion rate, some even claim that this is the real cause of what we call dark energy. This is not a widely held view, but is also not a crazy idea and is something people are looking at carefully. There are good reasons to think the approximation of a perturbed FRW metric is a good one, but the case it not completely settled yet I think.