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Imagine that the Universe is not expanding

Wetterich's cosmon claimed to be an alternative to the Big Bang singularity, inflation, and the recent apparent expansion

Image: NASA/JPL–Caltech...

Most papers trying to replace the usual cosmological concepts such as dark matter and dark energy by something entirely different may be shown to be wrong within minutes. As I learned from a Czech server called ("osel" is a horse-like animal known as an ass: I don't know of a shorter way to explain that it's not the other ass), a rather achieved cosmologist Christof Wetterich posted an unusual clever yet apparently equally provoking preprint to the astro-ph arXiv at the beginning of this month:

Variable gravity Universe
Be ready for a wild ride: the proposed model claims to explain all the known observations, eliminate the Big Bang singularity, account for the patterns we attribute to inflation, the radiation-dominated era, and the matter-dominated era. And Wetterich also wants to boast that his construction "produces" the arrow of time – as if cosmology were needed for that (but that didn't make me stop reading). A single scalar field – the cosmon – may do all these wonderful things, the gospel say.

It's weird if not exciting, isn't it? ;-)

The idea of a time-dependent Newton's constant (variable strength of gravity) goes back to Jordan and Dirac. The latter man tried to use it to explain the existence of vast and tiny parameters in the Universe. The explanation doesn't really work, especially because dimensionless constants of physics are measured to be really constant.

This is a field – a minefield, to be more precise – that is full of failed and dead bodies. You don't want to go through all these failures because there are too many. This Wetterich guy wants to avoid the basic traps by assuming that the Planck mass is changing with time but the masses of all objects are changing at the same rate so the ratios remain fixed.

Such a claim is already a bit provoking to me because one always has the freedom to define the masses in the Planck units so with the prescription described in the previous paragraph, we may say that nothing is changing in the Planck units. Well, on page 4, he's a bit more specific about the role of his cosmon field \(\chi\) ("chi"). The effective action is\[

\Gamma = \int d^4 x \sqrt{g} \left\{
-\!\frac 12\! F(\chi) R + \frac 12 \! K(\chi) \partial^\mu\chi\partial_\mu\chi +V(\chi)

\] To be authentic, I retyped the expression as he wrote it although the sign of the determinant of \(g\) seems problematic and so do other things. He considers two basic models, (A) and (B), which make the following fixed choices:\[

(A):& F(\chi) = \chi^2, \,\,V(\chi)=\mu^2\chi^2\\
(B):& F(\chi) = \chi^2+m^2, \,\,V(\chi) = \bar\lambda_c.

\] The coefficients in the kinetic terms \(K(\chi)\) are allowed to vary throughout the paper to adjust the models.

Well, you see that Newton's constant depends on the cosmon in some way. The cosmon has some field-dependent kinetic term and some potential. The first thing that comes to my mind is that one could rescale the metric and nonlinearly redefine the cosmon field so that he would effectively eliminate up to two of the three functions above. So unless there are some global constraints or inequalities, wouldn't it become just an ordinary GR coupled to an ordinary scalar field with some potential?

I am confused by this basic point but it's probably because I have only been reading the paper for a few minutes so far. If and when I spend an hour with it – or if a more experienced reader offers his or her thoughts and observations – chances are that all the uncertainty will go away and the ambitious claims by Wetterich will turn out to be either strictly viable or demonstrably wrong.

Which way it is? ;-) I am unlikely to learn the answer tonight because I want to watch the second soccer match Maribor [SI] vs FC Viktoria Pilsen [CZ]. "Our" Pilsner team is likely to win in the aggregate match after the 3-to-1 victory at home last week which would mean that it will earn over $10 million and penetrate to the standard group of the UEFA Champion League for the second time.

Off-topic: graphene \(\heartsuit\) metals and makes them 100+ times stronger. Via Bahamas

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reader Mario Herrero-Valea said...

You are true, it is possible (and a common thing to do) to rescale the metric by a conformal factor and thus just have GR coupled to a scalar with some sort of an evil potential term (after another redefinition of the scalar field).

Because of this I do not see how this proposal is better than or different from the usual conformal inflation scenarios or from more contrived models like the ones recently proposed by Kallosh and Linde.

In my opinion, I think that Wetterich is quite confused about the physical meaning of this field redefinition.

reader Luboš Motl said...

Thanks! I suppose you mean this

by the KL paper.

reader Mario Herrero-Valea said...

Yep, that one

reader OON said...

He does rescaling himself at page 15. All the "novelty" seems to be in the claim that this point of view allow to call the singularity unphysical...

reader Lurker said...

Sadly he is extremely powerful politically in German theoretical physics. I know this from the inside. He gets away with half-assed stuff all the time. And this paper is even basically a rip-off of earlier dumb work by Joao Magueijo. Why don't people understand that only dimensionless ratios are physical, and that one can always perform field redefinitions?

I'm so angry with the state of the theoretical physics community. Very many have become charlatans and there is great pressure to do the same. I wish we had Feynman and Fermi still around to tell these f*****s to get lost.

reader heldervelez said...

the universe is not expanding , no inflaton no cosmon no nothing.

Atoms were greater in the past.

as seen here:
A relativistic time variation of matter/space fits both local and cosmic data
and formal here:
A Self-Similar Model of the Universe Unveils the Nature of Dark Energy

Physics equations are insensitive to the actual «atom size» (we can scale mass, length and time units, in sync) . The observational requirement is that in any time (and now around us) all atoms are similar. Can you prove that atoms in the past were equal to the ones we see now ?

reader Luboš Motl said...

That would still make it somewhat interesting. But isn't it clearly wrong?

If his evolution is related to the normal cosmology just by a Weyl scaling of the metric and scalar field redefinitions, it should have the same Penrose diagram, right? And the normal cosmology's Penrose diagram *does* have a Big Bang singularity at the beginning, so the same should hold there. Or does he have infinitely many e-foldings or something like that?

reader and said...


reader and said...

Oh, I agree so much!

reader Mario Herrero-Valea said...

I think that is the point that Wetterich is loosing... I've been following his recent work since it is somehow related to my own work and he seems to be quite confused about the implications of field redefinitions for the metric.

The trick he is doing can be better understood if we go all the way back, starting with GR and performing the Weyl rescaling to recover Wetterich's action. If we do that, we can see that the singularities on curvature, which will go as some power r^-n, can be "eliminated" by choosing the scaling factor to behave as \Omega^2 ~ r^n.

That is naively true but as you said, that does not solve anything since even if now R is regular, other terms in the action receive negative powers of the Weyl factor and thus the singularity in dynamics is just moved from one term to the other. In this case, and now I'm just guessing, it seems that the GR singularity is substituted by a strong coupling regime for the dynamics of the scalar field.

Sorry if I'm not very didactic, I just woke up :)

reader anony said...

I am going to morally support Wetterich on this. Whatever his specific reasons and logic is for going down this discovery path, his exploration should be encouraged.

There are a few fundamental issues that warrant this exploration:

1) The ratio of fundamental masses to planck mass cannot be assumed to be stable. Whether the instability manifests itself discretely or continuously is not currently apparent.

2) The homogeneity and isotropy as used in cosmology only applies to spatial components. Slices of spacetime along space dimensions are manifolds that are not isotropic nor homogeneous.

2a) Manifolds from space slices appear to be asymptotically flat, e.g. there is a clear density variation in the time direction, which allows us to treat the initial singularity as an isolated object in a space with a minkowski metric at infinity.

3) Lagrangians serve the purpose of determining densities. At the end of the day its an accounting tool. Knowing 1 and 2 suggest the need for an auxiliary field (or fields if we assume some sort of symmetry) in order to account for the instability. How those are inserted into the Lagrangian becomes a simple question of complexity an optimization.

With those concepts in mind, I fully support any effort to "fix" cosmology.

reader Luboš Motl said...

Sorry, your comments contradict Wetterich's own text. For example, concerning your point (1), read his page 1 to see that he considers the models in which the masses of particles in the units of the Planck mass to be variable as models that are excluded.

(2) Similarly Wetterich isn't a complete crackpot so he of course assumes homogeneity and isotropy of the Universe - see 4th line of page 5 of his paper.

(3) And he uses Lagrangians everywhere.

So sorry to say but you are just a crackpot who is grateful for everything that looks like an attack on established scientific insights, something whose hatred you're obsessed by, but Wetterich, while highly nonstandard, doesn't actually support any of the crackpot theses you defend.

reader John Archer said...

Slightly off topic:

""osel" is a horse-like animal known as an ass: I don't know of a shorter way to explain that it's not the other ass"

How about "... a shorter way to explain that it's not an arse"? Five fewer letters!

Do I get a coconut? :)

By the way, talking of arses, here's the wished-for hole in this one.

reader Luboš Motl said...


And if I had known that an arse really can't be an animal, I would have said it just like you did.

reader anony said...

That's ok. I stated that homogeneity and isotropy only hold for spatial slices. That's how its used in cosmology. I don't hate science and I am only defending Wetterich's freedom of speech. I will continue to do the same for you or anyone regardless, but recognize there aren't many of us left.

reader beyondEinstein said...

Galaxies or planets are not going away from one
another. But this scenery appears to be different by sitting in the real world
which was not received by going to the last location of the boundary of the
depth of imagination of our brain. So, Expended velocity of the universe is
going forward towards the critical radius. This case, we are looking but just
at this moment, from the last location of the boundary is nothing creation in
the universe through that early.The Universe not