**Cosmological constant as an explanation of the accelerated expansion under attack**

*Scientific American* chose a dramatic title for a 1-week old astro-ph preprint that the astro/physics blogosphere missed:

Leading Dark Energy Theory Incompatible with New Measurement (SciAm)A "medium deep survey" looked at 146 Type Ia supernovae, found a small deviation, and allowed the experimental cosmologists to claim that Einstein's cosmological constant no longer plays the role of dark energy well.

Cosmological Constraints from Measurements of Type Ia Supernovae discovered during the first 1.5 years of the Pan-STARRS1 Survey (astro-ph arXiv)

Well, I find this claim exaggerated and/or premature.

The usual analyses of the supernovae's luminosity, they updated the value of some cosmological parameters and some of them look insufficiently well-behaved.

The proportion of dust in the energy density is measured to be\[

\Omega_M = 0.277 \pm 0.011 \pm 0.014

\] where the first error is statistical and the second one is systematic. I have used the average error margins instead of the asymmetric upper/lower ones because their precision seems excessive not only for a blog post.

Depending on the detailed inclusion of some things and the methodology, the parameter \(w=p/\rho\) is measured to be\[

\eq{

w & = -1.015\pm 0.025\pm 0.014\\

w & = -1.19 \pm 0.07\\

w & = -1.14 \pm 0.07

}

\] which disagrees from the \(\Lambda{\rm CDM}\) prediction either by zero or 2.4 or 2 standard deviations, respectively.

One may speculate and they do speculate about the reasons for the discrepancy. Well, in this case, I would choose to say that 2 and even 2.4 standard deviations is too little (1-in-20 or 1-in-100 chance for such things to occur accidentally). It's sort of surprising to see that a 2-sigma deviation is enough for cosmologists to nearly claim a discovery in 2013. I thought that 15 years ago, cosmology became a precision science whose standards are nearly on par with particle physics now (including the golden 5-sigma threshold for a discovery). Well, they're apparently not.

The value of \(w\) smaller (more negative) than \(w=-1\) seems like too radical a claim to me. Such a value not only contradicts the prediction \(w=-1\) of the cosmological constant but by being so extreme, it violates some energy conditions (various versions of the claim that "density of energy shouldn't be negative").

Note that the cosmological constant terms are derived from a scalar term proportional to \(\int d^d x\sqrt{-g}\) in the action. Such a term is field-independent Lorentz-invariant so the equations of motion must be modified by a Lorentz-invariant term, too. In particular, the cosmological constant may be interpreted as a term in the stress-energy tensor (density of energy, momentum, pressure, and stress etc.)\[

T_{\mu \nu} = \rho g_{\mu\nu}.

\] With the \(({+}{-}{-}{-})\) convention for the metric, you see that the component \(T_{00}=\rho\) while the spatial components \(T_{ii}=p=-\rho\) for \(i=1,2,3\). So the pressure carried by the dark energy is negative – that's why this cosmological constant tells the space to repel itself and to accelerate its expansion – and its absolute value agrees with the energy density.

You may get \(w\equiv p/\rho\) equal to other numbers such as \(-2/3\) for cosmic domain walls and \(-1/3\) for cosmic strings. The dust has \(w=0\), photons and other forms of radiation have \(w=+1/3\), and a favorite speculative form of matter of my ex-PhD-adviser Tom Banks, black hole gas, has \(w=+1\). But in all cases, we have\[

-1 \leq w \leq +1

\] This seems really necessary because one may at least formally calculate the speed of sound in the environment as\[

\frac{v_{\rm sound}^2}{c^2} = \abs{\pfrac{p}{\rho}}

\] and if \(|w|\gt 1\), we would get a sound speed that is greater than the speed of light! Alternatively, if the component \(T_{zz}\) were negative and greater than \(T_{00}\) in its magnitude, you could go to a highly boosted frame in which you would have \(T_{0'0'}\lt 0\). This also seems bad, especially if you blame this negative energy density on some localized "objects" (the cosmological constant is a non-object so for similar "global" modifications of the equations, the negative energy density is marginally allowed). If objects could have a negative energy, regardless of their momentum, they could be created in the vacuum along with positive-energy well-behaved objects out of nothing; the vacuum would be unstable.

All of this is interesting and it is plausible that a dragon is waiting underneath these data but I will personally wait at least for a 4-sigma discrepancy when it comes to radical claims such as the violation of the energy conditions.

## snail feedback (18) :

There is no dragon waiting, but the dark side of the force

http://www.youtube.com/watch?v=HcZ9kQ1h-ZY

PS: just kidding, I have not much to add to the article. It seems most mysteries in physics nowadays come from cosmology - dark matter, dark energy, dark flow

Lubos, isn't speed of sound always way greater than speed of light in the morning ? (just messing :-D)

LOL. ;-)

Just to mention one of dozens of contributions made by Jan Antonin Bata to the Allied Cause. A recent article entitled, "The Bata RAF Airmen."

http://fcafa.wordpress.com/2013/03/01/the-bata-raf-airmen/

Did you know this paper?

http://inspirehep.net/search?p=find+eprint+ASTRO-PH/0302506

Phantom energy and cosmic doomsday

Robert R. Caldwell (Dartmouth Coll.), Marc Kamionkowski, Nevin N. Weinberg (Caltech). Feb 2003. 4 pp.

Published in Phys.Rev.Lett. 91 (2003) 071301

By the way the, if Null Energy Condition is violated then the Hamiltonian for such systems should necessarily be unbounded from below. See e.g. arXiv:1209.2961

http://inspirehep.net/record/1185385?ln=en

The argument for the speed of sound is not always applicable because it is only valid for constant equation of state w.

Have a look at this paper:

http://inspirehep.net/search?p=find+eprint+ASTRO-PH/0302506

Phantom energy and cosmic doomsday

Robert R. Caldwell (Dartmouth Coll.), Marc Kamionkowski, Nevin N. Weinberg (Caltech). Feb 2003. 4 pp.

Published in Phys.Rev.Lett. 91 (2003) 071301

DOI: 10.1103/PhysRevLett.91.071301

If w<-1 then the Null Energy Condition is violated and this is only possible for systems with Hamiltonians unbounded from below: http://arxiv.org/abs/arXiv:1209.2961

The argument about the speed of sound only works for a constant equation of state w.

As Feynman emphasized, the easiest person to fool is one’s self. This is the reason that particle physicists have been forced to adopt such a stringent standard.

I would be willing to bet that there is nothing new here. I was more certain about the absence of superluminal neutrinos and I could lose this bet.

Sean Carroll wrote a paper about the possibilities of w<-1

http://arxiv.org/pdf/astro-ph/0301273v2.pdf

I don't think you're being entirely fair here. It isn't the cosmologists claiming it isn't a cosmological constant, it's Scientific American trying to make it sound more dramatic by using a fishy title.

Even the SciAm article contains quotes from the authors saying it's too early to believe it isn't a cosmological constant.

Wrong song....

http://www.youtube.com/watch?v=4wvpdBnfiZo

LOL, with this Big Rip, I would feel ripped. This astro-ph paper has over 1,000 citations - it looks weird to me as the paper only solves a trivial GR problem what such an equation of state would imply without giving any hint that it's possible to consistently incorporate it to particle physics or derive it from something.

Right, I wrote this too and agree that this is the primary problem and the null energy condition is therefore the most safely believable one among these energy conditions.

off course he did... ;)

Yes the Scientific American and Nature (they are often indistunguishable and just copy articles from each other) have reached the level and targetted audience of the German "Bild Zeitung"

http://www.moselpunk.de/news/bild/zeitung02.JPG

... at least concerning their "reporting" (or more accurately trolling) about fundamental physics.

So it is not surprising, that they blow up a random paper to a huge dramatically exagerated headline with a large amount of dark energy, it perfectly fits into the concept and marketing strategy of this magazine ... ;-)

Hi. If you actually read the paper, the w<-1 result seems to arise when we include the microwave background constraints from Planck. If we use WMAP values then w get closer to -1.

I noticed that, Chris (good to see you here), but I don't understand why it should affect any conclusions of mine.

Are you suggesting that Planck was defective or anything of the sort? I have no reasons to think so and the slight deviation from w=-1 for the data with Planck isn't a strong enough reason for such a conclusion, I think.

So with some choices, you are closer to -1, with other choices, you are further. WMAP as well as Planck should have worked well enough so that with neither of them, one should be getting results that are safely incompatible with some basic principles such as the energy conditions.

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