# Latest result for dark energy's equation of state

1. Aug 8, 2011

### bcrowell

Staff Emeritus
Helder Velez brought the following paper to my attention: Carnero et al., "Clustering of Photometric Luminous Red Galaxies II: Cosmological Implications from the Baryon Acoustic Scale," http://arxiv.org/abs/1104.5426.

They use a survey of galactic redshifts to measure baryon acoustic oscillations (BAO), and they also combine their results statistically with other people's BAO measurements based on the CMB. As far as I know, this gives the best current determination on the equation of state of dark energy: $w=-1.03\pm .16$, which is consistent with a cosmological constant (w=-1) but also consistent with a Big Rip (w<-1).

They also present a constraint on the rate of change of the equation of state, parametrized as $w=w_0+w_a(1-a)$, where a is the scale factor. The result is $w_a=.06 \pm .22$, i.e., consistent with a constant equation of state. I don't know if there's any strong theoretical motivation for or against time-variation of w...? Would it violate local mass-energy conservation (giving a nonzero divergence of the stress-energy tensor)?

Even a decade after the initial claims of accelerated expansion, I've still felt a little skeptical about the empirical evidence. It is interesting to find out that BAO can be measured in two independent ways (galactic redshifts as well as CMB), since that seems to make it less likely that there is just a systematic error in the measurements. It seems like "Hubble bubble" explanations are also ruled out these days. So maybe I'm finally ready to believe in dark energy wholeheartedly.

2. Aug 8, 2011

### Chronos

I've never been fond of time variation in physical constants. Omega = 1 and w = -1 seems intuitively correct to me - for absolutely no good reason. I guess it's a matter of aesthetics.

3. Aug 8, 2011

### mikeph

Inflation!

Thanks for the paper, I always tell myself I'll follow the latest results in cosmology, and always find myself re-learning what all the symbols mean!

4. Aug 8, 2011

### bcrowell

Staff Emeritus
If inflation is correct, then it does force the universe to be flat, but I don't think it has any implications for the value of w, does it?

5. Aug 8, 2011

### edgepflow

Thinking about this, the inflation model has constant energy density = cosmological constant / 8 PI G. This results in the time dependent term in the fluid equation to vanish and consequently: Pressure = - rho * c^2. This implies w = -1.

But if w = w(a), then the time dependent term in the fluid equation is non-zero and a different model universe?

6. Aug 8, 2011

### bcrowell

Staff Emeritus
Sorry, I don't follow you.

When you say "constant energy density," do you mean constant with respect to time? I would think that during the inflationary period, the energy density would be changing, as the wave-packet was rolling down the hill of the Mexican-hat potential.

These observations probe w long after the inflationary epoch (if it existed). I don't see how arguments about the structure of the stress-energy tensor during the inflationary epoch would relate to these observations.

What do you mean by "the fluid equation?"

7. Aug 8, 2011

### edgepflow

Sorry, I typed all this in a hurry. The "fluid equation" phrase came from "Introduction to Modern Cosmology" by Liddle. See Equation 5.2 in this book for example or see the slide in:

http://zuserver2.star.ucl.ac.uk/~hiranya/PHAS3136/PHAS3136/PHAS3136_files/Cosmo2_34_fried.pdf

In Section 7.2 of Liddle's book, he treats the "Fluid Description of the Cosmological Constant." He concludes that w = -1 for Inflation models but notes that "quintessence" models have accelerated expansion as long as w < - 1/3. Thus, I was comtemplating how w = w(a) may affect this treatment (if such a question has any significance).

8. Aug 9, 2011

### bcrowell

Staff Emeritus
I don't have access to the book, and this baffles me. Quintessence is a model of dark energy in the present universe. Inflation isn't a model of the present universe.

9. Aug 9, 2011

### edgepflow

Section 7.2 of Liddle's book was discussing the cosmological constant in general terms but I think the Quintessence discussion was dark energy in the present. But for modelling purposes, the Friedman equation with a (very large) cosmological constant can be applied for inflation, correct? In Chapter 13, he discusses inflation and he uses the same equations.

10. Aug 9, 2011

### edgepflow

bcrowell, going back to you earlier inquiry: "If inflation is correct, then it does force the universe to be flat, but I don't think it has any implications for the value of w, does it?"

Let me take another shot at this:

Cast the accleration equation in the form:

a2dot / a = (- 4 PI G / 3) * rho * (1 + 3w) + Lambda / 3

If w is not exactly = -1 but < -1/3, and if Lambda is large enough, we still have inflation as expected.

11. Aug 14, 2011

### matt.o

The WiggleZ survey has just released two papers which constrain the cosmic expansion history using the Alcock-Paczynski test and also the BAO peak as a function of redshift:

http://arxiv.org/abs/1108.2637

http://arxiv.org/abs/1108.2635

The BAO data, in combination with the supernova data, reveal w = -1.03 +/- 0.08.

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