[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results:

Authors:  D. N. Spergel, R. Bean, O. Dore', M. R. Nolta, C. L. Bennett, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, C. Barnes, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weila
Abstract:  A simple cosmological model with only six parameters (matter density, Omega_m h^2, baryon density, Omega_b h^2, Hubble Constant, H_0, amplitude of fluctuations, sigma_8, optical depth, tau, and a slope for the scalar perturbation spectrum, n_s) fits not only the three year WMAP temperature and polarization data, but also small scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the best fit values for cosmological parameters for the power-law flat LCDM model are (Omega_m h^2, Omega_b h^2, h, n_s, tau, sigma_8) = (0.127+0.007-0.013, 0.0223+0.0007-0.0009, 0.73 +- 0.03, 0.951+0.015-0.019, 0.09 +- 0.03, 0.74+0.05-0.06). The three year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, the WMAP data_alone_ require dark matter, and a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n_s=1,r=0). Models that suppress large-scale power through a running spectral index or a large-scale cut-off in the power spectrum are a slightly better fit to the WMAP and small scale CMB data than the power-law LCDM model (Delta chi^2 = 3) The combination of WMAP and other astronomical data yields significant constraints on the geometry of the universe, the equation of state of the dark energy, the gravitational wave energy density, and neutrino properties. Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps.
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Antony Lewis
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Antony Lewis » April 03 2006

This is obviously a very nice paper with numerous new and interesting results. Some comments have been made elsewhere.

Here I would just like to query the dark energy analysis. It is well known that if w \ne -1 the dark energy cannot be unperturbed (perturbations are implied by general relativity, [tex]\delta\rho_{\rm{de}}=0[/tex] is inconsistent). This paper gives results with and without perturbations, but it is unclear to me what the latter means. Have the authors devised some consistent 'unperturbed' model, e.g. taking a fluid model with c_s^2 \rightarrow \infty, or something similar? If not the unperturbed results seem to be rather meaningless - there are numerous inequivalent ways to calculate inconsistent results (c.f. the well known result that from any false statement you can prove anything you like; in astro-ph/0307104 we give 'unperturbed' results, but emphasise that this is some specific ad hoc recipe for modifying the code to produce an inconsistent result, and certainly did not intend to imply that the unperturbed model was at all physical).
Last edited by Antony Lewis on August 17 2006, edited 1 time in total.

Ben Gold
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Ben Gold » April 03 2006

I don't speak for WMAP, but I imagine they did just use the "no perturbations" switch in the code. I interpret the figure as just trying to get a rough idea of how much the cosmological constraints depend on the dark energy perturbation model, since we don't really know that dark energy obeys the usual cosmological fluid equations. I don't think the "no perturbation" model is mean to be particularly physical, but calculating perturbations for all the various non-quintessence models out there isn't particularly feasible. Certainly if you don't think dark energy is a fundamental fluid you're probably not too worried about how physical the assumptions about perturbations are.

In fact, off the top of my head I only know of one case (Skordis's work on TeVeS) where someone's actually gone through the effort of doing full perturbation theory for models where the acceleration comes from modifications to gravity or the Friedmann equation. For TeVeS, at least, it's a quite nasty affair.

Susana Landau
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Susana Landau » April 04 2006

what about reionization and degeneration with primordial scalar index fluctuations (n_s) and scalar amplitude (A_s) ?
In section 3.2 they say that the polarization measurements now strongly constrain tau, and that other parameters (n_s, A_s) are insesitive to the reionization history.
However from fig 10 it follows that \tau is still degenerated with A_S , and n_s.
what do you think?

Anze Slosar
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Re: [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe

Post by Anze Slosar » April 05 2006

Antony Lewis wrote: Here I would just like to query the dark energy analysis. It is well known that if w <> -1 the dark energy cannot be unperturbed (perturbations are implied by general relativity, [tex]\delta\rho_{\rm{de}}=0[/tex] is inconsistent). This paper gives results with and without perturbations, but it is unclear to me what the latter means.
I agree (to first order :) . However, I think it is useful to see "unperturbered" results as well: there are two faces of dark energy / cosmological constant, a 0th order effect on the background evolution and the corrections due to perturbations in the de component. While I agree that there is more than one way of doing things wrongly, I think there is also more than one way of doing things right (until we have a definite model for the dark energy), so I reckon that it is useful to see how much info comes just from changing the Friedman equation (which I think they refer to as no-perturb constraints), even if this is internally inconsistent. We would definitelly have a problem if constraints coming from the background would be at odds with constraints coming from evolution of perturbations.
(besides we are so close to w=-1 that perturbations make no difference whatsoever)

Jochen Weller
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Jochen Weller » April 05 2006

Hi Anze

so I think to summarize you, what they should have done is
to show different ways of doing it correctly, or ?

Niayesh Afshordi
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Post by Niayesh Afshordi » April 06 2006

I agree with Anthony and disagree with Anze.
Just because there is more than one way of doing something right, doesn't mean that anything goes. In particular, if \delta\rho_{de}=0 in one gauge, it won't be zero in other gauges. For example, codes in synchronous and longitudinal gauges give different answers if \delta\rho_{de} is set to zero while [tex]w\neq 0[/tex]. I suppose, you can get almost anything, with an arbitrary choice of gauge.

Michael Doran
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Post by Michael Doran » April 06 2006

Niayesh is right: it is a gauge-dependent statement to switch off the fluctuations.

Fergus Simpson
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Fergus Simpson » April 06 2006

No, I'd disagree.

As Ben said, the inclusion of perturbations makes the assumption that dark energy is a cosmological fluid. I don't see why we should have to make this assumption.

If dark energy results from some beyond-GR effect <insert wild speculation here> then the w(z) is no longer physical but could still be interpreted as the equation of state of a hypothetical field which would reproduce the same H(z) as what we observe.

Niayesh Afshordi
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Niayesh Afshordi » April 06 2006

If dark energy results from some beyond-GR effect <insert wild speculation here> then the w(z) is no longer physical but could still be interpreted as the equation of state of a hypothetical field which would reproduce the same H(z) as what we observe.
It doesn't matter if it is dark energy, phantom menace, or my craziest speculation. If gravity is a metric theory, then \delta\rho_{de} will depend on gauge if w<>0. Assuming that it would vanish in a particular gauge breaks causality.

Fergus Simpson
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Fergus Simpson » April 06 2006

Well, I was thinking along the lines of having \rho_{DE}=0, hence the lack of perturbations.

Ben Gold
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Post by Ben Gold » April 06 2006

I think we all can be right :)

I think choosing some funny dark energy and running the code without perturbations essentially amounts to asking "How does modifying the background expansion alone in this funny way affect the CMB?" Which may or may not be interesting, but there are theories out there that modify the expansion rate without dark energy (I don't know how viable most of these are, but they're out there). So I don't think it hurts to include extra information in your paper, even if it might not be of interest to everyone.

Niayesh Afshordi
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[astro-ph/0603449] Wilkinson Microwave Anisotropy Probe (WMA

Post by Niayesh Afshordi » April 06 2006

Again, this is not about the nature dark energy, but rather a very practical question about how you calculate say CMB power spectrum.

For example, if you only modify the bcakground evolution through some \rho_{DE}(z), and don't change perturbation equations (except for the implicit change in the timedependce of background variables), CMBfast (which is synchronous) and CMBeasy (in gauge invariant mode), will not give you the same answer.

Jochen Weller
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Post by Jochen Weller » April 07 2006

I definetly disagree with Fergus,
once you start arguing with w as an effective background parameter
from maybe a modified GR model, there is even more care required
for calculating perturbations. In this case you need a model how
large scale perturbation evolve, which might be completely different from
standard GR. One example would be DGP.
So it is as it stands. You need a descriptions of perturbations on large scales.

I think they just wanted to show that even if they might have messed it up last time (which I am not sure if they did or did not), that it does not make a difference as soon as you combine data sets.
So this is a bit of politics in the paper and not science.
Maybe one way they could have phrased this, is by saying we have one model with c_s^2 = 1 and one with c_s^2 = 0. I am aware this is NOT the same as having no perturbations. But at least this would have been a clear statement.

Alessandro Melchiorri
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Post by Alessandro Melchiorri » April 07 2006

Hi all,

I think they just wanted to show that there is no constraint on DE perturbations from the data.

Fergus Simpson
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Re: [astro-ph/0603449] Wilkinson Microwave Anisotropy Probe

Post by Fergus Simpson » April 07 2006

Jochen Weller wrote: In this case you need a model how
large scale perturbation evolve, which might be completely different from
standard GR. One example would be DGP.
So it is as it stands. You need a descriptions of perturbations on large scales.
Yes, I agree, the calculation of perturbations in modified gravity is an important issue. But I'm talking about something slightly different.

Most models (DGP, QCDM, MOND...etc...) are based on an H(z) controlled by the same "force" as that which is responsible for the growth of density perturbations.

However, it is surely worth considering that only H(z) requires modification from the standard theory. And since people are very familiar with w(z), it seems a reasonable way to define a particular background H(z). (Although the jerk, astro-ph/0408279, would be more appropriate in this case.)

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