[1003.3999] Cosmological parameters from large scale structure  geometric versus shape information
Authors:  Jan Hamann, Steen Hannestad, Julien Lesgourgues, Cornelius Rampf, Yvonne Y. Y. Wong 
Abstract:  The matter power spectrum as derived from large scale structure (LSS) surveys contains two important and distinct pieces of information: an overall smooth shape and the imprint of baryon acoustic oscillations (BAO). We investigate the separate impact of these two types of information on cosmological parameter estimation, and show that for the simplest cosmological models, the broadband shape information currently contained in the SDSS DR7 halo power spectrum (HPS) is by far superseded by geometric information derived from the baryonic features. An immediate corollary is that contrary to popular beliefs, the upper limit on the neutrino mass m_\nu presently derived from LSS combined with cosmic microwave background (CMB) data does not in fact arise from the possible smallscale power suppression due to neutrino freestreaming, if we limit the model framework to minimal LambdaCDM+m_\nu. However, in more complicated models, such as those extended with extra light degrees of freedom and a dark energy equation of state parameter w differing from 1, shape information becomes crucial for the resolution of parameter degeneracies. This conclusion will remain true even when data from the Planck surveyor become available. In the course of our analysis, we introduce a new dewiggling procedure that allows us to extend consistently the use of the SDSS HPS to models with an arbitrary sound horizon at decoupling. All the cases considered here are compatible with the conservative 95%bounds \sum m_\nu < 1.16 eV, N_eff = 4.8 \pm 2.0. 
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 Posts: 119
 Joined: March 02 2005
 Affiliation: University of Helsinki
[1003.3999] Cosmological parameters from large scale struct
The authors compare how much information there in the BAO peak compared to the overall shape of the largescale structure power spectrum. They basically conclude that at present, the information in the LSS data (when combined with the CMB) is dominated by the BAO scale.
For me, the modelindependent extraction of the BAO scale via spectral analysis was particularly interesting.
There is one statement which I did not understand. On page 6 the authors explain the positive correlation between the dark energy equation of state [tex]\omega[/tex] and the primordial spectral index by saying that as [tex]\omega[/tex] becomes closer to zero (i.e. grows), the late ISW becomes larger. I would have thought that as [tex]\omega[/tex] goes to zero, the late ISW effect would vanish.
For me, the modelindependent extraction of the BAO scale via spectral analysis was particularly interesting.
There is one statement which I did not understand. On page 6 the authors explain the positive correlation between the dark energy equation of state [tex]\omega[/tex] and the primordial spectral index by saying that as [tex]\omega[/tex] becomes closer to zero (i.e. grows), the late ISW becomes larger. I would have thought that as [tex]\omega[/tex] goes to zero, the late ISW effect would vanish.
[1003.3999] Cosmological parameters from large scale struct
They're using CAMB, which if I remember correctly defaults to always using a sound speed of 1 for dark energy, regardless of what [tex]w[/tex] is set to. So I don't think dark energy quite behaves like CDM as [tex]w\to0[/tex], which seems to be what you're thinking of.
But I think what's more important for late ISW is that as long as [tex]w<0[/tex], a larger [tex]w[/tex] (closer to zero) means dark energy remains dominant back to higher redshift than for a more negative [tex]w[/tex], and this longer duration of dark energy dominance leads to more ISW. To put it another way: if [tex]w\to \infty[/tex], then you get zero late ISW, because [tex]\Omega_{de}[/tex] was zero up until a fraction of a second ago.
But I think what's more important for late ISW is that as long as [tex]w<0[/tex], a larger [tex]w[/tex] (closer to zero) means dark energy remains dominant back to higher redshift than for a more negative [tex]w[/tex], and this longer duration of dark energy dominance leads to more ISW. To put it another way: if [tex]w\to \infty[/tex], then you get zero late ISW, because [tex]\Omega_{de}[/tex] was zero up until a fraction of a second ago.

 Posts: 119
 Joined: March 02 2005
 Affiliation: University of Helsinki
[1003.3999] Cosmological parameters from large scale struct
I see, that makes sense.
Re: [1003.3999]
I would just point out that this is a modeldependent as well as datasetdependent statement. In the SDSS DR7 analysis, we found that using the shape information improved constraints on both [tex]m_{nu}[/tex] and [tex]N_{eff}[/tex] when combined with the CMB alone (and considering these two parameters separately). However, in this paper they're allowing both parameters to vary simultaneously (which I would guess are highly degenerate in P(k)); moreover, they've included the Riess et al. [tex]H_0[/tex] constraint, which already buys you a lot in terms of breaking degeneracies with the CMB on these parameters.Syksy Rasanen wrote:The authors compare how much information there in the BAO peak compared to the overall shape of the largescale structure power spectrum. They basically conclude that at present, the information in the LSS data (when combined with the CMB) is dominated by the BAO scale.
In any case, it's a very interesting paper and I think they've made good improvements to how the likelihoods are implemented and clarified some confusion I had about generalizing BAO constraints to models with [tex]N_{eff} \neq 3.04[/tex].

 Posts: 119
 Joined: March 02 2005
 Affiliation: University of Helsinki
[1003.3999] Cosmological parameters from large scale struct
Right, I should have specified that for extended models, there is extra information in the overall shape. The authors point this out for the example of a variable number of neutrino species together with a variable dark energy equation of state. In this case, the neutrino masses, equations of state and the spectral index all benefit from the shape information.
How important do you think is the [tex]H_0[/tex] prior?
How important do you think is the [tex]H_0[/tex] prior?