Reading Komatsu, getting over a few notation hurdles

[Martin]

Komatsu et al is currently the best source on hard cosmology

http://arxiv.org/abs/0803.0547

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

 

So what if it's 99% incomprehensible. If you have watched the balloon animation movies at Wright's website, and tried stuff with the cosmo calculator there is an important 1% that you can get directly from the Komatsu paper. (Don't have to take my or anybody else's word for it.)

 

The authors of that paper include superheros like Joanna Dunkley, David Spergel, and Ned Wright.

The tables of numbers are not only just based on the latest WMAP, there are columns labeled "WMAP+SNe+BAO". That means the estimates are based on all types of relevant data. SNe is supernovae and BAO is based on galaxy counts at different distances---frozen waves in the 3D density of baryonic matter (baryon acoustic oscillations). So it's not just patterns in the microwave background temperature map---it's patterns in the overall distribution of matter.

 

The main obstacle to getting that key 1% out of Komatsu is notation. I know there are a few people at SFN now who can glean stuff directly from Table 2 once over minor notation hurdles. So I'll interpret some out of Komatsu Table 2, on page 4.

 

You can see the radius of curvature estimate (R_curv > 22 h^-1)

 

Gpc is gigaparsec and h is a conventional parameter which you take to be 0.71 if you think the Hubble rate is 71 km/s per Mpc. Maybe you think that is obscure obfuscated notation? That's just how it is. Notation grows up and people get used to it and it's difficult to reform.

 

I prefer to talk in lightyears, so to get this into lightyears I type "22/0.71 gigaparsec in lightyears" into Google and press return.

It does the computation and comes back with "101 billion lightyears". You can round it to 100 so as not to look too precise.

 

Also in Table 2, in the "WMAP+SNe+BAO" column they have a confidence interval for what they call Omega_k. That is a code name for

1 - Omega_total. You may be familiar with this parameter Omega (the total energy density compared to the level needed for exact spatial flatness) and you may be wondering if Omega is greater than one (which would make space a slightly positive curved finite volume, still nearly flat but finite).

So why don't they give you the confidence interval for the Omega you are familiar with? Well they don't, they give a 95% interval for Omega_k as follows:

-0.0179 < Omega_k < 0.0081

Let's round that off

-0.018 < Omega_k < 0.008

and translate it to a 95% interval for Omega_total or simply Omega, which more people are likely to have heard of.

0.992 < Omega < 1.018

Edited January 6, 2009 by Martin