I was asked over email how well it is known that the Universe is spatially flat. According to just released WMAP 5 year dataset , the spatial curvature contribution is bounded by $-0.0181 < \Omega_k < 0.0071$ at the 95% confidence level with prior on the equation of state for the dark energy 3. WMAP 5 year more (dark energy = cosmological constant) or $-0.0175 < \Omega_k < 0.0085$ at the 95% confidence level if the prior above is not set. Therefore, the precision of the statement that the Universe is spatially flat is more than 1 %.

Now, I would like to answer the question asked in comments – what was actually new in the 5 year data release compared to the 3 year data release.

First of all, they were able to measure polarization of CMB with much greater precision. In particular, in this release they used polarization data in Ka band in addition to polarization data in Q and V bands used for the 3 year data analysis. This allowed them to set much more stringent constraints for the optical depth of the Universe. As I wrote in the first post, while 3 year data gave $\tau=0.089 \pm 0.030$ , according to 5 year data $\tau=0.087 \pm 0.017$ , i.e., there takes place a very nice jump from 3 sigma to 5 sigma level.

The second thing is that temperature power spectrum 3. WMAP 5 year more is now measured much more precisely, in particular, one has very precise information about the third peak from WMAP alone now. Interestingly, improvement in analysis lead to the systematic 2.5% increase of at l > 200! At first, I was really scared reading about this (where is the guarantee that the same effect will not show up in the WMAP 9 year data release?), but it turned out that this systematic increase is within 1 sigma of 3 year data errors.

Another interesting fact is a certain change in the analysis of non-gaussinities. Analysing 5 year dataset, WMAP team applied the mask different from the one used for the 3 year data. In particular, newer mask is cutting more sky which actually leads to larger errors in estimating non-gaussianities compared to the 3 year data analysis. For example, from the 3rd year data we knew that

$6.5 < f_{NL}^{local} < 110.5$

at the 95% confidence level and concluded that $f_{NL}^{local}>0$ at 2.3 sigma level. Now this conclusion is gone and we cannot say anything as strong based on the analysis with the newer mask. The reason why they wanted to use the newer mask remains mystery for me; certainly, I would like to know more about it. Anyway, the WMAP team’s conclusion is that detection of any non-gaussinity is absent at the 95% confidence level.

Among other things they are talking about in the papers are running index and entroy perturbations. There is no serious impovement regarding the running index:

$\frac{dn_s}{d \log k}=-0.037\pm{}0.028$

from WMAP5 alone and

$\frac{dn_s}{d \log k}=-0.032{}+0.021-0.020$

from WMAP5 + BAO + SN combined.

Their bound on the contribution of isocurvature perturbations is the following:

isocurvature < 8.6 % at 95% confidence level for axion models (“axion” means in practice that isocurvature and curvature perturbations are uncorrelated),

isocurvature < 2% at 95% confidence level for curvaton models (entropy and curvature perturbations are anticorrelated).

The last thing I wanted to discuss are the bounds on different inflationary models from the 5 year data.

As you can see from the picture below, the $\lambda \phi^4$ chaotic inflation is now ruled out completely, $m^2 \phi^2$ chaotic inflation is within 95% confidence level curve (but outside 5 sigma level curve! that could mean something interesting). Easther-McAllister N-flation with $m^2 \phi^2$ potential is outside 95 % confidence level curve (this is due to the fact that r is now being known more precisely)

3. WMAP 5 year more

and inflation with slow power law regime ( $a(t)\sim t^p$ , 3. WMAP 5 year more ) is also ruled out (see below).

3. WMAP 5 year more

My main conclusion remains the same – revolution did not happen Something interesting happens with non-gaussianities, and I would like to know more about their analysis in this respect.