## Monday, February 4, 2013

### The “ISW mystery” deepens considerably

 Other than my initials, what secrets does the CMB hide that are waiting to be seen only when the CMB is examined in just the right way?

This time last year I wrote a few posts describing what I called the “ISW mystery” (Part I, II, III and IV). A year has passed, it is time for an update on the mystery.

The very short summary is that things are starting to get more than a little bit exciting. All of the plausible ways in which the calculation of the expected ISW signal could have been wrong have been checked and eliminated as possibilities; if the measured signal is real, it is too large for the standard cosmological model. Much, much more excitingly, the observation that generated the mystery has now been repeated in another region of the universe and a very similar and equally anomalous signal was found; the apparent anomaly was not a statistical fluke.

The preprint of the paper describing this new observation was released just a week ago.

What is the “ISW mystery”?

 The image that began the mystery. Why is that spot so hot, and how did it get that cold ring around it?

A quick recap will probably be useful. The integrated Sachs-Wolfe (ISW) effect describes the heating and cooling of light as it passes through gravitational peaks and valleys late in the evolution of the universe. In the standard cosmological model, these peaks and valleys decay with time, so a light ray gains (or loses) more energy entering an over-dense (or under-dense) region of the universe than it loses (or gains) leaving it. The effect is very, very small. Almost every source of light in the universe is not known well enough to be used to detect it. Only the cosmic microwave background (CMB) is uniform enough that these tiny fluctuations could ever be detected.

However, even then, the primary fluctuations in the the temperature of the CMB are bigger than the secondary ones created by the ISW effect. We can measure these fluctuations but we could never know how much is due to the ISW effect and how much is primordial. The only thing we can do is look at the structures in the universe nearby and see if on average the CMB is slightly hotter (colder) along lines of sight where the nearby universe is over-dense (under-dense). The bigger, primordial fluctuations in the CMB should have nothing to do with local structures (the CMB has come from much further away). Therefore, if this signal were to be found in the CMB, the most plausible explanation would be an ISW effect.

A group in Hawaii decided to look for this signal in a slightly unusual way. Firstly, they made a catalogue of significant over and under-dense regions in a particular survey of galaxies. Then, they only examined patches of the CMB that existed along the line of sight of each of these regions. They then found that the patches aligned with over-densities were hotter on average than a randomly selected patch and those aligned with under-densities were colder (with more than “$$4\sigma$$” significance). This is what one would expect from an ISW effect. The “ISW mystery” is that these patches were too hot and too cold. The ISW effect simply shouldn't be that big.

The importance of checking the anomaly from every angle

If this signal really is there and really is bigger than expected, then some new physical effect must be heating and cooling the CMB as it passes through these over/under dense regions. Clearly that would be big news. It would not be quite as dramatic as genuinely faster than light neutrinos would have been, but it would certainly require consideration of exotic things like modifying gravity, changing the primordial density perturbations of the universe, or having something other than a cosmological constant causing the accelerated expansion of the universe. Therefore, it is very important to be careful before jumping to conclusions.

How do we know the ISW effect can't be this big?

 From arXiv:1212.0776. Two different methods to arrive at very conservative over-estimates of the expected ISW signal. The solid line uses the hottest and coldest lines of sight, the dashed line uses spherically symmetric peaks in the density of the universe. The observed signal was  $$9.6\pm2.2 \mu K$$.

The structures that determined which lines of sight to use were found with a particular algorithm (called ZOBOV for under-densities and VOBOZ for over-densities). We can't see most of the matter in the universe (i.e. dark matter). Therefore it is necessary to instead apply ZOBOV/VOBOZ to the number density of objects that we can see (e.g. galaxies). Without doing a full simulation of the growth of structure in the universe, as well as estimating where astrophysical objects would form in this simulation, it is difficult to precisely determine what lines of sight ZOBOV (I'll just use ZOBOV, hereafter, to refer to both algorithms) would pick out.

In late 2011 my collaborators and I tried to get around this with a very conservative calculation. Although ZOBOV can only see galaxies, it is the total matter distribution that generates the gravitational wells that affect the CMB. Therefore, instead of trying to model ZOBOV accurately, we calculated the ISW signal from the widest and most under/over-dense, spherically symmetric, peaks expected in the total matter distribution. ZOBOV should miss some of these peaks and therefore this calculation should significantly over-estimate the ISW signal. However, perhaps ZOBOV is managing to see some other, non-spherical, structures that happen to give a bigger signal. This seemed unlikely, but we decided to check.

To do this we took our conservatism one step further. This time we asked “what is the maximum ISW effect expected along any line of sight?” If the answer to that question was a signal smaller than the observed signal then, irrespective of how ZOBOV picks its lines of sight, the observed signal has to be anomalous. This is exactly what we found. There is no wiggle room left on the theoretical side of this anomaly. If the signal is real, it is too big.

Are we really sure it isn't foregrounds?

 Figure A: The expected angular profile of a "fake CMB" with an amplitude proportional to the matter density. From  arXiv:1212.1174.
Can we trust the measurement?

The short answer is yes, because there is surprisingly little room for things that could have gone wrong.

Let's briefly review the measurement. Without looking at the CMB, a group in Hawaii came up with a bunch of lines of sight on the sky where they expected the ISW effect to produce the hottest hot spots and coldest cold spots. When they then looked at the CMB along those lines of sight, they found that the “hot” lines of sight were statistically hotter than average and the “cold” lines of sight were statistically colder. Either this was a very unlikely fluke, or some aspect of the method the Hawaiians used to pick these lines of sight must be related to the temperature of the CMB.

The algorithm that picked these lines of sight looked only at a collection of luminous red galaxies (LRGs). Therefore, those LRGs must be related, in some way, to something that is affecting what we measure to be the CMB temperature.

One very plausible candidate was the ISW effect. But we know now that the observed signal is far too big for an ISW effect, so what else could it be?

The next plausible explanation is that the LRGs are themselves emitting light that looks like the CMB. If they were, then this measurement might make sense. Where there are more LRGs, more fake CMB is being emitted, so we measure the CMB as hotter. Where there are fewer, less fake CMB is being emitted, so we measure the CMB as colder.

However, a number of checks have now been made to examine whether the measured signal has the properties one would expect of “foreground” radiation from the LRGs. Every one of them has come up false. If it is foreground radiation, it is quite a strange foreground.

 Figure B: The observed angular profile of the mystery "ISW" signal. Notice how different it is to what would be expected from a fake CMB (see figure A). From arXiv:1212.1174.

Here are some of the tests:

The CMB has a very well known, blackbody, spectrum (i.e. intensity of light as a function of its frequency/wavelength). The anomalous “ISW” signal is present, with equal magnitude, in all of the frequency bands measured by WMAP. If the signal is due to foreground, that foreground must look very similar to a blackbody.

If the signal is coming from LRGs, it would be natural to expect the magnitude of the signal to be proportional to the number density of LRGs. A group based in Munich and Teruel tested exactly this possibility. As part of a recent paper, they took a simulation and added a fake CMB signal that was proportional to the matter density in the simulation. When patches of the fake CMB are examined along the lines of sight of these LRG-type objects, the size of the signal as a function of the size of the patch (the angular profile) is completely different to what was observed (see figs A and B). It is worth noting that the expected angular profile of the ISW effect does match the observed signal closely.

[Continued in part two...]

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References:
• Samuel Flender, Shaun Hotchkiss, & Seshadri Nadathur (2012). The stacked ISW signal of rare superstructures in ΛCDM JCAP arXiv: 1212.0776v2
• Carlos Hernandez-Monteagudo, & Robert E. Smith (2012). On the signature of nearby superclusters and voids in the Integrated Sachs-Wolfe effect arXiv arXiv: 1212.1174v1

[I have corrected a mistake in the caption to the third figure in this post. The descriptions for the dotted and solid lines were swapped.]