Things that go bump in the CMB polarization

This post is written by Michael Mortonson, graduate student of Wayne Hu at the U. of Chicago. Michael has also asked me to thank Cora Dvorkin and Wayne Hu (U. of Chicago), and Hiranya Peiris (U. of Cambridge), who contributed to the post. Dmitry.

One of the most impressive results from experiments that have measured the cosmic microwave background is the remarkable agreement between the observed distribution of CMB intensity anisotropies on the sky and predictions of the standard cosmological theory. However, there are a few things that are a bit “off,” and while some of these glitches have gone away with the accumulation of more data or with improvements in analysis methods, other anomalies persist.

The particular glitch that is the subject of this post is a small oscillation in the angular power spectrum of CMB temperature anisotropies () on scales of a few degrees on the sky. These are larger scales (lower angular multipoles ) than the first CMB acoustic peak, so normally we would expect the spectrum to be smooth there, but it apparently isn’t. As the data below from 5 years of full-sky observations by the WMAP satellite show (blue points with error bars), there is a small dip in the spectrum at angular multipoles of and a bump at .

So why isn’t everyone rushing to abandon the standard cosmological picture over this anomalous feature? The main reason is because it’s not that anomalous – you can see that the error bars in the figure above get larger on large scales, so to some degree we expect that the model and the observed power spectrum won’t agree perfectly at low . The increasing uncertainty at large scales is due to cosmic variance: since there is only a finite amount of sky that we can observe from our position on Earth, we have a limited number of independent observations of large-scale correlations. In terms of the angular power spectrum, there are modes to average over for each multipole . This means that the glitches we observe may just be a statistical fluke that would go away if we could somehow get more independent observations of the temperature anisotropies on those scales. (The interpretation of other CMB anomalies at large scales, like the low value of the temperature quadrupole and asymmetry and alignment of the quadrupole and octopole moments, is similarly complicated by cosmic variance.)

On the other hand, it’s possible that the observed features in the CMB temperature power spectrum are actually a signature of new physics. In fact, Adams, Cresswell, and Easther, building on work from the early ’90s by Starobinsky, proposed a model that can produce just the sort of oscillation that is observed at few-degree scales. Their model introduces a small step in an otherwise smooth inflationary potential. When the scalar field that drives inflation encounters this step, oscillations are imprinted on scales that are exiting the horizon at the same time, and the effects of these oscillations show up in the CMB angular power spectra. An analysis of the 3-year WMAP temperature data by Covi et al. showed that if you put the step in the inflationary potential in just the right location with the right amplitude and width, the resulting oscillations in the CMB temperature spectrum give a better fit to the data at than a smooth spectrum. The curvature power spectrum and CMB spectra of this model are plotted as red curves in the figure below.

(Click on the image for the full-sized version.)

Transfer from the curvature power spectrum to CMB temperature and polarization angular power spectra.

This step model can reproduce the feature observed in the CMB data, but the improvement in the fit is a difference of about 10 with 3 new parameters for the step – so it’s an interesting possibility, but not convincing. Because of cosmic variance, the temperature measurements we have on these scales are good as any we’re likely to ever get, so CMB temperature anisotropies alone are not going to tell us whether the observed features are signs of new inflationary physics or merely a chance occurrence.

Fortunately, as we discuss in our recent paper (arXiv:0903.4920), we can use the polarization of the CMB to try to distinguish between these two possibilities. If the temperature features are created by a step in the inflationary potential, then we should see similar features in the angular power spectrum of E-mode polarization, . If not, then those features shouldn’t appear in polarization. In fact, inflationary features should show up even better in polarization than in temperature, which means we might see several oscillations in the spectrum instead of a single dip and bump. The reason for this is that the transfer function for polarization has a cleaner projection of wavenumbers k to angular multipoles as you can see in the contour plots of the transfer functions for temperature and polarization in the center of the plot above. The transfer functions relate the inflationary curvature power spectrum to the CMB power spectra through the following equation:

where X and Y can be either temperature (T) or E-mode polarization (E).

WMAP has measured CMB polarization, but the measurements on few-degree scales aren’t precise enough to be able to look for the features we’re interested in. For that, we’ll have to wait for data from the just-launched Planck satellite. With Planck’s measurements, we have a good chance of being able to test the origin of the temperature features. We found that the inflationary step that best matches the temperature data produces features in polarization that Planck can detect with a difference of 8-9 relative to the smooth model – that’s similar to the significance of the feature in temperature, but seeing the same feature in polarization would go a long way toward being a convincing indication of something new happening with inflation on those scales. But it turns out that we can do even better with CMB polarization. Planck’s polarization measurements on few-degree scales are expected to be limited by the instrument’s sensitivity, not by cosmic variance. If a future CMB satellite like the proposed CMBPol provides more precise polarization measurements that are limited only by cosmic variance, a definitive detection (or rejection) of the feature should be possible.

There are a few additional complications that we describe in our paper, and we encourage anyone interested to read more about the details there. One of the things that you might worry about is correlations between temperature and polarization that could make polarization features appear even if the temperature features are only a statistical anomaly; on the relevant scales, though, the correlation is small enough that this effect is not a significant concern. There is also the possibility of a large amplitude of tensor fluctuations from inflationary gravitational waves (which would be a very exciting discovery in itself) that could smooth out features in polarization and make them harder to detect. Similarly, the reionization history of the universe imprints features on the polarization spectrum on large scales, so there is the possibility of confusing features from reionization with features from inflation. While these are important effects to consider, especially when we analyze future polarization data, we find that the expected effects are small enough that they don’t change the basic conclusion that observations of CMB polarization will be very useful in determining the origin of the temperature features.

Recommended Reading

• Our paper: M. J. Mortonson, C. Dvorkin, H. V. Peiris, & W. Hu (2009) Phys. Rev. D 79, 103519 (arXiv:0903.4920).
• CMB: “The Cosmic Symphony,” W. Hu & M. White (2004) Scientific American 290, 44.
• A more technical review of the CMB: W. Hu & S. Dodelson (2002) ARA&A 40, 171 (astro-ph/0110414).
• Inflation review, including generation of perturbations: D. Baumann & H. V. Peiris, arXiv:0810.3022.
• TASI lectures on inflation: W. H. Kinney, arXiv:0902.1529.
• More large-scale anomalies: D. Huterer (2006) New Astron. Rev. 50, 868 (astro-ph/0608318).