High-resolution data demonstrate gravitational lensing of the cosmic microwave background

Most matter in the universe is dark matter, made up of as-yet-unidentified particles that don’t interact electromagnetically with the baryonic matter we’re familiar with. It doesn’t emit, absorb, or scatter radiation at any wavelength. But, like ordinary matter, it does exert a gravitational influence on photons, deflecting their paths as they travel over cosmic distances. That effect, called gravitational lensing, has been used to map the large-scale structure of dark matter through distortions in images of background galaxies (see PHYSICS TODAY, March 2007, page 20 ). But a more complete picture may be available from gravitational lensing of the cosmic microwave background.

Lensing of the CMB has been observed before, using data from the Wilkinson Microwave Anisotropy Probe (WMAP). ¹ But the only conclusive demonstrations of lensing from WMAP data involved cross-correlations between the CMB data and observations of foreground galaxy clusters. Because baryonic matter and dark matter are gravitationally drawn together, one can serve as a tracer for the other. But ultimately, the goal is to use CMB lensing to map dark matter without any foreknowledge of where the dark matter is expected to be.

Now, using new data from the Atacama Cosmology Telescope (ACT) in Chile, shown in figure 1, researchers have detected CMB lensing using CMB data alone. ² The ACT team’s most recent result is a statistical measurement that the CMB has been gravitationally lensed, but not a map of the lensing structures. The researchers anticipate that as better CMB data become available in the near future, it will be possible to reconstruct the full lensing field in real space.

Microwave statistics

The CMB is the universe’s baby picture—a snapshot of what it looked like at the young age of 380 000 years. Before that time, everything was so dense and hot that thermal photons were energetic enough to ionize hydrogen, so they were constantly being absorbed and reemitted. By age 380 000, the universe had expanded and cooled to the point where that was no longer the case. Stable neutral atoms formed for the first time, and the photons sped away. Those photons are what we now see as the CMB; the ensuing expansion of the universe has stretched their wavelengths from the UV regime into the microwave.

The CMB looks nearly the same everywhere on the sky: a thermal distribution of temperature 2.7 K. But small spatial temperature fluctuations, on the order of 30 µK, reflect the density variations of the 380 000-year-old universe. The fluctuations appear on all angular-size scales, but some scales are more prominent than others. Important cosmological information can be gleaned from the intensities and frequencies of the peaks in the CMB spatial power spectrum (or multipole expansion). The most prominent peak, at a multipole l of about 250, corresponds to hot and cold spots of about a degree in angular size, as are visible in figure 2.

Important for the study of CMB lensing are the statistical properties of those fluctuations. To a good approximation, the primordial, or unlensed, CMB is a so-called Gaussian random field: Any set of n points on the sky has a temperature probability distribution in the form of an n-dimensional Gaussian. Since, furthermore, the CMB temperature field is homogeneous and isotropic, the temperature correlation between any two points on the sky is a function only of their angular separation, and there is no additional information to be gained by looking at higher-order correlations among three, four, or more points. In other words, the real and imaginary parts, or phases, of the Fourier modes of the CMB temperature are independently distributed and uncorrelated.

Converging on convergence

Gravitational lensing destroys that independence. When temperature fluctuations of one characteristic size are lensed by structures of a different size, correlations form between the corresponding Fourier modes. Equivalently, in real space, multipoint correlation functions become nonzero. Lensing deflects CMB photons by an average of 3 arcminutes, with those deflections being coherent on the scale of degrees. With its spatial resolution of one-fifth of a degree, WMAP doesn’t allow for conclusive detection of lensing. But the ACT, with resolution 20 times better, does.

Theorists have worked out functions for using the multipoint correlations to extract the so-called lensing convergence field, a scalar field that represents how much the CMB is distorted by gravitational lensing. ³ The ACT researchers put those functions to work, with some improvements of their own: The functions require taking the small difference between two large quantities. Led by David Spergel (Princeton University) and Sudeep Das (University of California, Berkeley), they worked out a more accurate method for calculating one of those quantities to make the best possible use of their data.

Figure 3 shows the resulting convergence field’s multipole components. The black line is the expected power spectrum of the field, derived from a standard cosmological model. Assuming a power spectrum of that expected shape (but not necessarily the same amplitude), the ACT researchers found that their data establish at the 4σ level that the convergence field is nonzero—that the CMB has been distorted by gravitational lensing.

The ACT data do not, however, enable a full reconstruction of the convergence field itself. For that, it would be necessary to calculate each multipole component with a signal-to-noise ratio greater than 1. That’s not possible yet, but it should be next year using data from the Planck space observatory.

Dark energy, too

Even without finding the convergence field, the ACT researchers have already used their data to rule out the possibility of a universe without dark energy—the first time that result has been obtained from CMB data alone. ⁴ Dark energy, as opposed to dark matter, is an elusive form of energy that permeates all of space and acts to speed up the expansion of the universe; it’s needed to explain observations such as the distances and redshifts of type Ia supernovae and the ages of high-redshift galaxies. The appearance of the primordial CMB, a snapshot of the universe at one point in time, is not enough to es

tablish the need for dark energy; specifically, it can’t distinguish between the effects of the universe’s curvature and rate of growth. But with the lensed CMB one can, since it contains information about the distribution of matter both at high redshifts and in more recent epochs.

The ACT researchers found that their data demonstrate the need for dark energy at the 3.2σ level. That’s less solid evidence than other methods have provided so far, but as Spergel explains, “The existence of dark energy is such a surprising and important result that it is essential that we confirm it using as many approaches as possible.”