Detection of the Power Spectrum of Cosmic Microwave Background Lensing by the Atacama Cosmology Telescope

We report the first detection of the gravitational lensing of the cosmic microwave background through a measurement of the four-point correlation function in the temperature maps made by the Atacama Cosmology Telescope. We verify our detection by calculating the levels of potential contaminants and performing a number of null tests. The resulting convergence power spectrum at 2° angular scales measures the amplitude of matter density fluctuations on comoving length scales of around 100 Mpc at redshifts around 0.5 to 3. The measured amplitude of the signal agrees with Lambda cold dark matter cosmology predictions. Since the amplitude of the convergence power spectrum scales as the square of the amplitude of the density fluctuations, the $4\sigma$ detection of the lensing signal measures the amplitude of density fluctuations to 12%.

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Figure 1

Mean convergence power spectrum (red points) from 480 simulated lensed maps with noise similar to our data. The solid line is the input lensing power spectrum, taken from the best-fit $\mathrm{WMAP}+\mathrm{ACT}$ cosmological model. Error bars correspond to the scatter of power spectrum values obtained from individual maps.

Figure 2

Convergence power spectrum (red points) measured from ACT equatorial sky patches. The solid line is the power spectrum from the best-fit $\mathrm{WMAP}+\mathrm{ACT}$ cosmological model with amplitude $A_L=1$, which is consistent with the measured points. The error bars are from the Monte Carlo simulation results displayed in Fig. 1. The best-fit lensing power spectrum amplitude to our data is $A_L=1.16\pm 0.29$.

Figure 3

Convergence power spectrum for simulated thermal and kinematic SZ maps and point source maps [17] which are a good fit to the ACT data. Note that we only show the non-Gaussian contribution, as the Gaussian part which is of similar negligible size is automatically included in the subtracted bias generated by phase randomization. The solid line is the convergence power spectrum due to lensing in the best-fit $\mathrm{WMAP}+\mathrm{ACT}$ cosmological model.

Figure 4

Upper panel: Mean cross-correlation power spectrum of convergence fields reconstructed from different sky patches. The result is consistent with null, as expected. Lower panel: Mean convergence power spectrum of noise maps constructed from the difference of half-season patches, which is consistent with a null signal. The error bars in either case are determined from Monte Carlo simulations, and those in the lower panel are much smaller as they do not contain cosmic variance.