Evidence for Dark Energy from the Cosmic Microwave Background Alone Using the Atacama Cosmology Telescope Lensing Measurements

For the first time, measurements of the cosmic microwave background radiation (CMB) alone favor cosmologies with $w=-1$ dark energy over models without dark energy at a 3.2-sigma level. We demonstrate this by combining the CMB lensing deflection power spectrum from the Atacama Cosmology Telescope with temperature and polarization power spectra from the Wilkinson Microwave Anisotropy Probe. The lensing data break the geometric degeneracy of different cosmological models with similar CMB temperature power spectra. Our CMB-only measurement of the dark energy density ${\Omega }_{\Lambda }$ confirms other measurements from supernovae, galaxy clusters, and baryon acoustic oscillations, and demonstrates the power of CMB lensing as a new cosmological tool.

Figure 1

Upper panel: Angular power spectra of CMB temperature fluctuations for two geometrically degenerate cosmological models, one the best-fit curved universe with no vacuum energy (${\Omega }_{\Lambda }=0$, ${\Omega }_m=1.29$), and one the best-fit flat $\Lambda \mathrm{CDM}$ model with ${\Omega }_{\Lambda }=0.73$, ${\Omega }_m=0.27$. The seven-year WMAP temperature power spectrum data [18] are also shown; they do not significantly favor either model. Lower panel: The CMB lensing deflection power spectra are shown for the same two models. They are no longer degenerate: the ${\Omega }_{\Lambda }=0$ universe would produce a lensing power spectrum larger than that measured by ACT [16] (shown above).

Figure 2

Different terms in the kernel of the lensing integral of Eq. (1) as a function of conformal lookback distance for $\ell =120$, for models as in Fig. 1. Upper panel: geometry term. Middle panel: growth term, scaled to its value at decoupling for clarity. Bottom panel: total kernel.

Figure 3

Upper panel: Two-dimensional marginalized posterior probability for ${\Omega }_m$ and ${\Omega }_{\Lambda }$ (68% and 95% C.L.s shown). Shaded (colored) contours are for $\mathrm{WMAP}+\mathrm{ACT}$ lensing, and black lines are for WMAP only. Using WMAP data alone, universes with ${\Omega }_{\Lambda }=0$ lie within the 95% C.L. The addition of lensing data breaks the degeneracy, favoring models with dark energy. Lower panel: One-dimensional marginalized posterior probability for ${\Omega }_{\Lambda }$ (not normalized). An energy density of ${\Omega }_{\Lambda }\simeq 0.7$ is preferred even from WMAP alone, but when lensing data are included, an ${\Omega }_{\Lambda }=0$ universe is strongly disfavored.