Robert Knight, Lloyd Knox

The angular two-point correlation function of the temperature of the cosmic microwave background (CMB), as inferred from nearly all-sky maps, is very close to zero on large angular scales. A statistic invented to quantify this feature, $S_{1/2}$, has a value sufficiently low that only about 7 in 1000 simulations generated assuming the standard cosmological model have lower values; i.e., it has a $p$-value of 0.007. As such, it is one of several unusual features of the CMB sky on large scales, including the low value of the observed CMB quadrupole, whose importance is unclear: are they multiple and independent clues about physics beyond the cosmological standard model, or an expected consequence of our ability to find signals in Gaussian noise? We find they are not independent: using only simulations with quadrupole values near the observed one, the $S_{1/2}$ $p$-value increases from 0.007 to 0.08. We also find strong evidence that corrections for a "look-elsewhere effect" are large. To do so, we use a one-dimensional generalization of the $S_{1/2}$ statistic, and select along the one dimension for the statistic that is most extreme. Subjecting our simulations to this process increases the $p$-value from 0.007 to 0.03; a result similar to that found in Planck XVI (2016). We argue that this optimization process along the one dimension provides an $underestimate$ of the look-elsewhere effect correction for the historical human process of selecting the $S_{1/2}$ statistic from a very high-dimensional space of alternative statistics $after$ having examined the data.

Maximilian H. Abitbol, Jens Chluba, J. Colin Hill, Bradley R. Johnson

Measurements of cosmic microwave background spectral distortions have profound implications for our understanding of physical processes taking place over a vast window in cosmological history. Foreground contamination is unavoidable in such measurements and detailed signal-foreground separation will be necessary to extract cosmological science. We present MCMC-based spectral distortion detection forecasts in the presence of Galactic and extragalactic foregrounds for a range of possible experimental configurations, focusing on the Primordial Inflation Explorer (PIXIE) as a fiducial concept. We consider modifications to the baseline PIXIE mission (operating 12 months in distortion mode), searching for optimal configurations using a Fisher approach. Using only spectral information, we forecast an extended PIXIE mission to detect the expected average non-relativistic and relativistic thermal Sunyaev-Zeldovich distortions at high significance (194$\sigma$ and 11$\sigma$, respectively), even in the presence of foregrounds. The $\Lambda$CDM Silk damping $\mu$-type distortion is not detected without additional modifications of the instrument or external data. Galactic synchrotron radiation is the most problematic source of contamination in this respect, an issue that could be mitigated by combining PIXIE data with future ground-based observations at low frequencies ($\nu < 15-30$GHz). Assuming moderate external information on the synchrotron spectrum, we project an upper limit of $|\mu| < 3.6\times 10^{-7}$ (95\% c.l.), slightly more than one order of magnitude above the fiducial $\Lambda$CDM signal from the damping of small-scale primordial fluctuations, but a factor of $\simeq 250$ improvement over the current upper limit from COBE/FIRAS. This limit could be further reduced to $|\mu| < 9.4\times 10^{-8}$ (95\% c.l.) with more optimistic assumptions about low-frequency information. (Abridged)