Abstract
We study the covariance in the angular power spectrum estimates of CMB
fluctuations when the primordial fluctuations are non-Gaussian. The
non-Gaussian covariance comes from a nonzero connected four-point correlation
function --- or the trispectrum in Fourier space --- and can be large when
long-wavelength (super-CMB) modes are strongly coupled to short-wavelength
modes. The effect of such non-Gaussian covariance can be modeled through
additional freedom in the theoretical CMB angular power spectrum and can lead
to different inferred values of the standard cosmological parameters relative
to those in $Łambda$CDM. Taking the collapsed limit of the primordial
trispectrum in the quasi-single field inflation model as an example, we study
how the six standard $Łambda$CDM parameters shift when two additional
parameters describing the trispectrum are allowed. We find that the combination
of Planck temperature data along with type Ia supernovae from Panstarrs and the
distance-ladder measurement of the Hubble constant shows strong evidence for a
primordial trispectrum-induced non-Gaussian covariance, with a likelihood
improvement of $\Delta \chi^2 -15$ relative to $Łambda$CDM. The
improvement is driven by Planck data's preference for a higher lensing
amplitude, which leads to an upward shift of the Planck-inferred Hubble
constant.
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