Measurements of primordial non-Gaussianity (fNL) open a new window onto the physics of inflation. We describe a fast cubic (bispectrum) estimator of fNL, using a combined analysis of temperature and polarization observations. The speed of our estimator allows us to use a sufficient number of Monte Carlo simulations to characterize its statistical properties in the presence of real world issues ...

The bispectrum is the lowest-order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the evolution of the bispectrum is well understood theoretically from non-linear perturbation theory and numerical simulations, applications to galaxy surveys requir...

We measure the angular bispectrum of the cosmic microwave background (CMB) radiation anisotropy from the COBE Differential Microwave Radiometer (DMR) fouryear sky maps. The angular bispectrum is the harmonic transform of the three-point correlation function, analogous to the angular power spectrum, the harmonic transform of the two-point correlation function. First, we study statistical propert...

This paper derives completeness properties of the bispectrum for compact groups and their homogeneous spaces. The bispectrum is the Fourier transform of the triple correlation, just as the magnitude-squared spectrum is the Fourier transform of the autocorrelation. The bispectrum has been applied in time series analysis to measure non-Gaussianity and non-linearity. It has also been applied to pr...

We present a Fisher information study of the statistical impact galaxy bias and selection effects on estimation key cosmological parameters from redshift surveys; in particular, angular diameter distance, Hubble parameter, linear growth rate at given redshift, cold dark matter density, tilt running primordial power spectrum. The line-of-sight-dependent contributions we include here are known to...

We present a determination of the bispectrum of the flux in the Lyman-α forest of QSO absorption spectra obtained from LUQAS which consists of spectra observed with the high resolution Echelle spectrograph UVES. Typical errors on the observed bispectrum as obtained from a jack-knife estimator are ∼ 50 %. For wavenumbers in the range 0.03 s/km < k < 0.1 s/km the observed bis-pectrum agrees withi...

Bispectral and trispectral analyses are used to detect secondary and tertiary wave components resulting from nonlinear interactions among largeamplitude ocean surface gravity waves in 8and 13-m water depths. Bispectra of bottom-pressure measurements indicate forced secondary waves at frequencies 2fp about twice the primary power spectral peak frequency fp. However, the interpretation of the bis...

The cosmic microwave background (CMB) bispectrum of the temperature anisotropies induced by a network of cosmic strings is derived for small angular scales, under the assumption that the principal cause of temperature fluctuations is the Gott-Kaiser-Stebbins effect. We provide analytical expressions for all isosceles triangle configurations in Fourier space. Their overall amplitude is amplified...

We present the first application of isosceles bispectrum to MCMC parameter inference from cosmic 21-cm signal. extend sampler 21cmMC use fast code, BiFFT, when computing likelihood. create mock 1000h observations with SKA1-low, using PyObs21 account for uv-sampling and thermal noise. Assuming spin temperature is much higher than that CMB, we consider two different reionization histories our obs...