The cosmic microwave background bispectrum as a test of the physics of inflation and probe of the astrophysics of the low-redshift universe

TL;DR

This paper investigates the CMB bispectrum as a probe of inflationary non-Gaussianity and low-redshift astrophysics. It derives the reduced angular bispectrum $b_{l_1l_2l_3}$ with the full transfer function and shows that, for single-field slow-roll inflation, the primary bispectrum is too weak to detect, while secondary low-redshift bispectra are detectable. A Fisher-matrix framework is developed to separate primary and secondary contributions, revealing that Planck and MAP can detect secondary bispectra and place weak constraints on $f_{NL}$ from COBE data, while a large $f_{NL}$ would challenge simple inflationary models. Overall, the study positions the CMB bispectrum as a crucial observable for testing non-linear inflationary physics and for probing non-linear low-redshift processes.

Abstract

Why is non-Gaussianity interesting? One of generic predictions from inflationary scenarios is that primordial fluctuations are exactly Gaussian in linear order; however, the non-linearity in the inflation will produce weak non-Gaussianity. Thus, measuring the non-Gaussianity in the cosmic microwave background radiation anisotropy is a probe of the non-linear physics in the very early universe. Since the angular three point function is zero for the Gaussian field, it is sensitive to the non-Gaussianity. We predict its harmonic transform counterpart, the angular {\it Bispectrum}, down to arcminutes angular scales, including the full effect of the radiation transfer function. We find that even the Planck experiment cannot detect the primary bispectrum from the inflation, as long as the single field slow-roll inflation is right. Non-linearities in the low redshift universe also produce the non-Gaussianity. We find that secondary bispectra are detectable by both MAP and Planck experiments. The secondary bispectra probe the non-linear physics of the low-redshift universe. Although this could be a contaminant to the primary signal, MAP and Planck experiments are found to be able to separate the primary from secondary effects well. We present a tentative comparison of the primary bispectrum to the published COBE 4 year bispectrum. The data put a weak constraint on the parameter, and the constraint would become much tighter when we use all modes available in the COBE data, and certainly forthcoming satellite experiments. As a conclusion, the bispectrum is a key measure to confirm or destroy the simple inflationary scenario in non-linear order that seems quite successful in linear order.

Figures (2)

• Figure 1: The equilateral configuration of the reduced bispectra, $\left[l^2(l+1)^2b_{lll}/(2\pi)^2\right]\times 10^{16}$. The weight is motivated by the behavior of the primary component, $b_{lll}^{primary}\propto l^{-4}$. Solid line shows the primary bispectrum from inflation with $f_{NL}=100$ (see eq.(\ref{['eq:Phi']})). Dashed line shows the Sunyaev-Zel'dovich effect and weak lensing coupling in the Rayleigh--Jeans limit, while dotted line shows the extragalactic radio and infrared point sources.
• Figure 2: The comparison of theoretical primary bispectrum to the COBE 4 year data, $J_l^3$ (Eq.(\ref{['eq:Jl3']})), defined by Magueijo (2000). Filled circles are measured $J_l^3$, while thick solid, dashed, and dotted lines correspond to the primary bispectrum with $f_{NL}=2\times 10^4$, $10^4$, and $5\times 10^3$, respectively. Error bars are rms scatters from the Gaussian Monte Carlo realizations. Note that the beam-smearing effect has been taken into account. The thin solid line shows the un-smoothed case for $f_{NL}=2\times 10^4$.