The intrinsic bispectrum of the CMB from isocurvature initial conditions

Karim A. Malik; Pedro Carrilho

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The intrinsic bispectrum of the CMB from isocurvature initial conditions

Pedro Carrilho, Karim A. Malik

Cosmology and Nongalactic Astrophysics · Submitted 20 Apr 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim However, we find that a large compensated isocurvature mode can produce a detectable bispectrum when its correlation with the adiabatic mode is appreciable.

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Non-linear effects in the early Universe generate non-zero bispectra of the cosmic microwave background (CMB) temperature and polarization, even in the absence of primordial non-Gaussianity. In this paper, we compute the contributions from isocurvature modes to the CMB bispectra using a modified version of the second-order Boltzmann solver SONG. We investigate the ability of current and future CMB experiments to constrain these modes with observations of the bispectrum. Our results show that the enhancement due to single isocurvature modes mixed with the adiabatic mode is negligible for the parameter ranges currently allowed by the most recent Planck results. However, we find that a large compensated isocurvature mode can produce a detectable bispectrum when its correlation with the adiabatic mode is appreciable. The non-observation of this contribution in searches for the lensing bispectrum from Planck allows us to place a new constraint on the relative amplitude of the correlated part of the compensated isocurvature mode of $f_{\rm CIP}=1\pm100$. We compute forecasts for future observations by COrE, SO, CMB-S4 and an ideal experiment and conclude that a dedicated search for the bispectrum from compensated modes could rule out a number of scenarios realised in the curvaton model. In addition, the CMB-S4 experiment could detect the most extreme of those scenarios ($f_{\rm CIP}=16.5$) at 2 to 3-$\sigma$ significance.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Non-linear effects in the early Universe generate non-zero bispectra of the cosmic microwave background (CMB) temperature and polarization, even in the absence of primordial non-Gaussianity.	background 1.00	0.08	0.05	asserted 1.00
s1	In this paper, we compute the contributions from isocurvature modes to the CMB bispectra using a modified version of the second-order Boltzmann solver SONG.	method 0.72	0.95	0.03	asserted 0.97
s2	We investigate the ability of current and future CMB experiments to constrain these modes with observations of the bispectrum.	contribution 0.97	0.70	0.03	asserted 0.46
s3	Our results show that the enhancement due to single isocurvature modes mixed with the adiabatic mode is negligible for the parameter ranges currently allowed by the most recent Planck results.	result 1.00	0.86	0.24	asserted 1.00
s4	However, we find that a large compensated isocurvature mode can produce a detectable bispectrum when its correlation with the adiabatic mode is appreciable.	result 1.00	0.97	0.27	asserted 0.96
s5	The non-observation of this contribution in searches for the lensing bispectrum from Planck allows us to place a new constraint on the relative amplitude of the correlated part of the compensated isocurvature mode of $f_{\rm CIP}=1\pm100$.	result 0.95	0.87	0.22	asserted 0.99
s6	We compute forecasts for future observations by COrE, SO, CMB-S4 and an ideal experiment and conclude that a dedicated search for the bispectrum from compensated modes could rule out a number of scenarios realised in the curvaton model.	result 0.54	0.95	0.21	hedged possibility 0.79
s7	In addition, the CMB-S4 experiment could detect the most extreme of those scenarios ($f_{\rm CIP}=16.5$) at 2 to 3-$\sigma$ significance.	result 0.98	0.88	0.12	hedged possibility 1.00

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Original abstract

Non-linear effects in the early Universe generate non-zero bispectra of the cosmic microwave background (CMB) temperature and polarization, even in the absence of primordial non-Gaussianity. In this paper, we compute the contributions from isocurvature modes to the CMB bispectra using a modified version of the second-order Boltzmann solver SONG. We investigate the ability of current and future CMB experiments to constrain these modes with observations of the bispectrum. Our results show that the enhancement due to single isocurvature modes mixed with the adiabatic mode is negligible for the parameter ranges currently allowed by the most recent Planck results. However, we find that a large compensated isocurvature mode can produce a detectable bispectrum when its correlation with the adiabatic mode is appreciable. The non-observation of this contribution in searches for the lensing bispectrum from Planck allows us to place a new constraint on the relative amplitude of the correlated part of the compensated isocurvature mode of $f_{\rm CIP}=1\pm100$. We compute forecasts for future observations by COrE, SO, CMB-S4 and an ideal experiment and conclude that a dedicated search for the bispectrum from compensated modes could rule out a number of scenarios realised in the curvaton model. In addition, the CMB-S4 experiment could detect the most extreme of those scenarios ($f_{\rm CIP}=16.5$) at 2 to 3-$\sigma$ significance.

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What it cites · 82 sentences without a confident label

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This is detailed in Ref. [ref] , which includes all the approximate initial solutions in the tight coupling limit, which we use here.

Isocurvature initial conditions for second order Boltzmann solvers · Isocurvature modes · 0.87
We calculate the bispectrum of the CMB from sources at recombination using the second-order Boltzmann solver SONG [ref] .

The intrinsic bispectrum of the Cosmic Microwave Background · Introduction · 0.97
This is what is done in the Boltzmann solver SONG [ref] , which makes use of the linear solver CLASS [ref] to solve for the linear evolution.

The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview · Intrinsic bispectrum of the CMB · 1.00

Uses data or values from 5 papers

In certain versions of that model these isocurvatures can have amplitudes up to $f_CIP=16.5$ [ref] .

Compensated isocurvature perturbations in the curvaton model · Compensated isocurvature · 0.98
For Planck, the forecasted signal-to-noise was only $S/N≈0.5$, but future experiments with increased precision in polarization may detect this signal, as an ideal experiment is forecasted to get $S/N≈4$ for $ℓ_max=4000$ [ref] .

Impact of polarisation on the intrinsic CMB bispectrum · Results · 0.93
This is due to the known detection of the lensing contribution to the bispectrum, whose normalized amplitude has been measured to be $f^lens_NL=1.03±0.27$, taking into account both the temperature and polarization signals [ref] .

Planck 2018 results. IX. Constraints on primordial non-Gaussianity · Compensated isocurvature · 0.99

Compares with 2 papers

Even with an error of $O(2)$ due to the Gaussian covariance approximation, these results are already comparable with the forecasts using the power spectrum of Ref. [ref] , which found $σ_f_CIP≈22$ for Planck and $σ_f_CIP≈3$ for a cosmic variance limited (CVL) experiment.

Compensated isocurvature perturbations in the curvaton model · Compensated isocurvature · 0.99
Given that the squeezed configuration is dominant and the effects there are negligible, the addition of non-scalar modes only increases the signal-to-noise of the bispectrum by up to 3%, in line with what was found for the adiabatic case [ref] .

Impact of polarisation on the intrinsic CMB bispectrum · Single isocurvature · 0.89

Cites as background 20 papers

We now move to the case of the compensated isocurvature, often labelled CIP, for Compensated Isocurvature Perturbation [ref] .

Baryons still trace dark matter: probing CMB lensing maps for hidden isocurvature · Compensated isocurvature · 0.99
We now move to the case of the compensated isocurvature, often labelled CIP, for Compensated Isocurvature Perturbation [ref] .

Forecasted 21 cm constraints on compensated isocurvature perturbations · Compensated isocurvature · 0.99
We now move to the case of the compensated isocurvature, often labelled CIP, for Compensated Isocurvature Perturbation [ref] .

Do baryons trace dark matter in the early universe? · Compensated isocurvature · 0.99

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