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Gravitational Time Delay Effects on CMB Anisotropies
Astrophysics · Submitted 31 Jul 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim While unlikely to be extracted from the data in its own right, its omission in modeling would produce a systematic error comparable to this limiting statistical error and, in principle, is relevant for future high precision experiments.
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The abstract, sentence by sentence
We study the effect of gravitational time delay on the power spectra and bispectra of the cosmic microwave background (CMB) temperature and polarization anisotropies. The time delay effect modulates the spatial surface at recombination on which temperature anisotropies are observed, typically by ~1 Mpc. While this is a relatively large shift, its observable effects in the temperature and polarization fields are suppressed by geometric considerations. The leading order effect is from its correlation with the closely related gravitational lensing effect. The change to the temperature-polarization cross power spectrum is of order 0.1% and is hence comparable to the cosmic variance for the power in the multipoles around l~1000. While unlikely to be extracted from the data in its own right, its omission in modeling would produce a systematic error comparable to this limiting statistical error and, in principle, is relevant for future high precision experiments. Contributions to the bispectra result mainly from correlations with the Sachs-Wolfe effect and may safely be neglected in a low density universe.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the effect of gravitational time delay on the power spectra and bispectra of the cosmic microwave background (CMB) temperature and polarization anisotropies. | contribution 1.00 | 0.89 | 0.07 | asserted 0.67 |
| s1 | The time delay effect modulates the spatial surface at recombination on which temperature anisotropies are observed, typically by ~1 Mpc. | result 0.80 | 0.40 | 0.06 | asserted 0.97 |
| s2 | While this is a relatively large shift, its observable effects in the temperature and polarization fields are suppressed by geometric considerations. | interpretation 0.50 | 0.56 | 0.11 | asserted 1.00 |
| s3 | The leading order effect is from its correlation with the closely related gravitational lensing effect. | result 0.78 | 0.63 | 0.19 | asserted 1.00 |
| s4 | The change to the temperature-polarization cross power spectrum is of order 0.1% and is hence comparable to the cosmic variance for the power in the multipoles around l~1000. | result 0.97 | 0.82 | 0.18 | asserted 1.00 |
| s5 | While unlikely to be extracted from the data in its own right, its omission in modeling would produce a systematic error comparable to this limiting statistical error and, in principle, is relevant for future high precision experiments. | interpretation 0.96 | 0.65 | 0.34 | hedged possibility 0.71 |
| s6 | Contributions to the bispectra result mainly from correlations with the Sachs-Wolfe effect and may safely be neglected in a low density universe. | result 0.82 | 0.70 | 0.07 | hedged possibility 0.89 |
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The paper
Original abstract
We study the effect of gravitational time delay on the power spectra and bispectra of the cosmic microwave background (CMB) temperature and polarization anisotropies. The time delay effect modulates the spatial surface at recombination on which temperature anisotropies are observed, typically by ~1 Mpc. While this is a relatively large shift, its observable effects in the temperature and polarization fields are suppressed by geometric considerations. The leading order effect is from its correlation with the closely related gravitational lensing effect. The change to the temperature-polarization cross power spectrum is of order 0.1% and is hence comparable to the cosmic variance for the power in the multipoles around l~1000. While unlikely to be extracted from the data in its own right, its omission in modeling would produce a systematic error comparable to this limiting statistical error and, in principle, is relevant for future high precision experiments. Contributions to the bispectra result mainly from correlations with the Sachs-Wolfe effect and may safely be neglected in a low density universe.
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References
How the literature uses it
13 arXiv papers cite this in 26 sentences
Papers citing it · 21 sentences without a confident label
Builds on it 1 paper
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Expanding the polarization source tensor at the perturbed location $_ab([χ_*+δχ]',η_*)$ to linear order in $δχ$, the time delay gives the second-order correction to the observed polarization [equation] where $δχ/χ_* = ψ_d$ and we defined the polarization derivative potential[The source for $ψ_t$ is $χ_*/4k^2χ^2/η(g ζ)$ where $g$ is the visibility prior to reionization and the sign is using 's convention.] $ψ_t = χ_∗ψ_E / χ_∗$: [equation] The time-delay contribution to the second-order B-mode polarization is then [equation] The time-delay auto-spectrum together with the cross-correlation with the lensing and emission-angle terms gives an additional contribution to the power spectrum [equation] The first and last term have been calculated before in Ref. [ref] , but the middle term is the new contribution from the correlation with the emission-angle term.
Emission-angle and polarization-rotation effects in the lensed CMB · Total correction to the lensed B modes · 0.83
Compares with it 2 papers
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([ref]) and compare our results with the previous works [ref] .
Unified approach to secondary effects on the CMB B-mode polarization · Numerical calculation · 1.00
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The longitudinal displacement effect (time delay) is clearly much smaller than the perpendicular one, as found earlier in [ref] .
Universal Weak Lensing Distortion of Cosmological Correlation Functions · General Formalism · 0.80
Cites it as background 2 papers
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Finally, we note that we have neglected contributions from tensor modes, large scale structure vorticity, non-lensing GR effects and second order vectors sourced by scalars [ref] .
Impact of post-Born lensing on the CMB · Lensing power spectra · 0.97
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[ref] and the description in ref.
Unified approach to secondary effects on the CMB B-mode polarization · Basic idea: Liouville's theorem in curved spacetime · 0.97
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