The Sachs-Wolfe Effect

Martin White; Wayne Hu

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The Sachs-Wolfe Effect

Martin White, Wayne Hu

Astrophysics · Submitted 16 Sep 1996

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

The authors' main claim The result arises from a cancellation between gravitational redshifts and intrinsic temperature fluctuations which can be derived from a coordinate transformation of the background.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.95 · compares with prior results 0.07 · mentions code or data availability 0.02.

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We present a pedagogical derivation of the Sachs-Wolfe effect, specifically the factor 1/3 relating the temperature fluctuations to gravitational potentials. The result arises from a cancellation between gravitational redshifts and intrinsic temperature fluctuations which can be derived from a coordinate transformation of the background.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a pedagogical derivation of the Sachs-Wolfe effect, specifically the factor 1/3 relating the temperature fluctuations to gravitational potentials.	contribution 1.00	0.94	0.53	asserted 0.99
s1	The result arises from a cancellation between gravitational redshifts and intrinsic temperature fluctuations which can be derived from a coordinate transformation of the background.	interpretation 0.67	0.53	0.38	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We present a pedagogical derivation of the Sachs-Wolfe effect, specifically the factor 1/3 relating the temperature fluctuations to gravitational potentials. The result arises from a cancellation between gravitational redshifts and intrinsic temperature fluctuations which can be derived from a coordinate transformation of the background.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Statistics of Cosmic Microwave Background Polarization
astro-ph 1996-11 accept novelty 7.0 of 10

Polarization of the cosmic microwave background decomposes on the full sky into gradient and curl components, and the curl component is identically zero for scalar density perturbations, giving a clean probe of gravit...
Large Density Perturbations from Reheating to Standard Model particles due to the Dynamics of the Higgs Boson during Inflation
hep-ph 2020-09 conditional novelty 6.0 of 10

A spectator Higgs field with quantum fluctuations imprints Hubble-patch-dependent masses on inflaton decay products, generating curvature perturbations that exceed CMB bounds for most couplings to heavy SM states.
Towards a measurement of the spectral runnings
astro-ph.CO 2016-11 conditional novelty 4.0 of 10

Fisher forecasts give a Stage-4 CMB experiment sigma(alpha_s) = 0.0025 and sigma(beta_s) = 0.0045, enough to test primordial-black-hole scenarios but not the slow-roll predictions of 10^-3 and 10^-5.

How the literature uses it

12 arXiv papers cite this in 16 sentences

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Papers citing it · 11 sentences without a confident label

Contests it 1 paper

If we consider large scales, dominated by the Sachs-Wolfe effect [ref] , a local approximation exists in which the response and the noise covariance are diagonal in position space [ref] [Note that in Ref. [ref] , the response is falsely assumed to be $R=-3$.

Fast and precise way to calculate the posterior for the local non-Gaussianity parameter $f_\text{nl}$ from cosmic microwave background observations · Approximation of the $f_nl$ posterior · contest 0.85

Uses its method or tool 1 paper

This subsection closely follows Ref. [ref] , in which the SW effect is derived by moving from the comoving gauge to the conformal Newtonian gauge.

Deformation of the gravitational wave spectrum by density perturbations · Step 1: GW spectrum at the sourcing time · 0.96

Cites it as background 2 papers

We then take the derivative of continuitytheta, and we end up with [equation] whose solution is [equation] with [equation] the Sachs Wolfe term [ref] .

Probing new physics in the era of precision cosmology · Gravitational forces · 0.80
For adiabatic fluctuations in a matter-dominated universe, the temperature fluctuations generated by the Sachs-Wolfe effect are [equation] where the factor of $-1/3$ comes from gravitational redshifting as photons exit the potential (contributing $-Φ$) and clocks running slow within the gravitational potential (contributing $2Φ/3$) [ref] .

The Integrated Sachs Wolfe effect: unWISE and Planck constraints on Dynamical Dark Energy · Introduction · 0.96

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