Cosmological-Parameter Determination with Microwave Background Maps

Arthur Kosowsky (Harvard); David N. Spergel (Princeton); Gerard Jungman (Syracuse); Marc Kamionkowski (Columbia)

REVIEW

Cosmological-Parameter Determination with Microwave Background Maps

Gerard Jungman (Syracuse), Marc Kamionkowski (Columbia), Arthur Kosowsky (Harvard), David N. Spergel (Princeton)

Astrophysics · Submitted 20 Dec 1995 · 52 references

Pith's verdict: The paper that turned CMB parameter forecasting into a quantitative business: eleven parameters, full correlations, and headline numbers that mostly survived contact with real data.

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arXiv IDastro-ph/9512139 (version 2)

Pith IDGYRJDFFA, Pith's permanent record of this paper and its review

CitationArthur Kosowsky (Harvard), David N. Spergel (Princeton), Gerard Jungman (Syracuse), Marc Kamionkowski (Columbia). "Cosmological-Parameter Determination with Microwave Background Maps." arXiv:astro-ph/9512139 (1995). https://pith.science/paper/GYRJDFFA

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Editor's note

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Worth your time, and worth citing. This is the paper that made CMB parameter forecasting quantitative rather than hand-wavy. The Fisher machinery is textbook, but the execution is the contribution: eleven parameters varied simultaneously with full correlations, and a semi-analytic spectrum code extended to open geometry, Λ, tensors, and reionization so the derivatives are cheap enough to actually take. The comparison to Knox in Fig. 5 is the part I'd point students to — it shows explicitly that fixed-parameter forecasts overstate what an experiment can do, by a lot, for r and nT. That was a useful corrective at the time and it still is. The Ω and Λ numbers were broadly borne out later, which is the strongest thing you can say about a forecast paper from 1995. Note also that the classifier record claims no stated limitations; that's wrong. §II excludes secondary and non-linear effects, §VI concedes the Gaussian check is one-dimensional, §VII says the code isn't yet as accurate as full numerics outside a limited region. They're upfront about it. On the stress-test concern: it lands, but softly. The finite-difference derivatives are taken from a code benchmarked at standard CDM, so C_ℓ(s_0) is validated and ∂C_ℓ/∂s_i is not, and for Λ the signature really is a small correction built from fitting formulas (Eqs. 14–19) rather than a first-principles calculation. A sloppy Λ derivative would move ±0.1 to maybe ±0.12. That's a fair referee question and worth a paragraph in review, not a reason to discount the paper. The Ω result rests on Doppler-peak position, which is a large, well-resolved effect, and footnote 3 already says that number is conservative. The Gaussianity worry is the same shape: checked along eigenvectors and against Knox's Monte Carlo, not surveyed in eleven dimensions, and they say so. No shipped code, which is normal for the period but means anyone reproducing this rebuilds the solver from the cited fitting functions. Who should read it: anyone doing CMB forecasting, and anyone who wants a clean worked example of why marginalizing over nuisance parameters matters. Send it out for review.

Referee report

Significance

If the forecast holds, this is a high-value paper: it converts a qualitative statement ('CMB maps constrain cosmology') into a quantitative experimental-design tool, and it does so with a method that is cheap enough to scan noise levels, beam widths, and sky fractions without Monte Carlo resampling. Several things deserve explicit credit. The semi-analytic spectrum code is benchmarked against an independent Boltzmann calculation (§II) and released in description sufficient for others to reproduce the approach. The covariance-matrix framework generalizes earlier single-parameter sensitivity studies (Refs. [33], [37]) by keeping all cross-parameter correlations, and the authors are explicit that ignoring those correlations would overstate experimental capability — a point they make against their own earlier-generation results. The paper is also candid about what it does not model: post-recombination non-linear effects (§II), the reionization Doppler peak (Eq. 19 and following), and the incomplete survey of the eleven-dimensional likelihood (§VI). Finally, the Ω result is a falsifiable prediction — a Doppler peak at ℓ ≈ 200 implies Ω = 1 to a few percent — which is exactly the kind of

Major objections (4)

[§V.A and Eqs. (14)–(19)] The ±0.1 forecast for Λ rests almost entirely on the authors' own fitting formulas rather than on a benchmarked spectrum: the ISW multiplier g(Λ) (Eqs. 14–16), the conformal-distance rescaling 1 + 0.085 ln(1−Λ), and the open-Universe fits (Eqs. 17–18) are all ad hoc parameterizations with no stated accuracy. Because the Λ signature is a small correction on top of the standard-CDM spectrum, the derivative ∂C_ℓ/∂Λ entering Eq. (22) is a small difference of two nearly equal spectra, and a modest fractional error in that derivative propagates directly into σ(Λ). The benchmark quoted in §II ('a few percent for standard CDM') validates C_ℓ(s_0) at the expansion point, not the finite-difference neighborhood in the Λ direction. The general code-accuracy caveat in §VII does not cover this specific case. Please either benchmark the Λ fits against a Boltzmann code at Λ ≠ 0 and state the residual, or attach an explicit accuracy qualifier to the Λ number in §V.A and in abstract:s3, so that readers do not take ±0.1 as a hard forecast when the underlying response function is uncertain at the tens-of-percent level.
[§VI and Fig. 6] The validity of inverting Eq. (22) requires that the joint likelihood be approximately parabolic in all eleven parameters, and the paper says so. Fig. 6, however, shows one-dimensional slices only, and §VI states plainly that no survey of the eleven-dimensional contour was performed. The stronger claim in §VI — that there will be 'no degeneracy between various cosmological models with a CMB map (in contrast to the conclusions of Ref. [31])' — is not supported by one-dimensional slices, since a curved degeneracy between, e.g., Ω and Λ, or between Ω_b h² and h, would be invisible in Fig. 6 while still inflating the marginalized errors. The authors mention an eigenvector examination of the covariance matrix; that is the right diagnostic, and it should be shown (eigenvalues or condition number, and the parameter composition of the weakest eigenvector) rather than summarized. A two-dimensional likelihood map in the most correlated pair would settle the point. The paper acknowledges the gap, so this is a request to close it, not a charge of error.
[§IV, Eq. (20) and the f_sky scaling rule] The text gives two different prescriptions for extending the results to a partial-sky map, and they disagree in the noise-dominated regime. Eq. (20) carries an explicit f_sky^{-1/2} prefactor, and the surrounding text adds that if only a fraction f_sky is mapped, the integration time per pixel rises and w^{-1} should be replaced by w^{-1} f_sky. But §V and the figure captions then state that results for f_sky < 1 'can be obtained by scaling by f_sky^{-1/2}' alone. Applying only the prefactor while holding w^{-1} fixed overestimates the noise term by a factor f_sky^{-1} relative to the stated replacement rule, so the two instructions are not equivalent whenever the noise term is comparable to C_ℓ. Since the paper offers this scaling as a service to ground-based and balloon experimenters, please state unambiguously which convention the plotted w^{-1} values refer to (per-pixel noise achieved on the mapped region, or noise referred to the full sky) and give the corrected scaling rule.
[abstract:s3 and Fig. 3] The headline example — 0.5° resolution with 15 µK per pixel — corresponds to w^{-1} ≈ 2 × 10^{-15}, the most optimistic of the three noise levels plotted, while §IV states that foregrounds and systematics make the conservative expectation w^{-1} ≈ (0.9–4) × 10^{-14}. The abstract should say that the quoted ±0.1 is the low-noise end of the range the paper itself considers, and that at the conservative noise level the errors on h and Ω_b h² are visibly larger in Fig. 3. Relatedly, the abstract groups Ω, h, and Λ under a single '±0.1 or better', but at the adopted fiducial h = 0.5 a ±0.1 error is a 20% determination, which §V.B itself describes as merely 'competitive' with the existing distance ladder rather than transformative. The three numbers are not of equal weight and the abstract should not present them as though they were.

Minor objections (10)

[Abstract] The phrase 'the the underlying cosmological model' contains a duplicated word.
[Fig. 5 caption] The caption reads 'the standard=CDM values'; the equals sign should be a hyphen.
[Fig. 1 caption] The caption lists 'τ_reion = 0' among the parameters whose effects are shown, but no τ_reion curve appears in the figure; either add the curve or remove τ_reion from the list of varied quantities.
[Eq. (22)] The sum over ℓ does not state the multipole range used. Please give ℓ_min and the ℓ_max at which the sum is truncated for each beam width, since the truncation choice affects the quoted errors and is needed for reproducibility.
[§II, Eqs. (11)–(12)] The tensor transfer function and mode-function fits are attributed to Ref. [15], which is listed as a preprint, with a companion Wang and Knox analysis 'in preparation'. The stated one-percent accuracy of these fits therefore rests on unpublished work. Since the tensor sector drives the r and n_T entries of Fig. 5, please state the provenance of the accuracy claim or verify the fits against a published numerical spectrum.
[§II] The spectrum is evaluated every 40th multipole and splined. For the Fisher sum in Eq. (22), which is quadratic in derivatives, it would help to state whether the spline was checked against direct evaluation near the Doppler peaks, where the curvature of C_ℓ is largest.
[§IV] The beam window is written as σ_b = 7.42 × 10^{-3} (θ_fwhm/1°); please state explicitly that σ_b is in radians and that θ_fwhm in this expression is in degrees, since the same symbol appears with different units in the definition of w^{-1}.
[Eqs. (16) and (18)] Both fitting formulas diverge as Λ → 1 and as Ω → 0 respectively. The text gives a validated range for Eq. (16) but not for Eq. (18); please state the range over which Eq. (18) was checked.
[§V.E and Fig. 5] Fig. 5 uses a different fiducial model (r = 0.28, n_S = 0.94, n_T = −0.04) from Figs. 3 and 4, which is appropriate for the tensor parameters but means the Q curve in Fig. 5 is not directly comparable to the normalization discussion elsewhere. A sentence flagging this would prevent confusion.
[§V.F] The statement that a non-zero Λ, small h, or large Ω_b h² increases the signal-to-noise and therefore tightens the forecast is plausible but is not backed by a figure. A single additional curve, or a pointer to the relevant panel of Fig. 3, would make the claim checkable.

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The paper

The paper claims

A full-sky microwave background map with half-degree resolution can, in principle, measure the Universe's total density, its expansion rate, and its cosmological constant to about ±0.1 each, with no prior information about any other cosmic-

The reading

The paper asks a design question: if a satellite maps the microwave background across the whole sky at half-degree resolution with low noise, how precisely can the resulting angular power spectrum pin down the numbers that describe the Universe? The authors answer by building a fast approximate calculator for the predicted spectrum and then asking how sensitively that spectrum shifts when each of eleven parameters is nudged. The advertised payoff is large: the geometry of the Universe, the Hubble constant, and the cosmological constant would each come out to roughly ±0.1 or better from temperature data alone, with no help from distance ladders, cluster mass inventories, or any other traditional probe. The paper is written as a guide for experiment design, showing how the achievable errors scale with beam size, pixel noise, and the fraction of sky covered, and how much better things get when some parameters are already known.

What carries the argument

The machinery is a curvature-matrix (Fisher-matrix) forecast. Each parameter's partial derivative of the predicted multipole moments, $��C_��/��s_i$, is computed by evaluating the spectrum at the fiducial model and at one small step in each direction, so eleven parameters cost twelve spectrum evaluations. These derivatives are combined with the per-multipole error bars, which add cosmic variance to beam-diluted pixel noise, into $��_{ij} = ��_�� _��^{-2} (��C_��/��s_i)(��C_��/��s_j)$, and the inverse of that matrix is read as the covariance of the fitted parameters. Fixing some parameters is just inverting a submatrix; covering a fraction $f_{sky}$ of the sky scales the whole thing by $f_{sky}^{-1}$. The fast spectrum itself comes from extending a semi-analytic solution of the coupled Boltzmann, fluid, and Einstein equations to include an open Universe, a cosmological constant, tensor modes, and reionization, with fitting formulas for the integrated Sachs-Wolfe effect, the shift in conformal distance, curvature-scale suppression at low multipoles, and damping from reionization.

Extended reading notes

Core claim

The central claim is that a full-sky microwave background temperature map with $0.5^��$ angular resolution and a noise level of 15 $��$K per pixel can determine $��$, $h$, and $��$ with standard errors of $��0.1$ or better, even with no prior information on any of the other cosmological parameters. The physical carrier of this claim is the Doppler-peak structure of the angular power spectrum: the angular scale of the first peak tracks the geometry of the Universe, the peak heights and spacings respond to the baryon density and the redshift of matter-radiation equality, and the late-time integrated Sachs-Wolfe effect plus the shift in conformal distance break the near-degeneracy that otherwise lets a cosmological constant masquerade as a change in matter density. The authors also report that with sub-degree resolution a map can constrain the baryon density competitively with big-bang nucleosynthesis, restrict the optical depth to reionization to about 0.5 or less, and put limits on the effective number of light neutrino species. They are explicit that the inflationary observables fare badly unless other parameters are known: the tensor amplitude $r$ and tensor index $n_T$ get essentially no useful constraint from temperature maps alone, because the tensor contribution dies away on scales smaller than about a degree.

Load-bearing premise

The quoted error bars are the inverse of a curvature matrix, which is only a standard error if the likelihood is close to a parabola in all eleven parameters at once; the paper checks this only along one parameter at a time and says plainly that it has not surveyed the full eleven-dimensional contours.

Editorial extensions

If this is right

If the first Doppler peak is found near $�� \simeq 200$, the geometry of the Universe is flat to within a few percent, independent of the values of the other cosmological parameters — a direct test of the inflationary prediction.
A cosmological constant could be measured to better than $��0.1$, which separates a $��$-dominated Universe from either an open or a flat matter-dominated one, a distinction current lensing statistics cannot make.
With resolution approaching $0.1^��$, the baryon-to-photon ratio could be pinned down competitively with big-bang nucleosynthesis, giving an independent check on the baryon content implied by primordial element abundances.
The Hubble constant would be measured without any distance ladder, from the same map that measures the geometry.
Because the errors scale as $f_{sky}^{-1/2}$, the same forecast can be applied to combinations of balloon, ground-based, and satellite maps rather than only to a single all-sky survey.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The forecast is a statement about information content, not about data: the same machinery predicts that a poor map is worse than its noise level suggests, because the parameters trade against each other along directions in the eleven-dimensional space that a single-parameter error bar conceals.
Because the cosmological-constant and curvature effects push the Doppler peak in opposite angular directions, the paper's logic implies that a measured peak position alone cannot settle the geometry; the peak height and the low-multipole Sachs-Wolfe plateau must be measured together, which is a concrete argument for wide frequency coverage and large sky area rather than deep small fields.
The explicit finding that tensor modes are unconstrained without independent knowledge of the other parameters suggests that the natural next step is polarization: the same acoustic information carried in polarization spectra is sensitive to reionization and to gravity waves in a way the temperature spectrum is not.
The paper's own machinery implies a design trade: below about $0.5^��$ beam size the gains come mostly from better determination of the classical parameters, while the tensor information saturates, so a smaller beam buys geometry and baryon density but not a probe of the inflaton potential.

Original abstract

The angular power spectrum of the cosmic microwave background (CMB) contains information on virtually all cosmological parameters of interest, including the geometry of the Universe ($\Omega$), the baryon density, the Hubble constant ($h$), the cosmological constant ($\Lambda$), the number of light neutrinos, the ionization history, and the amplitudes and spectral indices of the primordial scalar and tensor perturbation spectra. We review the imprint of each parameter on the CMB. Assuming only that the primordial perturbations were adiabatic, we use a covariance-matrix approach to estimate the precision with which these parameters can be determined by a CMB temperature map as a function of the fraction of sky mapped, the level of pixel noise, and the angular resolution. For example, with no prior information about any of the cosmological parameters, a full-sky CMB map with $0.5^\circ$ angular resolution and a noise level of 15 $\mu$K per pixel can determine $\Omega$, $h$, and $\Lambda$ with standard errors of $\pm0.1$ or better, and provide determinations of other parameters which are inaccessible with traditional observations. Smaller beam sizes or prior information on some of the other parameters from other observations improves the sensitivity. The dependence on the the underlying cosmological model is discussed.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,159 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.38 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The angular power spectrum of the cosmic microwave background (CMB) contains information on virtually all cosmological parameters of interest, including the geometry of the Universe ($\Omega$), the baryon density, the Hubble constant ($h$), the cosmological constant ($\Lambda$), the number of light neutrinos, the ionization history, and the amplitudes and spectral indices of the primordial scalar and tensor perturbation spectra. We review the imprint of each parameter on the CMB. Assuming only that the primordial perturbations were adiabatic, we use a covariance-matrix approach to estimate the precision with which these parameters can be determined by a CMB temperature map as a function of the fraction of sky mapped, the level of pixel noise, and the angular resolution. For example, with no prior information about any of the cosmological parameters, a full-sky CMB map with $0.5^\circ$ angular resolution and a noise level of 15 $\mu$K per pixel can determine $\Omega$, $h$, and $\Lambda$ with standard errors of $\pm0.1$ or better, and provide determinations of other parameters which are inaccessible with traditional observations. Smaller beam sizes or prior information on some of the other parameters from other observations improves the sensitivity. The dependence on the the underlying cosmological model is discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The angular power spectrum of the cosmic microwave background (CMB) contains information on virtually all cosmological parameters of interest, including the geometry of the Universe ($\Omega$), the baryon density, the Hubble constant ($h$), the cosmological constant ($\Lambda$), the number of light neutrinos, the ionization history, and the amplitudes and spectral indices of the primordial scalar and tensor perturbation spectra.	background 1.00	0.06	0.07	asserted 0.98
s1	We review the imprint of each parameter on the CMB.	contribution 0.93	0.66	0.03	asserted 0.61
s2	Assuming only that the primordial perturbations were adiabatic, we use a covariance-matrix approach to estimate the precision with which these parameters can be determined by a CMB temperature map as a function of the fraction of sky mapped, the level of pixel noise, and the angular resolution.	method 0.94	0.89	0.12	asserted 0.93
s3	For example, with no prior information about any of the cosmological parameters, a full-sky CMB map with $0.5^\circ$ angular resolution and a noise level of 15 $\mu$K per pixel can determine $\Omega$, $h$, and $\Lambda$ with standard errors of $\pm0.1$ or better, and provide determinations of other parameters which are inaccessible with traditional observations.	result 1.00	0.78	0.61	asserted 0.80
s4	Smaller beam sizes or prior information on some of the other parameters from other observations improves the sensitivity.	result 0.69	0.43	0.06	asserted 0.96
s5	The dependence on the the underlying cosmological model is discussed.	contribution 0.77	0.59	0.03	unclear 0.62

What kind of paper the classifier reports this is: review 0.73 · evidence from simulation or computation 0.66.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. Predicted multipole moments for standard CDM and var

**Figure 2.** FIG. 2. Simulated data that might be obtained with a CMB mappi

**Figure 3.** FIG. 3. The standard errors for Ω, Λ, Ω

**Figure 4.** FIG. 4. Like Fig. 3, but for

**Figure 5.** FIG. 5. The standard errors on the inflationary observables,

**Figure 6.** FIG. 6. Plots of the log-likelihood as a function of Ω, Λ, Ω

Figures reproduced from arXiv:astro-ph/9512139 by the authors.

References

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View on Pith 1994

Forward citations

Cited by 21 Pith papers

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

The Rise and Fall of Acoustic Oscillations at Cosmic Dawn
astro-ph.CO 2026-07 conditional novelty 7.0 of 10

Ignoring the percent-level phase offset between BAO and VAO features in the cosmic-dawn 21-cm power spectrum biases H(z) by ~2%; joint BAO–VAO templates are required for standard-ruler inference.
Structure Formation with Generalized Dark Matter
astro-ph 1998-01 conditional novelty 7.0 of 10

A three-parameter, gauge-invariant description of dark matter stresses reproduces cold dark matter, radiation, massive neutrinos, and scalar fields as limiting cases, and lets the clustering scale be varied independen...
Expanding Ejecta Method: II. Framework for Cosmological Distance Measurements via Intensity Interferometry
astro-ph.CO 2025-05 conditional novelty 6.0 of 10

Geometric supernova distances from intensity interferometry could calibrate the distance ladder and measure H0 to between 0.4% and 9% depending on instrument capability and application, all without luminosity calibration.
Gravitational waves, CMB polarization, and the Hubble tension
astro-ph.CO 2019-08 conditional novelty 6.0 of 10

The B-mode recombination peak, tied to the light horizon at last scattering, can act as an independent early-universe standard ruler, measurable to about 2% with stage-IV CMB experiments.
Heating of Baryons due to Scattering with Dark Matter During the Dark Ages
astro-ph.CO 2015-08 accept novelty 6.0 of 10

Relative drift between dark matter and baryons turns kinetic energy into heat, so velocity-dependent dark-matter-baryon scattering warms the gas during the dark ages and leaves a detectable imprint on the 21-cm signal.

Show 16 more citing papers

Phases of New Physics in the CMB
astro-ph.CO 2015-08 accept novelty 6.0 of 10

Planck 2015 temperature and polarization data separate free-streaming from non-free-streaming dark radiation, giving Neff = 2.80 +/- 0.24 and Nfluid < 0.67 at 2 sigma, with the separation driven by a phase shift in th...
Searching for Dark Matter in the CMB: A Compact Parameterization of Energy Injection from New Physics
astro-ph.CO 2011-09 accept novelty 6.0 of 10

A principal-component decomposition reduces arbitrary dark-matter energy deposition during recombination to a handful of measurable coefficients, and shows conventional WIMP annihilation is captured by one universal r...
Cross-Correlation of Cosmological Birefringence with CMB Temperature
astro-ph.CO 2011-04 conditional novelty 6.0 of 10

A quintessence field that rotates photon polarization leaves a cross-correlation with CMB temperature that a massless spectator field does not, and the authors derive the estimator for it and forecast its detectability.
Cosmic Microwave Background Statistics for a Direction-Dependent Primordial Power Spectrum
astro-ph 2007-09 conditional novelty 6.0 of 10

A minimum-variance estimator for a direction-dependent primordial power spectrum shows that Planck could detect a 2% quadrupole anisotropy.
Searching for primordial features with radio surveys: synergy between the power spectrum and bispectrum
astro-ph.CO 2026-06 unverdicted novelty 5.0 of 10

Joint power spectrum and bispectrum analysis from future HI intensity mapping surveys improves constraints on primordial feature amplitudes by 30-40% and achieves percent-level precision on oscillation frequencies whe...
The Black Hole Mass Function from Gravitational Wave Measurements
astro-ph.CO 2016-11 conditional novelty 5.0 of 10

A Fisher-matrix forecast shows that a few years of Advanced LIGO data at design sensitivity could measure the black hole mass function's slope and lower cutoff to better than 10%, while the upper cutoff and merger rat...
Testing Parity-Violating Mechanisms with Cosmic Microwave Background Experiments
astro-ph.CO 2010-02 accept novelty 5.0 of 10

Chiral gravity and cosmological birefringence produce parity-violating CMB correlations at different angular scales, so a high-signal-to-noise detection can distinguish them.
Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements
astro-ph.CO 2009-07 conditional novelty 5.0 of 10

New Keck spectra of red-envelope galaxies in 24 clusters yield direct expansion-rate measurements H(z) = 97 +/- 62 at z about 0.5 and 90 +/- 40 km/s/Mpc at z about 0.8, which modestly tighten dark-energy and neutrino ...
Observing Dirac neutrinos in the cosmic microwave background
hep-ph 2019-08 accept novelty 4.0 of 10

Future CMB Stage IV measurements of N_eff will detect or exclude thermally populated right-handed neutrino partners in most Dirac-neutrino models, constraining new gauge bosons and scalar mediators more strongly than ...
Cosmological Constraints on Interacting Light Particles
astro-ph.CO 2017-03 conditional novelty 4.0 of 10

Allowing both free-streaming and interacting dark radiation in Planck 2015 plus BAO data caps extra relativistic species at Delta N_tot < 0.39 (2 sigma), with a mild, prior-driven preference for interacting species on...
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.
Probing primordial features with future galaxy surveys
astro-ph.CO 2016-06 conditional novelty 4.0 of 10

Combining future galaxy clustering with CMB data would tighten constraints on four Planck-favoured primordial feature models by factors of a few to tens, with Euclid and the sharper SPHEREx configuration performing best.
Constraints on massive sterile neutrino species from current and future cosmological data
astro-ph.CO 2011-02 conditional novelty 4.0 of 10

Current CMB, galaxy clustering and supernova data allow two sub-eV sterile neutrinos alongside three sub-eV active ones, though thermal sterile abundances conflict with Big Bang Nucleosynthesis.
Neutrino Physics from the Cosmic Microwave Background and Large Scale Structure
astro-ph.CO 2013-09 accept novelty 3.0 of 10

Combining a Stage-IV CMB polarization experiment with the DESI galaxy survey is forecast to reach 16 meV uncertainty on the sum of neutrino masses and 0.020 on the effective number of neutrino species.
The Hubble Tension and Early Dark Energy
astro-ph.CO 2022-11 unverdicted novelty 2.0 of 10

The Hubble tension between local and early-universe expansion-rate measurements may be resolved by early dark energy that speeds up expansion before recombination while satisfying existing constraints.
The Cosmological Constant
astro-ph 2000-04 accept novelty 2.0 of 10

Independent supernova, microwave-background, and cluster-mass measurements converge on a flat universe with about 30% matter and 70% vacuum energy, leaving the origin of that vacuum energy unexplained.

How later papers used it

70 later papers cite it

Evidence: substantial. 54 of the citing papers share no author with it, and 21 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 74 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 2 used its method or tool. 3 more papers by the same authors are listed: 3 used its method or tool.

Uses its method or tool 5 of 27 papers with this label · 3 by the same authors

Performed a Fisher matrix analysis using this paper's method.

Anisotropies in the Cosmic Neutrino Background after WMAP 5-year Data (2008) · 0.99 · paraphrased: the licence does not allow quoting
Used a Fisher-matrix formalism as introduced in this paper.

Breaking degeneracies in the first galaxies with clustering (2023) · 0.96 · paraphrased: the licence does not allow quoting

By the same authors

Evaluated the corresponding Fisher Matrix for a given future experiment and set of inflationary parameters using this paper's approach.

Red Density Perturbations and Inflationary Gravitational Waves (2007) (same authors) · 0.99 · paraphrased: the licence does not allow quoting
Estimated the error on alpha using this paper's method.

Oscillations in the inflaton potential? (2008) (same authors) · 0.94 · paraphrased: the licence does not allow quoting
Calculated the Fisher matrix using this paper's method.

Cross-correlation between thermal Sunyaev-Zeldovich effect and the integrated Sachs-Wolfe effect (2016) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

53 arXiv papers cite this in 57 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 22 sentences without a confident label

Uses its method or tool 19 papers

To determine the degeneracies between $σ_B, n_B$, and other possible cosmological and astrophysical parameters, we perform an information matrix analysis without priors according to [ref] [equation] where $α$ and $β$ represent the varied parameters of our model deemed to have the highest impact on 21-cm observables [ref] [equation] Here, the varied cosmological parameters involve the Hubble constant $h ≡ H_0 / 100 km/s/Mpc$, the total matter and baryon densities $Ω_m$ and $Ω_b$, and the power spectral amplitude $A_s$.

21-cm fluctuations from primordial magnetic fields · Information Matrix Analysis · 1.00
We begin by evaluating, for a given future experiment and for a given set of inflationary parameters, the corresponding Fisher Matrix [ref] [equation] where the $C_l^αβ$ are the power spectra for the temperature (TT), temperature-polarization (TE), E-mode polarization (EE), and B-mode polarization ($α$ and $β$ run over TT, EE, TE, BB), $θ_i$ is the set of parameters used in the Markov Chain, and $Cov_l$ is the “spectra covariance matrix” [ref] .

Red Density Perturbations and Inflationary Gravitational Waves · Introduction · 0.99
We forecast HERA's sensitivity to EDE's fractional energy density, $$, by employing a Fisher analysis, following the formalism in Refs. [ref] to construct the Fisher matrix for the 21cm power spectrum, [equation] where $θ_i$ denotes the cosmological and astrophysical parameters we vary in our analysis[We ensure that parameters defined logarithmically are varied linearly.], [equation] Here $L_X^(II/III)$ are the X-ray luminosity of pop-II/III stars (normalized by the SFR in units of $erg s^-1 M_⊙^-1 yr$), $f_*^(II/III)$ are the pop-II/III star formation efficiency, $f_esc^(II/III)$ are the fraction of photons that were produced by pop-II/III stars and managed to escape the host galaxy and ionize the IGM, $α_*^(II/III)$ are the pop-II/III star formation efficiency power law index, whereas $A_LW$ and $A_v_cb$ are the amplitudes of the Lyman-Werner (LW) [ref] and CDM-baryon relative velocity

Early Dark Energy Effects on the 21cm Signal · Fisher analysis · 1.00

Uses its data or values 2 papers

Taylor-expanding about the best-fit standard cosmological parameters $θ⃗_0$ given in Ref. [ref] (with $f_pbh, 0 = 0$), we rewrite this as χ^2(θ⃗) ≈ χ^2(θ⃗_0) + Δθ_i ∂C_ℓ^X/∂θ_i |_θ_0 (Σ^-1)^X X'_ℓℓ'(C_ℓ'^X'(θ⃗_0) - Ĉ^X'_ℓ') + 1/2 Δθ_i F_ij Δθ_j , where $Δθ_i ≡θ_i -θ_0, i$ and F_ĳ ≈∂C^X_ℓ/∂θ_i (Σ^-1)^X X'_ℓℓ'∂C^X'_ℓ'/∂θ_j + δ_i, i_τ δ_j, i_τ/σ_τ^2 is the Fisher-information or curvature matrix [ref] , for which we have neglected the smaller term linear in $(C^X_ℓ(θ⃗_0) - Ĉ^X_ℓ)$.

Cosmic microwave background limits on accreting primordial black holes · Analysis of Planck data · 0.84
The current measurement of the baryon-to-entropy ratio of the Universe is given by [ref] Y_B≡n_B/s = (0.87 ±0.02) ×10^-10,

Electron EDM and soft leptogenesis in supersymmetric B-L extension of the standard model · Introduction · 0.93

Cites it as background 12 papers

Dark matter is hypothesized to explain discrepancies in galactic rotation curves and other astronomical anomalies [ref] .

A possible explanation for NuTeV's anomalous dimuon events · Introduction · 0.92
The Fisher matrix has been utilized in numerous, similar contexts in the cosmology literature [ref] , so we give only a brief review of important results and the caveats in our particular application.

Effects of Unstable Dark Matter on Large-Scale Structure and Constraints from Future Surveys · Forecasting Methods · 0.97
The Fisher matrix has been utilized in numerous, similar contexts in the cosmology literature [ref] , so we give only a brief review of important results and the caveats in our particular application.

Weak Gravitational Lensing as a Method to Constrain Unstable Dark Matter · Forecasting Methods · 0.95

Discussion

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