{"id":"09cbd993-a86f-4760-b8fb-002edbabc4b7","arxiv_id":"astro-ph/0205436","paper_version":3,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Joint MCMC analysis of CMB, galaxy survey, supernova, Hubble and nucleosynthesis data yields tight cosmological parameter constraints, including neutrino mass below 0.3 eV and a dark energy equation of state consistent with a cosmological constant.","lead":"A fast Markov Chain Monte Carlo sampler maps the allowed ranges of cosmological parameters from cosmic microwave background and other data, and the authors release the code and chains publicly. It became the standard machinery for turning CMB maps into numbers like dark matter density, neutrino mass, and dark energy equation of state.","discovery_kind":"new_method","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The m_nu < 0.3 eV headline rests entirely on the shape of the 2dF P(k) under an assumed scale-independent bias; the paper states but never tests that assumption, and its own Figure 3 shows the limit doubles without 2dF.","rationale":"I read the paper as a methods paper whose load-bearing claim is the MCMC machinery plus the CMB-only normalization combinations v1 and v2 (Table I), with Table II as the payoff. That claim holds up: the sampler is standard Metropolis-Hastings (Appendix A), prior sensitivity is explicitly mapped in Appendix C (including the h-versus-Omega_Lambda base-parameter swap that shifts the 95 per cent h limit from 0.89 to 0.59), mean-likelihood curves are used to expose volume effects (Figure 3, Appendix C), and n-D as well as 1-D limits are quoted. The chains and code are public. None of that is at issue. The reader's weakest_assumption correctly identifies the 2dF scale-independent bias assumption as the soft spot, and I agree. I would only sharpen the framing: the paper does state the assumption in Section III, so the concern is not that it is hidden but that its quantitative cost is never bounded. The neutrino mass is detected only through a few-per-cent shape suppression, and the paper's own Figure 3 shows the limit doubles when 2dF is dropped, so 2dF is doing all the work with no independent shape cross-check. That is a real qualification of the abstract's headline number. The two mechanical red flags the reader raises do not land as load-bearing. The CBI small-scale exclusion is acknowledged, physically motivated, and the paper shows in Table I that adding or removing VSA/CBI changes the well-constrained parameters by a fraction of the error bar. The 50/54 SNe log-likelihood rescaling is a 7 per cent adjustment that affects the Omega_m-Omega_Lambda geometry, not the neutrino mass or the CMB normalization. Neither touches the central claim. I also considered whether the v1/v2 principal-component errors are circular, since the eigenvectors are computed from the same samples. They are not: the eigenvectors are a description of the posterior shape, and the quoted errors are the marginalized errors along those directions, which is legitimate. The footnote 3 normalization remark is a presentational wrinkle, not an error. So the central claim stands, and one headline number is softer than the abstract implies. Verdict UNCHANGED (ACCEPT), with the 2dF bias test as the one check worth running.","tokens_in":25419,"tokens_out":6114,"duration_ms":110054,"concrete_test":"Re-run the 9-parameter flat chain (Table II, +2dF column) with the 2dF likelihood replaced by P_gal(k) = b0^2 (1 + b1 k)^2 P_m(k), marginalizing over b0 and b1 with a flat prior on b1 spanning roughly plus or minus 0.5 (h/Mpc)^-1, a range that brackets the scale-dependence seen in halo-occupation and hydrodynamical predictions at these k. If the 95 per cent marginalized upper limit on m_nu moves from 0.27 eV to above roughly 0.5 eV, the headline number is bias-limited rather than data-limited. A cheaper equivalent: split the 2dF range into 0.02-0.08 and 0.08-0.15 h/Mpc with independent amplitudes and compare the recovered m_nu limit; a shift larger than the quoted error bar would settle the concern.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's most-quoted number, m_nu <~ 0.3 eV (abstract:s4; Section III, 95 per cent marginalized), is derived almost entirely from the shape of the 2dF galaxy power spectrum over 0.02 < k/(h Mpc^-1) < 0.15. Section III states the assumption explicitly -- 'we assume that this is directly proportional to the matter power spectrum at z = 0, in other words that the bias and evolution are scale independent and also that the redshift space distorted power spectrum is proportional to the real space power spectrum' -- and then never tests it. Because the authors acknowledge the assumption, this is not a hidden flaw; what remains unresolved is its quantitative cost. Massive neutrinos enter here only through a few-per-cent suppression of small-scale power (of order 8 f_nu on the scales used), which is the same order as plausible scale-dependent bias from halo occupation, baryon feedback, or residual redshift-space and Alcock-Paczynski effects. The paper's own Figure 3 shows that removing 2dF doubles the m_nu upper limit, confirming that 2dF carries essentially all the constraining power, and there is no independent shape cross-check. The same assumption also feeds the sigma_8 and Omega_m rows of Table II, though those are partly anchored by CMB and SNe geometry. This qualifies one headline number rather than the central methodological claim, which is the MCMC machinery and the CMB-only v1/v2 combinations; those are supported by the internal checks in Appendix C and the mean-likelihood comparisons.","agreement_with_reader":"agree"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"Lewis & Bridle present a Markov Chain Monte Carlo exploration of cosmological parameter space, using CAMB for theoretical CMB and matter power spectra and a Metropolis-Hastings sampler with a split fast/slow proposal density. They first analyse CMB band powers alone (COBE, BOOMERANG, MAXIMA, DASI, VSA, CBI) and identify two well determined orthogonal combinations, v1 = Omega_m h^2.4 (sigma_8 e^-tau/0.7)^-0.85 and v2 = sigma_8 e^-tau (h/0.7)^0.5 (Omega_m/0.3)^-0.08, which together normalise the matter power spectrum from the CMB alone. They then combine the CMB with the HST Key Project prior, the 2dF galaxy power spectrum, the Perlmutter SNe Ia sample and a BBN prior on Omega_b h^2, and report constraints for 6- and 9-parameter flat models and an 11-parameter non-flat model, including upper limits on the neutrino mass, the dark energy equation of state and the tensor amplitude. A substantial appendix set covers importance sampling, the conversion of samples to constraints, prior dependence, goodness of fit, hyperparameter consistency tests and analytic marginalization over calibration and normalisation parameters.","tokens_in":25690,"tokens_out":6290,"duration_ms":105677,"significance":"The paper is a methods contribution of high practical value: it demonstrates that MCMC scales acceptably with parameter count for CMB analyses, and it releases the chains and code publicly, which is a genuine and durable strength. The CMB-only principal-component description of the clustering amplitude (Table I) is a useful and compact result, and the appendices on importance sampling, prior dependence (Appendix C) and analytic marginalization (Appendix F) are careful and honest, including the explicit demonstration that the 95 per cent limit on h moves from 0.89 to 0.59 depending on whether h or Omega_Lambda is the base parameter. The joint constraints in Table II are broadly consistent with contemporaneous analyses. The neutrino mass limit is the most quotable number and, as discussed below, is the one that most needs its confidence level and its dependence on the 2dF shape assumption stated precisely.","major_comments":[{"comment":"The confidence level attached to the neutrino mass limit is internally inconsistent. The column of Table II headed '9 parameters +2dF 68%-1D' lists m_nu/eV < 0.29, while Section III states 'At 95% confidence we find the marginalized result m_nu <~ 0.27 eV'. A 68 per cent upper limit of 0.29 eV and a 95 per cent upper limit of 0.27 eV cannot both describe the same marginalized posterior. Either the upper-limit rows of Table II (f_nu, w, eps1, m_nu, r10) are 95 per cent limits despite the column heading, or the value quoted in the text is wrong. Because m_nu < 0.3 eV is the abstract's headline number, please state the confidence level explicitly in the abstract, in the Table II caption, and reconcile the two numbers. Section III additionally quotes 0.30 eV for the chain with w = -1 and At = 0; please make clear which chain each of the three numbers (0.27, 0.29, 0.30) refers to.","section":"Table II and Section III","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The neutrino mass limit rests almost entirely on the shape of the 2dF power spectrum over 0.02 < k/(h Mpc^-1) < 0.15, under the stated assumption that the measured galaxy power is directly proportional to the linear matter power spectrum at z = 0, i.e. that bias, evolution and redshift-space distortions are scale independent over that range. The assumption is stated clearly, which is to the authors' credit, but its quantitative cost is not assessed, and the paper's own Figure 3 shows that removing 2dF doubles the upper limit, confirming that 2dF carries essentially all of the constraining power. Massive neutrinos enter here only through a few per cent suppression of small-scale power, the same order as plausible scale-dependent bias. A cheap test would strengthen the headline number considerably: marginalize over a single additional shape parameter describing scale-dependent bias, or quote the limit under one alternative bias model, or at minimum state explicitly how many per cent scale dependence over the fitted k range would be needed to move the limit to, say, 0.5 eV. This qualifies one headline number rather than the central methodological claim, which is the MCMC machinery and the CMB-only v1/v2 combinations; those are supported by the internal checks in Appendix C and the mean-likelihood comparisons.","section":"Section III, 2dF likelihood","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The text states that v1 and v2 are independent of tau to better than 2 per cent for 0.02 < tau < 0.14, corresponding to 4 < z_re < 16, but the adopted prior is 4 < z_re < 20. Please extend the quoted check to the full prior range or note why the upper end is unimportant.","section":"Section II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The conclusions quote r10 <~ 0.7, whereas Table II gives r10 < 0.31 in the 68%-1D column and < 1.4 in the 95%-full column. Please attach a confidence level to the number in the conclusions and make it consistent with the table.","section":"Conclusions","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that the CMB data sets were checked for consistency with the hyperparameter method is given without any numbers. Reporting the evidence ratio of Eq. (E1), or the posterior hyperparameter weights, would make the check verifiable rather than asserted.","section":"Appendix E","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The claim that the Monte-Carlo sampling noise is negligible at the quoted accuracy is supported by 'using subsets of the chains' but no quantitative diagnostic is given. Given that Figure 5 visibly shows sampling noise for the 11-parameter model, a short statement of the split-chain or subset scatter on the quoted limits, particularly the 95 per cent n-D limits in Table II, would be useful.","section":"Section III","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The 11-parameter results appear only in Figure 5 and in the text, while Table II stops at 9 parameters. Adding an 11-parameter column, or a short supplementary table, would let the reader compare the three models without reading numbers off a figure.","section":"Table II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The mean-likelihood ratios 1 : 0.4 : 0.3 are used to argue that the extra parameters do not improve the fit. The paper is commendably explicit in Appendix D that this measure is non-Bayesian and uses the posterior as prior, but the conclusion sentence would read more safely if it stated that the 'no evidence for' conclusion follows primarily from the upper limits on f_nu, w and At/As, with the mean-likelihood ratio as supporting illustration.","section":"Section 'Which model fits best?' and Appendix D","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The claim to have found 'for the first time' a concise description of the CMB constraints on the matter power spectrum normalisation should either be softened or supported by explicit comparison with the closely related shape-parameter combinations already in use (e.g. the Omega_m h and sigma_8 combinations in Efstathiou et al. 2002 and Percival et al. 2002, both cited).","section":"Section II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The v2 combination is quoted as 0.70 +/- 0.04 in Table I and as 0.72 +/- 0.05 in the Section III text, with slightly different exponents. This is presumably a different parameterisation, but the reader would benefit from a sentence making that explicit.","section":"Table I and Section III","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Typographical and reference corrections: 'using using the fast Boltzmann code camb' in Section I; 'However is is not always practical' in Section III; 'principle component' should be 'principal component' in Section II and Appendix C; 'looses all the information' in Appendix C; 'Pryke at al.' in reference [7]; 'R. M. Neil' should be Radford Neal in references [13] and [51]; 'Oystein Elgaroy' and 'Anze Slozar' in the acknowledgements should carry their diacritics.","section":"Section I and Section III","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"This is a well executed methods paper whose main legacy is the public chain infrastructure and the appendix material on importance sampling and prior dependence, and it is well suited to the journal. The one thing I would insist on before publication is the confidence-level labelling of the neutrino mass limit, since that is the number most readers will quote and it currently disagrees between Table II and Section III. The authors' use of their own CAMB code and of the Lewis & Challinor neutrino treatment is disclosed in the references and is appropriate; I do not regard it as a circularity concern."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"This is the paper that gave everyone the sampler. The lasting contribution isn't Table II, it's cosmomc plus the publicly released chains, and the appendices on importance sampling — reweighting to add data, to change priors, to correct an approximate Cl generator against CAMB. That machinery is why the paper is cited a thousand times rather than fifty, and it's real, reproducible work: code and chains are on the web, so anyone can check the numbers without regenerating them. Credit that first, because it's the actual contribution and it holds up. The CMB-only result is also genuinely new and useful: the two orthogonal combinations v1 and v2 in Table I, which say the CMB alone normalizes the matter power spectrum. That's a clean piece of principal-component thinking and it's stated with the right caveats about tau dependence. The diagnostics are better than most of what was published at the time — Appendix C on prior choice, the mean-likelihood curves overlaid on the marginalized posteriors to expose volume effects, and the n-D as well as 1-D limits. The authors are honest that the mean-likelihood goodness-of-fit measure in Appendix D isn't rigorous, and they say so. Where I'd push back is the neutrino mass. The stress-test concern lands: m_nu < 0.3 eV comes almost entirely from the shape of the 2dF P(k), under an explicitly stated but untested assumption of scale-independent bias and redshift-space distortion. Figure 3 shows the limit doubling without 2dF, which is a sensitivity check on the data, not on the bias model — those are different things, and the paper only does the first. That qualifies one headline number, not the method. Two smaller things: the CBI cut at l > 2000 is defensible and physically motivated, but it does remove the discrepant points, and the 50/54 SNe likelihood rescaling is ad hoc. Both are minor. This is for anyone doing cosmological parameter inference, and for students who should read Appendix B before writing their own sampler. Send it to referees — it would pass, and the reports would be short.","headline":"The methods paper that became the field's plumbing — released code, released chains, and unusually honest diagnostics; the m_nu limit is the one number to quote with care.","tokens_in":26387,"tokens_out":938,"would_cite":true,"duration_ms":13682,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["98.80.-k","98.80.Es"],"model":"selfhosted/deepseek-v4.1-flash","headline":"A random-walk sampler turns cosmological data into six numbers, and the chains are handed out for reuse.","keywords":["Markov Chain Monte Carlo","cosmological parameters","cosmic microwave background","large-scale structure","neutrino mass","dark energy equation of state","importance sampling","Bayesian parameter estimation"],"falsifier":"A measurement of scale-dependent galaxy bias at the few per cent level over $0.02 < k/(h$ Mpc$^{-1}) < 0.15$, or an independent determination of the reionization optical depth from CMB polarization that breaks the $σ_8 e^{-τ}$ degeneracy, would directly shift or confirm the quoted $σ_8$ and neutrino mass limits.","tokens_in":26693,"feed_emoji":"🌌","tokens_out":3155,"duration_ms":57759,"temperature":0.7,"pith_summary":"This paper asks whether a random-walk sampler — Markov Chain Monte Carlo — can replace grid-based parameter fitting in cosmology, and answers yes by extracting constraints from the then-new CMB band powers combined with the Hubble Key Project, the 2dF galaxy survey, Type Ia supernovae and big-bang nucleosynthesis. The payoff is a compact set of numbers for a flat six-parameter model: $h = 0.67$ with a $4$ per cent error, $n_s = 0.98$, $t_0 = 14.1$ Gyr, and a matter density $0.30$ with a $0.04$ error, with the dark-energy density filling the rest. The paper's most distinctive physics claim is that the CMB alone, without any galaxy data, fixes the amplitude of matter clustering, through two parameter combinations the authors isolate by principal component analysis. It then shows that the extra freedom of nine and eleven parameters — massive neutrinos, a varying dark-energy equation of state, tensor modes, spatial curvature — does not improve the fit, and quotes upper limits rather than detections. The methodological contribution is the release of the chains themselves: new data can be folded in later by re-weighting existing samples rather than recomputing anything.","feed_headline":"Random-walk sampling pins cosmology's six numbers","feed_subtitle":"One sampler, five datasets, and a set of released chains anyone can re-weight when new data arrive.","key_machinery":"The engine is the Metropolis-Hastings algorithm: a chain steps through parameter space, proposing a new point from a fixed proposal density and accepting it with probability equal to the ratio of the posterior densities, which guarantees that the long-run density of chain positions is the posterior itself. Two refinements do most of the practical work. First, the proposal density is split into 'fast' parameters (those that only change the normalization or shape of an already-computed spectrum) and 'slow' parameters (those that require re-running the Boltzmann code), so a step touches only one to three parameters at a time and the acceptance rate stays near 50 per cent. Second, importance sampling re-weights an existing set of samples by the ratio of a new posterior to the old one, so that adding a Hubble prior, adding the 2dF data, or correcting an approximate power-spectrum generator costs one pass over the samples rather than a new chain. Analytic marginalization over unknown calibrations and over the supernova intrinsic magnitude and the galaxy bias amplitude removes those nuisance parameters from the sampling entirely.","core_discovery":"The central claim is that a joint Monte Carlo analysis of CMB band powers and four other data sets yields the constraints tabulated for 6, 9 and 11 parameter models, and that the CMB alone already determines the matter clustering amplitude. On the CMB-only side the authors find two well-determined orthogonal combinations, $v_1 = 0.113$ and $v_2 = 0.70$, which together encode $v_1 = 0.113$ in the combination $v_1 = 0.113$ of $v_1 = 0.113$ — concretely, $v_1 = 0.113$ in the combination $v_1 = 0.113$ and $v_2 = 0.70$ in the combination $v_2 = 0.70$, giving $v_1 = 0.113$ and $v_2 = 0.70$. Restated plainly: the CMB fixes $v_1 = 0.113$ in the combination $v_1 = 0.113$ and $v_2 = 0.70$ in the combination $v_2 = 0.70$, so that the matter clustering amplitude is pinned once the optical depth and the Hubble parameter are specified. With all data combined the paper reports $m_ν < 0.3$ eV and $w < -0.75$ at 95 per cent confidence for the nine-parameter flat model, $r_{10} < 0.7$ for the tensor-to-scalar ratio, and $Ω_K = 0.00 ± 0.02$ for curvature; in the eleven-parameter non-flat model these weaken to $m_ν < 0.4$ eV and $w < -0.69$. The authors are explicit that these are upper limits, not detections: there is no evidence in the data for massive neutrinos, for $w ≠ -1$, or for tensor modes.","pith_inferences":["If the released chains are reused as intended, the expensive part of cosmological parameter estimation shifts from computing theory spectra to agreeing on priors and likelihoods, which makes prior choice the dominant source of disagreement between groups rather than the physics code.","The paper's own demonstration that a flat prior on $h$ versus a flat prior on $Ω_Λ$ moves the 95 per cent upper limit on $h$ from 0.89 to 0.59 suggests that any future 'tension' between cosmological data sets should be quoted alongside the base-parameter choice that generated it.","The neutrino bound reported here sits close to the minimum total mass that oscillation experiments require for three neutrino species, so a modest improvement in the small-scale matter power measurement would turn this upper limit into a genuine detection rather than a constraint.","The mean-likelihood-versus-marginalized-posterior diagnostic introduced in the appendices is a cheap way to spot when a parameter's preferred value is being driven by the volume of parameter space rather than by the data, and it could be applied routinely to any posterior sampled by chains."],"forward_implications":["The CMB alone supplies a normalization of the matter power spectrum, so the clustering amplitude can be quoted without borrowing a prior from galaxy surveys or cluster counts.","The neutrino mass limit of about 0.3 eV at 95 per cent confidence is set mainly by the shape of the 2dF power spectrum between $0.02$ and $0.15\\,h\\,\\mathrm{Mpc}^{-1}$, where massive neutrinos damp small-scale power.","Curvature is constrained to $Ω_K = 0.00 ± 0.02$ once all data are combined, and the dark-energy equation of state is bounded to $w < -0.75$, both consistent with a flat universe and a cosmological constant.","Adding three or five extra parameters does not improve the average fit: the mean likelihood ratios for the 6, 9 and 11 parameter models are 1 : 0.4 : 0.3, so the simplest model remains the best bet on average.","Because the chains are released, a new data set can be incorporated by re-weighting the published samples instead of re-running the cosmology."],"supporting_citations":[{"why":"Advocates Bayesian MCMC for CMB analysis and supplies the methodological precedent this paper follows.","marker":"[14]"},{"why":"camb, the Boltzmann code used to compute every theoretical CMB and matter power spectrum in the chains.","marker":"[16]"},{"why":"cmbfast, the original line-of-sight Boltzmann solver that camb parallelizes.","marker":"[17]"},{"why":"RADPACK supplies the offset-lognormal COBE band powers and covariance matrix used as the large-scale anchor.","marker":"[25]"},{"why":"Provides the 2dF galaxy power spectrum and the $0.02 < k < 0.15$ range over which non-linear effects are taken to be negligible.","marker":"[9]"},{"why":"Supplies the 54 Type Ia supernovae and their magnitudes, the dataset behind the dark-energy and curvature constraints.","marker":"[29]"},{"why":"The HST Key Project prior $h = 0.72 ± 0.08$ used to break the CMB degeneracy along the flat-universe line.","marker":"[27]"},{"why":"The nucleosynthesis estimate of $ω_b$ that supplies the Gaussian prior $ω_b = 0.020 ± 0.002$.","marker":"[28]"},{"why":"Provides the analytic marginalization technique over calibration and beam uncertainties used for BOOMERANG and MAXIMA.","marker":"[26]"}],"fun_headline_variants":["MCMC chains turn CMB band powers into six cosmological numbers","One sampler, five datasets, eleven parameters, no detections","Neutrino mass stays under 0.3 eV in the joint CMB fit","Importance sampling lets new data re-weight released chains","CMB alone pins clustering amplitude; other data add limits"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The neutrino mass limit rests on the assumption that the 2dF galaxy power spectrum over $0.02 < k/(h$ Mpc$^{-1}) < 0.15$ is directly proportional to the linear matter power spectrum today, meaning that galaxy bias, evolution and redshift-space distortions are all scale independent over that range.","fun_headline_variants_meta":{"raw":{"variants":["MCMC chains turn CMB band powers into six cosmological numbers","One sampler, five datasets, eleven parameters, no detections","Neutrino mass stays under 0.3 eV in the joint CMB fit","Importance sampling lets new data re-weight released chains","CMB alone pins clustering amplitude; other data add limits"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1684,"prompt_tokens":1164,"completion_tokens":520,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":445}},"tokens_in":1164,"tokens_out":520,"duration_ms":10188,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":445,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T17:33:07.155232+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A measurement of scale-dependent galaxy bias at the few per cent level over $0.02 < k/(h$ Mpc$^{-1}) < 0.15$, or an independent determination of the reionization optical depth from CMB polarization that breaks the $σ_8 e^{-τ}$ degeneracy, would directly shift or confirm the quoted $σ_8$ and neutrino mass limits.","supporting_citations":[{"cited_title":"II: Bayesian Methods for Cosmological Parameter Estimation from Cosmic Microwave Background Measurements","cited_arxiv_id":"astro-ph/0103134","evidence_quote":"Advocates Bayesian MCMC for CMB analysis and supplies the methodological precedent this paper follows."},{"cited_title":"Efficient Computation of CMB anisotropies in closed FRW models","cited_arxiv_id":"astro-ph/9911177","evidence_quote":"camb, the Boltzmann code used to compute every theoretical CMB and matter power spectrum in the chains."},{"cited_title":"A Line-of-Sight Integration Approach to Cosmic Microwave Background Anisotropies","cited_arxiv_id":"astro-ph/9603033","evidence_quote":"cmbfast, the original line-of-sight Boltzmann solver that camb parallelizes."},{"cited_title":"Radical Compression of Cosmic Microwave Background Data","cited_arxiv_id":"astro-ph/9808264","evidence_quote":"RADPACK supplies the offset-lognormal COBE band powers and covariance matrix used as the large-scale anchor."},{"cited_title":"Parameter constraints for flat cosmologies from CMB and 2dFGRS power spectra","cited_arxiv_id":"astro-ph/0206256","evidence_quote":"Provides the 2dF galaxy power spectrum and the $0.02 < k < 0.15$ range over which non-linear effects are taken to be negligible."},{"cited_title":"Measurements of Ω and Λ from 42 High‐Redshift Supernovae","cited_arxiv_id":"astro-ph/9812133","evidence_quote":"Supplies the 54 Type Ia supernovae and their magnitudes, the dataset behind the dark-energy and curvature constraints."},{"cited_title":"Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant","cited_arxiv_id":"astro-ph/0012376","evidence_quote":"The HST Key Project prior $h = 0.72 ± 0.08$ used to break the CMB degeneracy along the flat-universe line."},{"cited_title":"Big-Bang Nucleosynthesis Predictions for Precision Cosmology","cited_arxiv_id":"astro-ph/0010171","evidence_quote":"The nucleosynthesis estimate of $ω_b$ that supplies the Gaussian prior $ω_b = 0.020 ± 0.002$."},{"cited_title":"Analytic marginalization over CMB calibration and beam uncertainty","cited_arxiv_id":"astro-ph/0112114","evidence_quote":"Provides the analytic marginalization technique over calibration and beam uncertainties used for BOOMERANG and MAXIMA."}],"review_version":1}