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Cosmic variance of $z>7$ galaxies: Prediction from BlueTides

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Pith's one-line read For galaxies at redshift 7 and beyond, field-to-field cosmic variance—not Poisson counting noise—dominates the error budget of every planned survey, according to the BlueTides simulation.

desk verdict Useful BlueTides-based cosmic variance numbers for JWST/WFIRST survey planning, but the claim that cosmic variance dominates Poisson except for N≲10 is contradicted by the paper's own Table 2. read the letter →

arxiv 1908.02787 v2 pith:PNYW3WMD submitted 2019-08-07 astro-ph.CO

classification astro-ph.CO
keywords cosmicvariancehigh-redshiftgalaxiesgalaxyclusteringluminosityfunctionJWSTsurveysWFIRSTBlueTidessimulationUV
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the dominant uncertainty in future JWST and WFIRST measurements of galaxies at redshift 7 and above is not the finite number of galaxies detected but the field-to-field scatter caused by strong clustering—cosmic variance. Using the large-volume BlueTides hydrodynamic simulation, the authors predict this variance for UV magnitudes $M_{\rm UV}$ from $-16$ to $-22$ over survey areas from roughly $0.1\,\mathrm{arcmin}^2$ to $10\,\mathrm{deg}^2$, finding that it scales as a power law in survey area with exponents around $-0.25$ to $-0.45$. The forecast is $3\text{--}10\%$ cosmic variance for WFIRST's $10\,\mathrm{deg}^2$ field, $20\text{--}50\%$ for JWST medium/deep fields of about $100\,\mathrm{arcmin}^2$, and $\gtrsim40\%$ for lensed fields. Across essentially all current and upcoming surveys, cosmic variance exceeds Poisson variance; only samples with fewer than about ten galaxies are Poisson-limited. This matters because the luminosity functions and brightness distributions at $z>7$ will be interpreted against these same error budgets.

What carries the argument

The load-bearing object is the cosmic variance statistic $\sigma_g^2 = (1/V^2)\int_V \int_V \xi_{gg}(r_1,r_2)\,d^3r_1\,d^3r_2$, where $\xi_{gg}$ is the two-point galaxy correlation function; it measures the excess field-to-field scatter in counts beyond Poisson noise. BlueTides supplies $\xi_{gg}$ for a UV-magnitude-limited galaxy population, and the paper condenses it into power-law fits $\xi(r)=(r/r_0)^\gamma$ and $\sigma_g=\Sigma A^\beta$, with a universal redshift-width scaling $(\Delta z/\Delta z_{\rm ref})^{-0.32}$. For small surveys (JWST medium/deep and lensed fields), the paper also counts galaxies in many simulated sub-volumes to obtain the full probability distribution of overdensities, which yields rare-outlier detection probabilities.

What would settle it

Compare the observed number-count scatter across many independent JWST fields, for example repeated $100\,\mathrm{arcmin}^2$ pointings at fixed $M_{\rm UV}<-16$ and $z\approx9$–$11$; the sample variance of those counts should equal the predicted $\sigma_g\approx20$–$50\%$, and a measured scatter outside this range after accounting for selection effects would falsify the BlueTides bias.

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Extended reading notes

Core claim

The central claim is that for $z>7$ galaxies, cosmic variance is substantial and is the dominant component of the total uncertainty in every planned survey except those with fewer than about ten expected galaxies. Specifically, the paper predicts $\sigma_g\sim3\text{--}10\%$ for WFIRST's $10\,\mathrm{deg}^2$ field, $\sigma_g\sim20\text{--}50\%$ for JWST medium/deep surveys up to $A\sim100\,\mathrm{arcmin}^2$, and $\sigma_g\gtrsim40\%$ for lensed surveys; to keep the variance below $100\%$, effective volumes of $\gtrsim(8\,\mathrm{Mpc}/h)^3$ at $z\sim12$ and $\gtrsim(12\,\mathrm{Mpc}/h)^3$ at $z\sim14$ are required. The authors obtain these numbers from BlueTides, a $(400\,\mathrm{Mpc}/h)^3$ hydrodynamic simulation, by integrating the simulated two-point correlation function over mock survey volumes and, for small volumes, by building the full distribution of number counts across thousands of realizations.

Load-bearing premise

The simulation's mapping between galaxy UV brightness and dark-matter halo mass—and hence the clustering bias of $M_{\rm UV}$-limited samples—matches the real universe at $z=7.5$–$14$; if that mapping is wrong, every predicted cosmic variance shifts.

Editorial extensions

If this is right

  • JWST's JADES-medium/deep and CEERS surveys should expect 20–50% field-to-field scatter in $M_{\rm UV}<-16$ to $-20$ samples at $z\sim7.5$–$11$; for example, roughly $2200\pm450$ galaxies at $z\sim7.5$ in a $100\,\mathrm{arcmin}^2$ field.
  • WFIRST's $10\,\mathrm{deg}^2$ survey keeps cosmic variance at 3–10% for most samples, making it the cleanest platform for luminosity-function shape measurements at $z>7$.
  • Lensed surveys probing the faint end have $\sigma_g\gtrsim40\%$, so their luminosity-function constraints are meaningful only if effective volumes exceed roughly $(8\text{--}12\,\mathrm{Mpc}/h)^3$, depending on redshift.
  • Cosmic variance rather than Poisson noise sets the error budget for essentially all upcoming surveys; published luminosity functions at $z>7$ should carry cosmic-variance terms or risk overstating constraints.

Reading between the lines

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

  • If the simulation's galaxy–halo connection is representative, the predicted scatter can be tested directly: the field-to-field dispersion in number counts across independent JWST fields should match $\sigma_g$, and a mismatch would localize where the galaxy–halo connection fails.
  • The shallow power-law scaling $\sigma_g\propto A^{-0.25\ldots-0.45}$ means that enlarging a single field is an inefficient cure; several well-separated medium fields would reduce cosmic variance more effectively than one deep pencil beam.
  • Because BlueTides contains no regions underdense by more than $2\sigma$, the predicted distribution of overdensities is asymmetric; survey teams can use this to decide whether a claimed 'void' field is physically plausible.
  • The same machinery could be extended to stellar-mass-selected samples or to $z\sim6$–$7$ if the simulation's clustering is recalibrated, making the estimator useful beyond UV luminosity functions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper uses the BlueTides cosmological hydrodynamic simulation (400 Mpc/h box, WMAP9 cosmology) to estimate the cosmic variance of z>7 galaxies selected by rest-frame UV absolute magnitude thresholds M_UV ~ -16 to -22, over survey areas from ~0.1 arcmin^2 to 10 deg^2 and redshifts 7.5-14. The authors fit the simulated two-point correlation function with power laws, integrate it over model survey volumes to obtain sigma_g, validate against subvolume number-count distributions for small/medium fields, and package the results as fitting functions and a public online calculator. They apply the estimator to JWST medium/deep surveys, WFIRST 1 and 10 deg^2 fields, and lensed surveys, concluding that cosmic variance ranges from a few percent for large WFIRST fields to tens of percent for JWST fields and >=40% for lensed surveys, and that cosmic variance generally dominates the Poisson uncertainty for samples with more than about 10 galaxies.

Significance. If the underlying BlueTides galaxy-halo connection is representative, these are useful, directly usable predictions for interpreting and planning high-redshift surveys. The paper's strengths are the large simulation volume, the transparent pipeline from correlation function to sigma_g, the explicit fitting functions and public calculator, and the internal cross-check between the correlation-integral method and the subvolume number-count method. The main scientific conclusions are however currently overstated in two ways: the claim that cosmic variance dominates Poisson variance 'in all current and upcoming surveys' is contradicted by the paper's own Table 2, and the quantitative predictions are presented without an uncertainty budget despite acknowledged shot-noise and modeling limitations.

major comments (3)
  1. [Abstract; Section 5; Table 2] The claim that cosmic variance is larger than Poisson variance except for samples with N ≲ 10 is internally contradicted by Table 2. In the 10 deg^2 rows, z=11, M_UV<-20 has ⟨N⟩=168 with δN_cosmic=7 and δN_poisson=13, and z=14, M_UV<-18 has ⟨N⟩=102 with δN_cosmic=4 and δN_poisson=10; in both cases N>10 and the Poisson uncertainty exceeds the cosmic-variance uncertainty. The 1 deg^2 row at z=14, M_UV<-18 likewise has N=10.6 with δN_cosmic=2.1 and δN_poisson=3.3. These rows make the abstract sentence 'cosmic variance is larger than Poisson variance and forms the dominant component of the overall uncertainty in all current and upcoming surveys' false as written, and they also conflict with Section 5's statement that cosmic variance dominates except for bins with ≲10 objects. The authors should either restrict the dominance claim to the small-area/JWST-like geometries shown in Figure 5 or provide a corrected quantitative condition (e.g., involving both N and the amplitude of sigma_g); the 10 deg^2 WFIRST-like points should be added to Figure 5.
  2. [§3.2.2, Eq. (5); §3.4] The redshift-bin-width scaling sigma_g(Δz)/sigma_g(Δz_ref) = (Δz/Δz_ref)^{-0.32} is presented as universal, but the supporting Figure 3 shows only M_UV<-16 galaxies. The calculator CV_AT_COSMIC_DAWN then applies this exponent to every M_UV threshold and redshift in Table 1 via interpolation (§3.4). If the exponent depends on magnitude or redshift at z>7, the public estimates will be biased outside the single tested case. Please show the Δz dependence for at least a bright sample (e.g., M_UV<-20) and for a higher-redshift snapshot, or restrict Eq. (5) with appropriate caveats.
  3. [§3.1, Table 1; §4] The quantitative predictions are presented without an uncertainty budget. Table 1 lists power-law parameters r0 and gamma (and the derived Sigma, beta) with no error bars, and Figures 2 and 4 show no uncertainties on sigma_g; Section 4 provides only a qualitative discussion of systematic differences (e.g., 25-30% from cosmology) and does not propagate these or the fitting errors into the quoted values. This matters most at the bright end: Section 3.3.1 states that M_UV<-22 clustering 'could not be accurately probed due to excessive shot noise,' yet Table 1 still reports fits for M_UV=-22 at z=7.5-12 and the text quotes >10% cosmic variance for M_UV<-20 at z>10. Please provide uncertainties on the fitted parameters and sigma_g values, or explicitly flag the affected regimes as upper/lower limits.
minor comments (5)
  1. [§3.2.1, Eq. (4)] Equation (4) defines the power law with exponent beta, but the text states 'where α is the power-law exponent'; the symbol should be beta.
  2. [Table 1] At z=9, M_UV=-18, the fitted value gamma=-2.98 is likely a typo and breaks the monotonic trend with luminosity and redshift; please check and correct.
  3. [Figure 3 caption] The caption states that squares correspond to a survey area of 10 arcsec^2, which is inconsistent with the stated range of BlueTides validity (~0.1 arcmin^2 and above); this should likely be 10 arcmin^2.
  4. [Table 2 caption] Please state explicitly that deltaN_cosmic and deltaN_poisson are 1-sigma uncertainties, and clarify whether they are computed from the correlation-function integral or from the subvolume distribution, since both estimators are used in the paper.
  5. [References] The reference 'McCracken, H. J. et al., 2012' is formatted inconsistently with the other author-year references; it should be formatted in the same style.

Circularity Check

0 steps flagged · score 0.0 of 10

Cosmic variance is computed from simulated correlation functions via the standard volume integral; the fitting functions are data compressions, not fitted to the predicted variances, so no circularity.

full rationale

The central quantity sigma_g is obtained by Eq. (2) as an integral of the simulated two-point correlation function xi_gg over the survey volume, following the standard Peebles (1980) relation. xi_gg is measured directly from BlueTides galaxies and is not defined in terms of sigma_g or survey number counts, so the derivation does not reduce to its own output by definition. The power-law fits in Table 1 and Eq. (4)-(5) are compressions of the simulated clustering and computed variances, not parameters fitted to the target observable. The paper also cross-checks the integral method against direct sub-volume number-count distributions in Section 3.3.1, providing an independent internal check. The galaxy bias entering the calculation is an external modeling assumption of BlueTides, and the paper explicitly acknowledges in Section 4 that different cosmology or galaxy-formation physics would change the estimates; this is a modeling uncertainty, not circularity. Self-citations to Bhowmick et al. (2018a,b) are prior simulation predictions with independent content and are not invoked as a uniqueness theorem forcing the present result. No step in the derivation is equivalent to its input by construction. A possible inconsistency between the paper's blanket statement that cosmic variance dominates Poisson variance and the numbers in Table 2 would be an internal quantitative issue, not a circularity.

Assumptions & free parameters 3 free parameters · 9 assumptions · 0 invented entities

The central claim rests on the BlueTides simulation's galaxy population, which is itself dependent on cosmological and subgrid astrophysical inputs, and on the power-law fits that compress its clustering signal. The fitting parameters in Table 1 and Eq. (5) are free parameters fitted to simulation output. No new physical entities are introduced.

free parameters (3)
  • r0 and gamma power-law fit to BlueTides xi(r) for each M_UV threshold and redshift = See Table 1
    Fitted to the simulated galaxy two-point correlation functions; used in Eq. (2) to compute sigma_g. The fit is a summary of simulation output, not a fundamental constant.
  • Sigma and beta power-law fit to sigma_g(A) for each M_UV threshold and redshift = See Table 1
    Fitted to the computed cosmic variance values from the simulation; used in Eq. (4) and in the online calculator.
  • Redshift bin width scaling exponent alpha = -0.32
    Best-fit power-law exponent for the normalized sigma_g dependence on redshift bin width (Eq. 5), found to be roughly universal across magnitudes and redshifts.
assumptions (9)
  • domain assumption BlueTides simulation with WMAP9 cosmology and its subgrid star formation, feedback, and reionization models produces realistic z>7 galaxies.
    Section 2.1; the simulation's galaxy population is the sole source of clustering estimates, so all sigma_g values inherit this assumption.
  • domain assumption The galaxy SEDs computed with PEGASE-v2 and a Chabrier IMF give accurate rest-frame M_UV magnitudes.
    Section 2.1; all galaxy samples are defined by M_UV thresholds, so errors in SED synthesis would shift the sample definitions.
  • domain assumption Dust extinction is negligible for M_UV-limited samples with M_UV > -22.
    Section 2.1; no dust correction is applied. The authors state dust matters only at M_UV ~ -22 to -25, but the bright-end samples may still be affected.
  • domain assumption The two-point correlation function of BlueTides galaxies is well-described by a single power law on all scales contributing to the cosmic variance integral.
    Section 3.1, Eq. (3); the power law is fitted over the plotted range and used in Eq. (2). Poor fit quality at very small or large scales would propagate into sigma_g.
  • domain assumption Survey volumes can be approximated as cuboids with fixed transverse extent and no redshift evolution across the bin.
    Section 2.2 and Section 4; lightcone effects, redshift evolution, and geometry variations are ignored. The authors expect these errors to be small but do not quantify them.
  • domain assumption Subvolumes extracted from the periodic simulation box are independent realizations of the survey field.
    Section 2.2; used to construct the full number-count distributions. Overlap or lack of independence would bias the estimated distributions.
  • domain assumption The lensed-survey effective volumes from Livermore et al. (2017) are correct.
    Section 3.3.2; these effective volumes are used as the basis for the lensed-survey cosmic variance estimates.
  • domain assumption Linear interpolation between tabulated M_UV and redshift entries is sufficiently accurate for the calculator.
    Section 3.4; the CV_AT_COSMIC_DAWN estimator uses linear interpolation between the Table 1 grid points.
  • standard math Standard cosmological and mathematical tools, including the Peebles (1980) integral formula and Poisson counting statistics, apply.
    Section 2.2, Eq. (2); the variance decomposition into cosmic and Poisson components follows standard theory.

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Pith. "Pith review of Cosmic variance of $z>7$ galaxies: Prediction from BlueTides." pith.science (2026). https://pith.science/paper/PNYW3WMD

@misc{pith2026190802787,
  author       = {Pith},
  title        = {Pith review of: Cosmic variance of $z>7$ galaxies: Prediction from BlueTides},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PNYW3WMD}},
  note         = {Machine review of arXiv:1908.02787}
}
abstract

In the coming decade, a new generation of telescopes, including JWST and WFIRST, will probe the period of the formation of first galaxies and quasars, and open up the last frontier for structure formation. Recent simulations as well as observations have suggested that these galaxies are strongly clustered (with large scale bias $\gtrsim6$), and therefore have significant cosmic variance. In this work, we use \texttt{BlueTides}, the largest volume cosmological simulation of galaxy formation, to directly estimate the cosmic variance for current and upcoming surveys. Given its resolution and volume, \texttt{BlueTides} can probe the bias and cosmic variance of $z>7$ galaxies between magnitude $M_{UV}\sim-16$ to $M_{UV}\sim-22$ over survey areas $\sim0.1\ \mathrm{arcmin}^2$ to $\sim 10~\mathrm{deg}^2$. Within this regime, the cosmic variance decreases with survey area/ volume as a power law with exponents between $\sim-0.25$ to $\sim-0.45$. For the planned $10~\mathrm{deg}^2$ field of WFIRST, the cosmic variance is between $3\%$ to $10\%$. Upcoming JWST medium/ deep surveys with areas up to $A\sim100\ \mathrm{arcmin}^2$ will have cosmic variance ranging from $\sim 20-50\%$. Lensed surveys have the highest cosmic variance $\gtrsim 40\%$; the cosmic variance of $M_{UV}\lesssim-16$ galaxies is $\lesssim100\%$ up to $z\sim11$. At higher redshifts such as $z\sim12~(14)$, effective volumes of $\gtrsim(8~\mathrm{Mpc}/h)^3$ ($\gtrsim(12\ \mathrm{Mpc}/h)^3$) are required to limit the cosmic variance to within $100\%$. Finally, we find that cosmic variance is larger than Poisson variance and forms the dominant component of the overall uncertainty in all current and upcoming surveys. We present our calculations in the form of simple fitting functions and an online cosmic variance calculator (CV_AT_COSMIC_DAWN) which we publicly release.

Figures

Figures reproduced from arXiv: 1908.02787 by the authors.

Figure 1
Figure 1. Two-point correlation functions (circles) and their power law fits (lines) for BlueTides galaxies as a function of pairwise comoving distance r. The lines with different colors represent different MUV thresholds. 3) has a somewhat universal power-law dependence on ∆z, independent of magnitude, redshift and survey type. This behavior is also reported for z < 3 galaxies (Moster et al. 2011). We determine the best fit … view at source ↗
Figure 2
Figure 2. The filled circles show the cosmic variance as a function of survey area A and a redshift width of ∆z = 1 for various MUV threshold samples. Dashed lines of corresponding color show power law fits. 0.5 0.0 0.5 1.0 log10¢z=¢zref + ± 0.3 0.6 1 2 ¾ g ( ¢ z ) = ¾ g ( ¢ z r e f ) z = 7: 5 z = 8: 0 z = 9: 0 z = 10: 0 z = 11: 0 z = 12: 0 z = 13: 0 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Cosmic variance as a function of redshift bin width ∆z normalized with respect to a reference redshift width ∆zref = 1. We show this for galaxies with MUV < −16. δ is a small (< 0.1) horizontal offset added to the x axis to avoid overlap between the data points. The black dashed line corresponds to the best fit power-law. Circles and stars correspond to survey areas of 10 deg2 and 1 deg2 respectively. Squares corres… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Filled circles show the cosmic variance as a function of MUV threshold for various survey areas (A) with ∆z = 1. The filled data points are computed by integrating the correlation function. The open data points for A = 1 arcmin2 , 10 arcmin2 ,1 deg2 are computed from t…
Figure 5
Figure 5. Figure 5: hNi is the mean value of the number count of galax￾ies in a survey [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The probability distribution of galaxy overdensi￾ties (in the units of the standard deviation σ of the distribu￾tions) within the ensemble of subvolumes corresponding to JWST fields (JADES-medium and JADES-deep). The three different colors correspond to redshifts 7.5,1…
Figure 7
Figure 7. Figure 7: The detection probability of bright/ luminous (MUV < −21) galaxies in current and upcoming JWST surveys. The solid lines and dashed lines correspond to JADES-medium and the JADES-deep survey respectively. The redshift width has been assumed to be 1. MUV < −22 (red line…
Figure 8
Figure 8. Figure 8: Cosmic variance in lensed surveys: σgalaxy is the cosmic variance as a function of volumes for lensed surveys for various MUV thresholds. We consider a range of volumes (Veff ) based on effective volumes of HST Frontier fields surveys (Koekemoer et al. 2017) as compute…
Figure 9
Figure 9. Figure 9: The color map shows the cosmic variance as a function of threshold MUV magnitude and survey area A as calculated by CV_AT_COSMIC_DAWN. The solid black lines show contours representing σg ∼ 0.1, 0.3, 1, 3, 10. We show upcoming (JWST, WFIRST) and current (HUDF, SDF, CAND…
Figure 10
Figure 10. Figure 10: Top Panels: Φ is the rest frame UV luminosity function. Different colors represent galaxies within simulation sub-volumes corresponding to different survey areas with ∆z = 1. For each color, the shaded region corresponds to uncertainty due to cosmic variance. For each…

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.