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Alcock–Paczyński distortion measured from Lyman-alpha forest full shape reaches 1% precision at z=2.33

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2026-08-01 07:46 UTC pith:YB5XX33J

load-bearing objection A genuinely important Lyα AP measurement with clean blinded methodology; the main caveat is that the error budget rests on mock realism and in-prep companion validation. the 2 major comments →

arxiv 2607.27410 v1 pith:YB5XX33J submitted 2026-07-29 astro-ph.CO

DESI DR2 Results IV: Alcock-Paczy\'nski Measurements from the Lyman Alpha Forest and Cosmological Constraints

DESI Collaboration: A. G. Adame , J. Aguilar , S. Ahlen , O. Alves , A. Anand , U. Andrade , E. Armengaud , S. Avila
show 145 more authors
A. Aviles P. Bansal A. Bault J. R. Bermejo-Climent F. Beutler D. Bianchi C. Blake S. Blasby M. Bonici S. Brieden A. Brodzeller D. Brooks A. Carnero Rosell K. Carrion L. Casas F. J. Castander E. Chaussidon J. Chaves-Montero D. Chebat X. Chen Z. Chen Y. Cho T. Claybaugh A. Cuceu T. M. Davis K. S. Dawson R. de Belsunce A. de la Macorra J. Della Costa A. Dey M. Doshi H. Ebina D. J. Eisenstein W. Elbers G. Farren V. A. Fawcett E. Fern\'andez-Garc\'ia S. Ferraro A. Font-Ribera D. Forero-S\'anchez J. E. Forero-Romero C. S. Frenk G. Gambardella C. Garcia-Quintero L. H. Garrison H. Gil-Mar\'in S. Gontcho A Gontcho A. X. Gonzalez-Morales C. Gordon D. Green R. Gsponer G. Gutierrez J. Guy B. Hadzhiyska C. Hahn S. He M. Herbold H. K. Herrera-Alcantar M.-F. Ho K. Honscheid J. Hou D. Huterer V. Ir\v{s}i\v{c} M. Ishak J.-Q. Jiang S. Jos S. Juneau N. V. Kamble N. G. Kara\c{c}ayl{\i} T. Karim D. Kirkby A. Kremin A. Krolewski O. Lahav C. Lamman M. Landriau J. Lasker J.M. Le Goff L. Le Guillou A. Leauthaud Q. Li W. Liu K. Lodha Y. Luo O. Manasoiu M. Manera P. Martini M. Maus A. Meisner R. Miquel J. Morawetz J. Moustakas E. Mueller P. Mukherjee A. Mu\~noz-Guti\'errez A. D. Myers S. Nadathur J. Najita G. Niz H. E. Noriega E. Paillas N. Palanque-Delabrouille J. Pan M. P. Ibanez W. J. Percival A. Porredon F. Prada H. Pulido-Hern\'andez A. P\'erez-Fern\'andez I. P\'erez-R\`afols A. Raichoor M. Rashkovetskyi J. Ratajczak C. Ravoux A. Robertson A. Rocher J. Rohlf A. J. Ross G. Rossi R. Ruggeri M. F. Ruiz-Herrera Bernal L. Samushia E. Sanchez C. Saulder D. Schlegel H. Seo A. Shafieloo R. Sharples J. Silber F. Sinigaglia M. Siudek T. Tan G. Tarl\'e W. Turner R. Vaisakh M. Vargas-Maga\~na B. A. Weaver M. Wolfson H. Yang J. Yu C. Y\`eche H. Zhang Y. Zhang R. Zhao R. Zhou
This is my paper
classification astro-ph.CO
keywords Lyman-alpha forestAlcock-Paczynski effectbaryon acoustic oscillationscosmological distancesdark energyexpansion historyHubble constantlarge-scale structure
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the full shape of Lyman-alpha forest correlations — not just the baryon acoustic oscillation peak — can measure the Alcock–Paczyński distortion of the cosmos at 1% precision. The distortion appears because angles and redshifts are converted into comoving distances using an assumed cosmology; if that assumption is wrong, structures look stretched along or across the line of sight. Using more than 820,000 forest spectra and 1.2 million quasars at effective redshift 2.33, the paper reports φs = 1.007 ± 0.011 for the broadband AP parameter, a 1.1% constraint on DM/DH. Combined with the BAO peak, this yields DM/rd = 39.32 ± 0.33 and DH/rd = 8.600 ± 0.066, where rd is the sound-horizon scale at the drag epoch — the tightest distance constraints from large-scale structure at z>1. The result matters because it anchors the expansion history deep in the matter-dominated era, where dark energy is subdominant, and it directly tests whether the low-redshift hints of evolving dark energy survive a high-redshift anchor.

Core claim

The paper's central claim is that the smooth, broadband part of the Lyman-alpha forest correlation functions carries a clean Alcock–Paczyński signal, independent of the BAO peak, and that measuring it delivers a 1.1% constraint on the distance ratio DM/DH at effective redshift 2.33: φs = 1.007 ± 0.011. This is roughly twice as tight as the BAO-only AP constraint from the same data. Combining the broadband AP with the BAO-peak parameters (φp = 1.001 ± 0.020, αp = 1.001 ± 0.006) gives DM(zeff)/rd = 39.32 ± 0.33 and DH(zeff)/rd = 8.600 ± 0.066, which the paper presents as the tightest distance constraints from large-scale structure at z>1. In ΛCDM, the Lyα result alone implies Ωm = 0.325 ± 0.01

What carries the argument

The argument hinges on treating the Lyman-alpha correlation model as a sum of a BAO peak and a smooth broadband component, each rescaled separately. The AP anisotropy is isolated by φ = q⊥/q∥ = (DM/DH)/(DM/DH)_fid, the ratio of scale factors perpendicular and parallel to the line of sight, while α = sqrt(q⊥q∥) absorbs the isotropic scale; the smooth component's φs is the new measurement. To keep that measurement clean, the analysis introduces small-scale marginalization: because fitting each quasar's continuum removes and mixes modes, the distortion matrix spreads power from small separations into all large-scale bins, so the model adds one free amplitude per small-scale bin in undistorted s

Load-bearing premise

The load-bearing premise is that one free amplitude per small-scale bin fully absorbs the small-scale power that continuum fitting leaks into the large-scale AP bins; the paper's evidence is mock-based, and the paper itself notes the mocks lack some real-data effects (CIV clustering, sky-subtraction subtleties, transverse proximity effects, uncertain HCD clustering) and that detailed validation is in an unpublished companion paper.

What would settle it

Fit the same DR2 correlation functions with a modified small-scale marginalization that splits each marginalized bin into two amplitudes (e.g., by sign of line-of-sight separation or by sub-bin within the transverse direction); if the recovered φs moves by more than 0.38% (one-third of the quoted statistical error) from 1.007, the single-amplitude leakage model is incomplete. A complementary check is to rerun the analysis on hydrodynamical-simulation mocks that include CIV clustering, sky noise, and transverse proximity effects and see whether φs remains unbiased at the same threshold.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The same survey data now yields a 1.0% combined AP constraint on DM/DH at z=2.33, about twice as tight as BAO alone, showing that the smooth component carries most of the geometric information in the Lyα forest.
  • Distance ratios DM/rd and DH/rd at z=2.33 reach 0.84% and 0.77% precision — better than the survey's original design requirement, reached with just three years of data.
  • Under ΛCDM, the Lyα measurement alone implies Ωm = 0.325 ± 0.018, and with a BBN prior gives H0 = 66.5 ± 1.3 km/s/Mpc, a ~2% Hubble constant determined without CMB anisotropies.
  • The high-redshift anchor pulls the low-redshift BAO results closer to CMB predictions, lowering the survey–CMB tension from 2.4σ to 2.2σ and the preference for w0wa dark energy from 3.2σ to 2.7σ (and from 3.4σ to 3.1σ when supernovae are added); the w0wa best fit lies about 2σ from the Lyα AP data point.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The quoted 1.4σ gap between Lyα Ωm (0.325 ± 0.018) and low-redshift BAO Ωm is currently inside the error budget; if it persists in the next data release, it would favour models that raise the matter density at high redshift (mildly massive neutrinos or dark energy acting before z≈2) over a simple ΛCDM-plus-systematics explanation.
  • The small-scale marginalization formalism transfers the systematic risk to a single assumption: that contamination is featureless within each small-scale bin. A natural, cheap test is to split the marginalized bins (e.g., by sign of line-of-sight separation or into sub-bins) and check for shifts beyond the 0.38% tolerance; that test could be run before the next data release without new observation
  • Because the broadband AP signal is about twice as tight as BAO on the same data, future survey design could prioritize the smooth-component signal; pushing the minimum scale below 30 h−1 Mpc with an emulator or effective-field-theory model is the most direct route to sub-percent distance ratios from the forest.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper presents an Alcock–Paczyński (AP) measurement from the full shape of DESI DR2 Lyman-alpha forest auto- and cross-correlation functions. The analysis uses a template split into a BAO peak component and a smooth broadband component, with scale parameters ϕp/αp for the peak and ϕs/αs for the broadband. Two methodological additions are introduced: a small-scale marginalization (SSM) formalism to remove contamination leaked by continuum fitting from small to large scales (Sec. III C, Appendix A), and a model for scale-dependent Lyα bias from UV background fluctuations (Sec. III D). The main new result is ϕs = 1.007 ± 0.011, a 1.1% constraint on DM/DH at zeff = 2.33. Combined with the BAO parameters this gives DM(zeff)/rd = 39.32 ± 0.33 and DH(zeff)/rd = 8.600 ± 0.066 (Eq. 26). In ΛCDM, the Lyα data alone yield Ωm = 0.325 ± 0.018, and with a BBN prior H0 = 66.5 ± 1.3 km/s/Mpc. The paper also reports updated constraints in extended models: the DESI-CMB tension decreases from 2.4σ to 2.2σ, and the preference for w0waCDM is 2.7σ with DESI+CMB and 3.2σ with DESI+CMB+SNe. Validation is based on two mock suites, a blinded analysis, and several data splits.

Significance. If correct, this is a significant result: it is the first 1%-level AP measurement at z > 2 from the Lyα forest alone, roughly twice as tight as the corresponding BAO-only AP constraint, and it provides the tightest large-scale-structure distance anchors at zeff = 2.33. The analysis has several strengths: it is blinded, uses a pre-registered 1/3-statistical validation threshold, checks convergence with conservative scale cuts, splits the data by SNR and by auto/cross-correlation, and reports a good fit (χ2_red ≈ 1.011, PTE = 0.20). The UVB fluctuation amplitude is measured at bΓ = 0.143 ± 0.047, in agreement with the theoretical expectation, providing a nontrivial falsifiable consistency check. However, the central systematic-error claim for ϕs relies heavily on the companion validation paper H26, which is currently unpublished, and on mock prescriptions whose realism the paper itself qualifies as incomplete. The significance is therefore conditional on the deferred validation being made available and passing scrutiny.

major comments (2)
  1. [Secs. III C, IV A, IV C; Appendix A] The primary new result ϕs = 1.007 ± 0.011 is enabled by the SSM formalism, which assigns one free amplitude per small-scale bin in undistorted space to absorb leakage from r < rmin. The paper states that this removes percent-level biases seen in AbacusSummit mocks and that the baseline scale cuts rmin = 30 (auto) and 40 h−1Mpc (cross) were validated. But the detailed validation—mock-population tests, scale-cut studies, and most model variations—is deferred to H26, listed as "in prep." The manuscript's own Sec. IV C lists missing realism in the mocks (CIV clustering, sky-contamination subtleties, transverse proximity effects, uncertain HCD clustering). Because no extra systematic is added to ϕs and the 1/3σ threshold is 0.38%, the claim that the error budget is complete cannot be verified from the submitted material. This is load-bearing: the SSM template assumption is exactly what protec
  2. [Sec. V B, Eqs. (20)–(23), Fig. 3] The mock validation finds a small but significant bias in the BAO AP parameter ϕp of about 0.8%, consistently in both AbacusSummit and CoLoRe mocks. The paper's response is to add Δϕp = 0.8% in quadrature to the covariance without shifting the central value. Inflating the uncertainty does not correct a known one-sided bias; if the true shift is of the order suggested by the mocks, the central values of the BAO parameters entering Eq. (26) remain offset by roughly that amount. This matters for the advertised joint distance ratios DM(zeff)/rd and DH(zeff)/rd. Please either apply a justified central correction, quote results both with and without such a correction, or demonstrate that the sign and magnitude of the shift are uncertain enough to justify treating it as a zero-mean systematic.
minor comments (4)
  1. [Sec. IV B, Fig. 4 caption] The caption contains a duplicated phrase: "cross-correlations in orange (orange)." Also, "two Lyα auto-correlations" should be "the two Lyα auto-correlations."
  2. [Sec. III D and Table V] The UVB bias parameter is written bΓ in the text and bγ in Table V. Please unify the notation.
  3. [References [27]–[29]] The three companion papers are all listed as "in prep." Given that H26 carries a substantial part of the validation, an arXiv number or a DOI should be provided before or at acceptance.
  4. [Sec. V A] The statement of the fit quality says χ2/(Ndata − Nparam) = 11492.0/(11388−21) = 1.011. Since 21 counts only the explicitly sampled parameters while 402 analytically marginalized amplitudes are subtracted from Ndata, please state this convention explicitly to avoid confusion.

Circularity Check

0 steps flagged

No significant circularity: broadband AP is an empirical fit with external mock validation; modeled parameters are not defined in terms of the target result.

full rationale

The paper's central claim (phi_s = 1.007 +/- 0.011) is obtained by fitting the Ly-alpha auto- and cross-correlation models of Eqs. (7)-(15) to 11,790 data points, with phi_s as a free scale parameter that rescales the smooth component (Section III A); no equation defines the data in terms of phi_s. The continuum-distortion projection (Eq. 2) and SSM marginalization (Eqs. 16-18) are nuisance treatments, and the paper demonstrates with AbacusSummit and CoLoRe mocks that the recovered phi_s is unbiased at r_min >= 30 h^-1 Mpc (Fig. 2). The UVB parameter b_Gamma = 0.143 +/- 0.047 is a free nuisance parameter compared to the external [65] prediction, not an input to the AP result, and the paper states it has no significant impact on AP constraints (Section III D). The distance ratios of Eq. (26) are a reparameterization of the fitted (phi_s, phi_p, alpha_p), which is a standard combination rather than a claim that these are independent predictions. The paper itself flags validation gaps: the detailed tests are deferred to the unpublished H26 companion paper, and the mocks are incomplete (missing CIV clustering, transverse proximity, sky-subtraction subtleties, uncertain HCD clustering; Section IV C). Those are completeness/robustness caveats, not circular reductions: no step of the derivation takes as input the value it claims to output, and no load-bearing self-citation is used to forbid alternative models. The result is an empirical measurement rather than a derivation, so no circularity score above 0 is warranted.

Axiom & Free-Parameter Ledger

17 free parameters · 8 axioms · 0 invented entities

No new particles, forces, dimensions, or physical entities are postulated; the UVB fluctuation term is a known physical effect (fluctuating photoionization rate) with an external theoretical prediction. The measurement rests on the standard Lyα template model anchored to a Planck ΛCDM fiducial, a set of nuisance parameters (21 fitted plus 402 SSM amplitudes), and the paper's own validation strategy, which depends on the realism of FGPA-based and 2LPT mocks.

free parameters (17)
  • ϕs (broadband AP) = 1.007 ± 0.011
    Main result: ratio of DM/DH relative to fiducial, fitted to the smooth component of the Lyα correlations (Table II).
  • ϕp (AP from BAO peak) = 1.001 ± 0.020
    AP parameter from the BAO peak, fitted jointly; systematic Δϕp = 0.8% added in quadrature (Table II, Sec. V B).
  • αp (isotropic BAO scale) = 1.0007 ± 0.0061
    Isotropic BAO scale relative to fiducial sound horizon (Table II).
  • αs (isotropic smooth scale) = 1.044 ± 0.036
    Isotropic scale of the smooth component; treated as a nuisance and marginalized, as in prior analyses (Sec. III A 1).
  • f (linear growth rate) = 1.43 (+0.17/−0.20)
    Growth rate in the quasar term of the cross-power spectrum; marginalized as nuisance after fσ8 was de-scoped pre-unblinding (Table V).
  • bF (Lyα bias) = −0.167 (+0.010/−0.015)
    Effective Lyα flux bias, free (Table V).
  • βF (Lyα RSD parameter) = 1.193 (+0.083/−0.12)
    Lyα RSD parameter, free; absorbs the unknown velocity-divergence bias bη (Table V).
  • bQ (quasar bias) = 3.49 ± 0.22
    Quasar linear bias, free (Table V).
  • σz (quasar redshift-error scale) = 4.8 ± 1.6 Mpc/h
    Lorentzian damping scale for quasar redshift errors and FoG in the cross-correlation (Eq. 10, Table V).
  • bΓ (UV background fluctuation bias) = 0.143 ± 0.046
    Amplitude of the scale-dependent Lyα bias from UVB fluctuations (Eq. 19); detected at 3–5σ; compared to a theory prediction of ≈0.13 (Sec. III D).
  • LHCD (undetected HCD absorber scale) = 4.9 ± 1.8 Mpc/h
    Exponential line-of-sight scale of undetected high-column-density absorbers, free (Table V).
  • bHCD, βHCD (HCD bias/RSD) = bHCD > −0.027; βHCD = 0.498 ± 0.089
    Bias and RSD of undetected HCDs, freed with priors (Table V).
  • Metal biases (SiII 1190/1193/1260, SiIII 1207, CIV) = ≈ −3.0 to −9.5 ×10⁻³ (Si); CIV = −19.8 ± 5.1 ×10⁻³
    Metal contamination amplitudes, free with priors; CIV uses a prior three times wider than the [60] measurement (Sec. III B 4, Table V).
  • ξTP0, anoise (proximity effect and sky noise) = ξTP0 < 0.24; anoise = 2.24 ± 0.2 ×10⁻⁴
    Amplitudes of the transverse proximity effect and correlated sky-noise templates, free (Sec. III B 5, Table V).
  • Small-scale nonlinearity parameters (q1, q2, kv, av, bv, kp) = q1=0.303, q2=0.267, kv=0.576, av=0.443, bv=1.66, kp=11.062
    Fixed to values from companion paper [29] (in prep); insensitivity tested by freeing them or removing the term entirely (Secs. III B 1, IV B).
  • UVB model constants (b′a, λ0, bs−ba) = b′a = −2/3, λ0 = 300h⁻¹Mpc, bs−ba = 1
    Fixed following [65]; small variations tested with no significant impact (Sec. III D).
  • 402 SSM template amplitudes = analytically marginalized
    One free amplitude per small-scale bin (r < r_min) in undistorted space; the paper argues each pairs with a fitted data bin so the effective number of degrees of freedom does not increase (Sec. III C).
axioms (8)
  • standard math The linear matter power spectrum template P_fid(k) computed with camb in the Planck ΛCDM fiducial cosmology (Table I) describes the shape of the Lyα correlations at z_eff = 2.33.
    Invoked in Eqs. (7)–(8); the AP signal is measured by rescaling this template.
  • domain assumption The observed correlation function is related to the true one by a pure coordinate rescaling q∥, q⊥ applied to both the peak and smooth components (Eqs. 3–6).
    The geometric Alcock–Paczyński premise, standard since [17] and used in [43].
  • domain assumption The projection matrices η (Eq. 2) and the distortion matrices D_MN (Eqs. 13–15) fully capture the correlation-function distortion caused by continuum fitting per forest.
    This is the established Lyα methodology from [41], used by prior DESI analyses; the new SSM is built on it.
  • domain assumption AP anisotropy and RSD anisotropy are separable for the Lyα forest at β ≈ 1.2, so marginalizing over RSD does not remove the AP signal.
    Argued in Sec. III A 2 and Figure 1, and validated on mocks; for galaxy tracers at low β this degeneracy is much stronger.
  • domain assumption The UV background fluctuation model of [65] with b′a = −2/3 and λ0 = 300h⁻¹Mpc describes the scale-dependent Lyα bias on the fitted scales.
    Adopted in Sec. III D; the fitted bΓ is consistent with the theory prediction, but the model form is an assumption.
  • ad hoc to paper The AbacusSummit (FGPA) and CoLoRe 2LPT mocks reproduce the real data's small-to-large-scale leakage well enough that the 1/3 statistical threshold on mock bias bounds the real-data systematic.
    This is the paper's core validation strategy (Sec. IV); the paper itself lists real effects absent from mocks (CIV clustering, sky, transverse proximity, UVB) and warns of a future systematic floor.
  • ad hoc to paper The systematic budget for the BAO parameters is captured by adding Δαp = 0.15% and Δϕp = 0.8% in quadrature without shifting the central value.
    Sec. V B: chosen from mock biases whose direction disagrees with EFT predictions [72, 73], and explicitly acknowledged as a judgment call.
  • domain assumption Interpreting the measured distances in terms of Ωm, H0, neutrino masses, or w0wa requires assuming ΛCDM or the CPL parametrization and standard pre-recombination physics (via the BBN prior).
    Used throughout Sec. VI when converting distances to cosmological parameters.

pith-pipeline@v1.3.0-daily-deepseek · 50721 in / 20580 out tokens · 218226 ms · 2026-08-01T07:46:08.341515+00:00 · methodology

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read the original abstract

We present Alcock-Paczy\'nski (AP) measurements from the full shape of Lyman-$\alpha$ (Ly$\alpha$) forest correlation functions measured from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI). Our measurements include information from the Ly$\alpha$ forest auto-correlation and its cross-correlation with quasars. We constrain the AP effect with $1\%$ precision at an effective redshift $z_\mathrm{eff}=2.33$, which is twice as tight as the Baryon Acoustic Oscillation (BAO) constraint from the same data. When using the joint Ly$\alpha$ AP and BAO results, we measure the ratios $D_\text{H}(z_\mathrm{eff})/r_\text{d}=8.600 \pm 0.066$ and $D_\text{M}(z_\mathrm{eff})/r_\text{d}=39.32 \pm 0.33$, where $D_\text{M}$ is the transverse comoving distance, $D_\text{H}$ is the Hubble distance, and $r_\text{d}$ is the sound horizon at the drag epoch. Assuming $\Lambda$CDM, Ly$\alpha$ forest measurements combined with a nucleosynthesis prior produce a constraint on the Hubble constant $H_0=66.5\pm1.3\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. The Ly$\alpha$ AP result corresponds to a matter fraction constraint $\Omega_\text{m}=0.325\pm0.018$ in $\Lambda$CDM, which is $1.4\sigma$ higher than DESI BAO. This impacts the DESI results relative to the Cosmic Microwave Background (CMB), slightly reducing their discrepancy from $2.4\sigma$ to $2.2\sigma$. We present updated constraints on extended models using the joint DESI DR2 BAO and Ly$\alpha$ forest full shape data, together with external data sets. When considering a time-evolving dark energy equation of state parametrized by $w_0$ and $w_a$, we find it is preferred over $\Lambda$CDM at $2.7\sigma$ for the combination of DESI and CMB data, and at $3.2\sigma$ when also including supernovae. With the new Ly$\alpha$ AP measurement, DESI provides its most precise anchor for the expansion history at $z > 1$ in the matter-dominated Universe.

Figures

Figures reproduced from arXiv: 2607.27410 by A. Anand, A. Aviles, A. Bault, A. Brodzeller, A. Carnero Rosell, A. Cuceu, A. de la Macorra, A. Dey, A. D. Myers, A. Font-Ribera, A. J. Ross, A. Kremin, A. Krolewski, A. Leauthaud, A. Meisner, A. Mu\~noz-Guti\'errez, A. P\'erez-Fern\'andez, A. Porredon, A. Raichoor, A. Robertson, A. Rocher, A. Shafieloo, A. X. Gonzalez-Morales, B. A. Weaver, B. Hadzhiyska, C. Blake, C. Garcia-Quintero, C. Gordon, C. Hahn, C. Lamman, C. Ravoux, C. Saulder, C. S. Frenk, C. Y\`eche, D. Bianchi, D. Brooks, D. Chebat, DESI Collaboration: A. G. Adame, D. Forero-S\'anchez, D. Green, D. Huterer, D. J. Eisenstein, D. Kirkby, D. Schlegel, E. Armengaud, E. Chaussidon, E. Fern\'andez-Garc\'ia, E. Mueller, E. Paillas, E. Sanchez, F. Beutler, F. J. Castander, F. Prada, F. Sinigaglia, G. Farren, G. Gambardella, G. Gutierrez, G. Niz, G. Rossi, G. Tarl\'e, H. Ebina, H. E. Noriega, H. Gil-Mar\'in, H. K. Herrera-Alcantar, H. Pulido-Hern\'andez, H. Seo, H. Yang, H. Zhang, I. P\'erez-R\`afols, J. Aguilar, J. Chaves-Montero, J. Della Costa, J. E. Forero-Romero, J. Guy, J. Hou, J. Lasker, J.M. Le Goff, J. Morawetz, J. Moustakas, J. Najita, J. Pan, J.-Q. Jiang, J. Ratajczak, J. R. Bermejo-Climent, J. Rohlf, J. Silber, J. Yu, K. Carrion, K. Honscheid, K. Lodha, K. S. Dawson, L. Casas, L. H. Garrison, L. Le Guillou, L. Samushia, M. Bonici, M. Doshi, M.-F. Ho, M. F. Ruiz-Herrera Bernal, M. Herbold, M. Ishak, M. Landriau, M. Manera, M. Maus, M. P. Ibanez, M. Rashkovetskyi, M. Siudek, M. Vargas-Maga\~na, M. Wolfson, N. G. Kara\c{c}ayl{\i}, N. Palanque-Delabrouille, N. V. Kamble, O. Alves, O. Lahav, O. Manasoiu, P. Bansal, P. Martini, P. Mukherjee, Q. Li, R. de Belsunce, R. Gsponer, R. Miquel, R. Ruggeri, R. Sharples, R. Vaisakh, R. Zhao, R. Zhou, S. Ahlen, S. Avila, S. Blasby, S. Brieden, S. Ferraro, S. Gontcho A Gontcho, S. He, S. Jos, S. Juneau, S. Nadathur, T. Claybaugh, T. Karim, T. M. Davis, T. Tan, U. Andrade, V. A. Fawcett, V. Ir\v{s}i\v{c}, W. Elbers, W. J. Percival, W. Liu, W. Turner, X. Chen, Y. Cho, Y. Luo, Y. Zhang, Z. Chen.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of parameter sensitivity in configura [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Broadband AP constraints in mocks relative to the [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. BAO constraints in mocks. The gray dashed con [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Wedge compression of the Ly [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Shell compression of the Ly [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Constraints on the distance pair ( [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Constraints on the transverse comoving dis [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. 68% and 95% confidence contours on the dark [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Marginalized posterior distributions for the sum of [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Marginalized constraints in the Ω [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Measurements of cosmological distances, [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Fractional contributions to one bin of the distorted [PITH_FULL_IMAGE:figures/full_fig_p033_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Best-fit model compressed into wedges as a function [PITH_FULL_IMAGE:figures/full_fig_p034_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Constraints on the dark energy equation of state [PITH_FULL_IMAGE:figures/full_fig_p035_16.png] view at source ↗

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