2000 character limit reached
Cosmological constraints from the DESI DR1 Bispectrum Full-Shape and DR2 BAO
Published 22 Jun 2026 in astro-ph.CO | (2606.23936v1)
Abstract: We present cosmological constraints from the combination of DESI DR1 full-shape measurements, including for the LRG bispectrum, and DESI DR2 BAO data. The joint analysis accounts for cross-covariance using mocks, while ShapeFit compression mitigates prior volume effects that hinder beyond-$Λ$CDM analyses. In $Λ$CDM, the bispectrum (P+B) shifts $σ8$ up by $1.1σ$ and $S_8$ by $1.2σ$, reducing their uncertainties by $26\%$ and $28\%$, respectively. For $w_0w_a$CDM, DESI-only analyses with the bispectrum shift dark energy parameters toward $Λ$CDM, staying consistent with a cosmological constant within $1σ$. Adding CMB creates a preference for evolving dark energy: DESI+CMB (P+B) shows a $2.8σ$ deviation from $Λ$CDM. Including DES-Dovekie supernovae alone reduces this to $1.6σ$, while the full combination DESI+CMB+DES-Dovekie gives $3.1σ$, driven primarily by the CMB. The bispectrum consistently weakens evidence for time-varying dark energy relative to power-spectrum-only analyses. The bispectrum also enhances sensitivity to massive neutrinos: in DESI-only analysis, the power-spectrum-only posterior for $\sum mν$ is consistent with zero, whereas adding the bispectrum yields a mean of $0.26\pm0.17$~eV and a $95\%$ upper limit of $0.57$~eV, shifting the peak into the positive region and agreeing with oscillation lower bounds. For modified gravity, the bispectrum further constrains $μ_0 = 0.12\pm0.49$ from DESI-only data, consistent with general relativity. Our analysis shows that accounting for cross-dataset covariances and avoiding prior volume effects yields robust constraints, with the bispectrum raising amplitude parameters and tightening their uncertainties.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Explain it Like I'm 14
What this paper is about (big picture)
Scientists used maps of galaxies from the DESI project to learn more about what the Universe is made of and how it’s growing. They combined two kinds of DESI measurements:
- DR2 BAO (a very precise way to measure cosmic distances), and
- DR1 “full-shape” clustering that includes not only pairs of galaxies (the power spectrum) but also triangles of galaxies (the bispectrum).
By mixing these together carefully—and by accounting for how the two datasets overlap—they tightened the limits on key cosmic ingredients like matter, dark energy, and neutrino masses.
What questions the researchers asked
In simple terms, they wanted to know:
- How fast and in what way is the Universe expanding?
- How “clumpy” is matter today, and how does that clumpiness grow over time?
- Is dark energy (the thing speeding up the Universe’s expansion) constant, or does it change over time?
- How heavy are neutrinos, the tiny “ghost” particles that pass through almost everything?
- Is Einstein’s gravity still the best description on the largest scales we can see?
How they did it (with everyday analogies)
To answer these questions, they used several tools and tricks:
- BAO as a “standard ruler”: In the early Universe, sound waves left behind a faint “ripple” pattern in how galaxies are arranged, like ripples on a pond that froze in place. Measuring the spacing of these ripples (called BAO, for Baryon Acoustic Oscillations) lets you figure out distances in the Universe very accurately—like using a known-length ruler on a far-away object.
- Power spectrum (pairs) and bispectrum (triangles):
- Power spectrum: Imagine a starry sky made of galaxy “dots.” The power spectrum measures how clumpy the dots are at different sizes—pairs of points at many separations.
- Bispectrum: Now don’t just look at pairs—look at triangles formed by three galaxies. The shapes and sizes of these triangles reveal extra information about how structures grow and which physics is at work. The bispectrum helps untangle things that look the same to the power spectrum alone.
- “ShapeFit” compression: Think of a long novel (the raw data) summarized into a clear one-page outline. ShapeFit compresses the detailed clustering into a small set of “summary” numbers that still capture the most important physics (like the overall scale, growth rate, and shape). This keeps the analysis accurate but avoids getting lost in unnecessary details.
- Mock universes: They generated many realistic “fake” Universe maps (mocks). These help estimate uncertainties and, importantly, how the DR1 (full-shape) and DR2 (BAO) measurements are correlated because DR1 is part of DR2. It’s like practicing an experiment many times to understand how results can wiggle around by chance.
- Careful combinations: They combined different tracers of the Universe (different types of galaxies and the Lyman-alpha forest, which is a pattern of absorption in quasar light) and also tested how results shift when adding outside information like the CMB (the Universe’s baby picture) and supernova distances.
What they found and why it matters
Here are the key results, with why each is important:
- Adding the bispectrum strengthens results
- Main idea: When they included triangles (the bispectrum) along with pairs (the power spectrum), estimates of “amplitude” quantities—how clumpy the Universe is today—moved slightly upward and became more precise.
- Why it matters: More precise measurements help distinguish between explanations for cosmic acceleration, structure growth, and particle properties.
- ΛCDM (the standard model) remains a good fit with DESI alone
- With DESI data by itself (plus very light external priors), the results are consistent with a simple, constant dark energy (a cosmological constant, Λ). The bispectrum pulls the answers even closer to this simple model and shrinks errors by about a quarter for some amplitude parameters.
- Why it matters: It strengthens confidence that DESI’s more advanced measurements (including triangles) don’t introduce weird biases and that the standard model still works well with galaxy clustering alone.
- Time-varying dark energy: mixed signals when adding other data
- With DESI + CMB, there is a statistical hint that dark energy might change over time (a deviation from the simple constant model). But when they include the new DES-Dovekie supernova set alone, that hint gets weaker; when all three (DESI + CMB + supernovae) are combined, the evidence grows again and is mostly driven by the CMB.
- Why it matters: Whether dark energy changes over time is a huge question. These results say: DESI alone is fine with a constant dark energy; adding other datasets can suggest change, but the bispectrum tends to reduce the push away from the simple model. It encourages caution and more cross-checks.
- Neutrino masses: DESI-only prefers a positive mass
- Using DESI alone, the power-spectrum-only analysis was happy with a near-zero total neutrino mass. When they added the bispectrum, the best estimate shifted to a small positive value with a 95% upper limit below about 0.6 eV, consistent with what we know from neutrino oscillation experiments (which require a non-zero minimum).
- When the CMB is added, the combined limit becomes very tight and prefers very low masses, which can nudge against the lower bounds from oscillation experiments depending on exactly which CMB settings are used.
- Why it matters: Neutrino masses are fundamental physics. The bispectrum helps DESI’s galaxy data “see” those tiny effects better, making galaxy maps a competitive way to weigh neutrinos.
- Gravity tests: still consistent with Einstein
- A modified-gravity parameter (think of it as a dial for “how gravity behaves on cosmic scales”) comes out consistent with general relativity.
- Why it matters: Tests of gravity on the biggest scales support Einstein’s theory so far.
- Methodological win: accounting for overlap and avoiding “prior traps”
- They modeled the correlation between DR1 and DR2 datasets and used the ShapeFit summary to avoid accidentally letting “prior choices” overly steer the result.
- Why it matters: It’s not just what data you have, but how carefully you combine it. This makes the conclusions more trustworthy.
What this means going forward
- DESI’s triangle information (the bispectrum) is not just a fancy add-on; it meaningfully improves how well we can measure how clumpy the Universe is and how structures grow.
- With DESI alone, the simplest model—ΛCDM with a constant dark energy—continues to fit very well, and the bispectrum reduces any pull toward more complicated dark energy stories.
- The DESI bispectrum helps weigh neutrinos better using galaxy maps alone, pushing the most likely values into the positive (physically expected) range.
- When combining DESI with other powerful datasets (like the CMB and supernovae), hints of evolving dark energy can appear—but the bispectrum tends to soften those hints. This tells scientists to keep refining methods, compare different CMB analyses, and add more data to reach a stable answer.
Overall, the study shows that smarter use of galaxy maps—counting not just pairs but also triangles—gives clearer, tighter clues about what our Universe is made of and how it’s changing.
Knowledge Gaps
Unresolved gaps, limitations, and open questions
The following points summarize what remains missing, uncertain, or left unexplored in the paper, phrased to guide concrete follow-up work:
- Limited tracer coverage of the bispectrum: only LRG bispectra are used; ELG and QSO bispectra are excluded due to systematics or low S/N. Develop mitigation and modeling to incorporate ELG/QSO bispectra and assess their incremental cosmological leverage.
- Incomplete use of BGS information: BGS contributes only BAO because DR2 BGS EZmocks were not generated. Produce DR2-quality BGS mocks to enable inclusion of BGS full-shape (P and B) and quantify its impact.
- Lyman-α full-shape use is restricted: the adopted Lya-FS likelihood contributes only geometric AP constraints (via DH/DM) from external work. Extend to include growth-sensitive information (e.g., RSD-like parameters) and assess cross-covariance with galaxy samples.
- Bispectrum modeling limited in k-range and content: GEO-FPT is used only up to k ≈ 0.12 h/Mpc with the bispectrum monopole. Test robustness to:
- higher kmax and additional triangle configurations,
- inclusion of bispectrum quadrupole (and higher multipoles),
- alternative bispectrum models (EFT-based, emulators), and
- explicit theoretical-error budgets on P and B.
- Power spectrum modeling choices not fully stress-tested: the analysis uses RPT (not EFT) and adds P4 to the data vector. Quantify sensitivity of cosmological posteriors to alternative theory choices (EFT vs RPT), scale cuts, and inclusion/exclusion of P4.
- Restrictive galaxy-bias treatment: a coevolution bias model is assumed. Evaluate impacts of a more flexible bias model (b1, b2, bs2, b3nl, velocity bias, stochastic terms, redshift evolution, assembly bias) on the recovered f, σ8, and w0–wa constraints.
- Covariance accuracy and stability: the compressed-space covariance uses ~100 mocks and mixes mock-derived cross-blocks with data-derived auto-blocks; no explicit precision-matrix corrections are described. Validate with:
- larger mock ensembles and/or shrinkage estimators,
- analytic covariance models for P–B–BAO in compressed space, and
- N-body–calibrated mocks to verify bispectrum and non-Gaussian covariances.
- Cross-bin and cross-tracer correlations: redshift bins are treated as independent; quantify inter-bin and inter-tracer correlations in compressed parameters (especially for overlapping volumes) and their effect on cosmology.
- Cross-dataset covariances are only partially addressed: DR1 FS × DR2 BAO cross-covariance is modeled for LRGs, but cross-covariances involving BGS, Lya-FS, SNe, or between different DESI tracers are not explicitly treated. Assess whether ignoring these induces biases at the current precision.
- Sensitivity to external priors: results rely on a BBN prior with fixed Neff = 3.044 and a broadened Planck-informed ns prior. Quantify sensitivity to:
- alternative BBN calibrations and nuclear cross-section uncertainties,
- freeing Neff (and Yp) jointly with DESI data, and
- loosening/tightening the ns prior or inferring ns from DESI full-shape alone.
- Model-selection methodology: the paper reports DIC-based preferences that differ from Bayesian evidence results in the literature. Perform full evidence calculations (e.g., nested sampling) for all dataset combinations and models (ΛCDM, w0waCDM, νΛCDM, etc.) to robustly assess model preference.
- Neutrino mass inference is CMB-likelihood dependent: DESI-only prefers a positive ∑mν, while CMB combinations push toward low masses. Systematically test:
- alternative CMB likelihoods (Planck PR3 vs PR4 CamSpec; ACT/SPT), lensing reconstructions, and A_L variations,
- consistency with oscillation lower bounds under different CMB assumptions, and
- LSS-only constraints (DESI + weak lensing) to cross-validate CMB-driven results.
- Modified gravity analysis is minimal: the abstract reports a constraint on a single MG parameter (p0), but details are sparse. Extend to scale- and time-dependent MG parameters (e.g., μ(z,k), Σ(z,k), γ) with consistent modeling of bias, RSD, and bispectrum, and assess the bispectrum’s unique constraining power on gravitational slip.
- Primordial non-Gaussianity is not explored: the bispectrum offers sensitivity to fNL (local/equilateral/orthogonal). Develop a pipeline for PNG constraints (including systematics control and covariance) and quantify attainable precision with current DESI data.
- Systematic-error treatment for bispectrum is limited: while [28]’s systematic budget is adopted, additional DESI-specific systematics (fiber assignment, redshift failures, imaging depth/selection inhomogeneities) require dedicated null tests and end-to-end injections to ensure they do not bias P–B compressed parameters.
- Potential S8 tension is not jointly addressed: the raised S8 (vs DES Y6) is noted but not analyzed in a joint framework. Perform combined analyses with weak-lensing datasets (DES/KiDS/HSC), including cross-covariance where relevant, to adjudicate the tension and sources of discrepancy.
- Information loss and prior-volume mitigation with ShapeFit: while ShapeFit aims to mitigate prior-volume effects, a quantitative audit of information loss vs full modeling (FM) across extended models is not provided. Calibrate compression fidelity with controlled synthetic tests and end-to-end recovery on mocks.
- Lya-FS likelihood reuse and independence: the Gaussian compressed Lya-FS likelihood from external work is adopted without recomputation. Verify independence from the DESI BAO2 likelihood used here (avoid double-counting) and test non-Gaussianity of its posteriors.
- Parameterization choices for dark energy: strong w0–wa anti-correlations persist. Explore pivoted parameterizations (wp, wa) and redshift-evolving growth tests to isolate physically interpretable directions and reduce projection effects.
- Baryonic effects and small-scale systematics: even with kmax = 0.12–0.15 h/Mpc, residual baryonic feedback and non-linearities can affect P and B. Include baryonic uncertainty models or emulator-based corrections and test sensitivity of cosmological inferences.
- Roadmap for DR2 full-shape and higher S/N: results are based on DR1 FS; forecast and validate how DR2 FS (and future releases) with improved bispectrum S/N alter constraints, especially for w0–wa and ∑mν, under the improved covariance and systematics models above.
Practical Applications
Immediate Applications
The paper introduces analysis techniques and results that can be deployed now to improve inference, workflows, and decision-making in cosmology and allied data-intensive fields. The following bullets summarize concrete use cases, their sectors, and key dependencies.
- DESI-style joint large-scale structure (LSS) inference using ShapeFit compression and bispectrum
- What: Adopt the ShapeFit-based, model-agnostic compression of full-shape power spectrum plus bispectrum (P+B) measurements, with proper cross-covariance handling between overlapping datasets (e.g., DR1 FS and DR2 BAO).
- Why: Breaks the f–σ8 degeneracy, tightens amplitude constraints (≈20–30%), and reduces prior-volume artifacts in extended cosmologies.
- How/Tools: desilike and Cobaya likelihoods; Brass for P+B; GEO-FPT (bispectrum modeling) and RPT (power spectrum) up to stated k-ranges; EZmocks-based cross-covariance in compressed space.
- Sector: Academia (cosmology/astrophysics), Software/Data.
- Dependencies/Assumptions: Validity of Gaussian likelihood in compressed space; fidelity of EZmocks for cross-covariance; modeling validity ranges (P up to k≈0.2 h/Mpc; B up to k≈0.12 h/Mpc); systematic error budgets.
- Immediate integration of Lyman-α full-shape AP constraints at z≈2.33
- What: Include Lyman-α FS geometric information (DH/DM) with BAO in joint fits to boost high-z distance precision (~2.4× over BAO-only).
- Sector: Academia (cosmology), Software/Data.
- Dependencies: Use of the provided Gaussian compressed likelihood and covariance; consistent combination with DESI BAO/FS.
- Safer extended-cosmology studies (w0waCDM, curvature, modified gravity) with reduced prior-volume effects
- What: Use ShapeFit compression to mitigate prior-driven biases in beyond-ΛCDM analyses; adopt bispectrum to pull posteriors toward ΛCDM when P-only analyses weakly prefer evolving dark energy.
- Why: Robustness when combining DESI with CMB and SNe; better separation of real signal vs. prior/degeneracy artifacts.
- Sector: Academia (cosmology), Policy (program review panels, collaborations).
- Dependencies: Minimal priors (BBN on ωb, broad ns) where possible; careful choice and disclosure of CMB likelihoods (Planck PR3/PR4 Plik vs CamSpec) and lensing data; evidence-based model comparison in addition to DIC.
- Neutrino mass sensitivity from LSS with bispectrum
- What: Use DESI P+B to improve cosmological sensitivity to ∑mν and move the posterior peak into the positive-mass region (DESI-only: mean 0.26 ± 0.17 eV; 95% CL < 0.57 eV).
- Why: Informs joint cosmology–particle physics analyses; helps set informative priors or consistency checks for lab experiments.
- Sector: Academia (cosmology, particle physics), Policy (experiment planning).
- Dependencies: Strong sensitivity to CMB likelihoods and σ8/Ωm interplay; careful degeneracy management; consistency with oscillation bounds.
- Cross-covariance-aware data combination workflows
- What: Implement cross-covariance estimation via mocks in compressed space for partially overlapping samples (e.g., DR1 vs DR2), avoiding subtle biases in amplitude-sensitive parameters.
- Why: The paper shows biases at the ~0.4σ level when cross-covariance is ignored; these can propagate into neutrino mass and dark energy inferences.
- How/Tools: “Compressed-parameter” covariance builder using phase-matched mocks; plug-ins for desilike/Cobaya.
- Sector: Academia (all large surveys), Software/Data (analytics pipelines), Finance (see below).
- Dependencies: Adequate number and fidelity of mocks; stable compression mapping.
- Rapid performance wins: fewer mocks needed via compressed-space covariance
- What: Move from bandpower-space to compressed-parameter-space covariance estimation to reduce computational cost by orders of magnitude—especially for bispectrum.
- Sector: Academia (HPC reduction), Software/Data (cost optimization).
- Dependencies: Verified equivalence of compressed covariance to bandpower outcomes within targeted accuracy.
- Immediate cross-domain analytics: higher-order statistics for non-Gaussian signals
- What: Port the “bispectrum mindset” to domains with complex fields where non-Gaussianity matters (e.g., Earth observation imagery, materials/defect characterization, neuro/medical imaging, seismology).
- Why: Three-point statistics can break degeneracies that two-point-only pipelines cannot; better anomaly detection and parameter disentanglement.
- Sector: Software/Data, Healthcare (medical imaging analytics), Geospatial/Climate, Materials.
- Dependencies: Domain-specific modeling of 3-point functions; validation datasets; computational kernels for 3-point estimators.
- Risk and portfolio analytics with overlapping datasets
- What: Adopt compressed-factor cross-covariance estimation and bias checks when fusing partially overlapping financial datasets (legacy + new feeds), analogous to DR1–DR2 overlap.
- Why: Avoid under/over-estimated risks when cross-data dependencies are ignored; scalable with limited samples via compression.
- Sector: Finance.
- Dependencies: Appropriate factor compression; resampling/mocking strategy matching market dynamics.
- Training and reproducibility
- What: Use this pipeline as a teaching module on degeneracy-breaking (P vs P+B), prior-volume effects, and model comparison (DIC vs evidence); publish compressed likelihoods and code configs.
- Sector: Academia/Education.
- Dependencies: Open access to DESI likelihoods, Brass, desilike configurations; reproducible seeds for mocks and MCMC.
Long-Term Applications
These opportunities require additional research, engineering, scaling, or standardization before broad deployment.
- Next-generation survey design optimized for bispectrum science
- What: Incorporate bispectrum signal-to-noise forecasts into fiber assignment, target density, triangle-configuration coverage, and redshift bin design (DESI extensions, Euclid, Rubin spectroscopy, Subaru/PFS, MegaMapper).
- Outcome: Hardware and observing strategies explicitly tuned to higher-order statistics; improved constraints on growth, neutrino mass, and modified gravity.
- Sector: Academia (instrumentation), Policy (facility roadmaps).
- Dependencies: Fast bispectrum estimators, robust systematics control, end-to-end simulations.
- Standardization of cross-covariance practices in compressed space
- What: Community-endorsed protocols, benchmarks, and FAIR repositories for compressed-parameter mocks, covariances, and systematics budgets across multi-probe analyses (BAO, FS, SNe, CMB lensing).
- Outcome: Interoperable likelihoods; lower barrier for multi-collaboration data fusion; fewer contradictory claims.
- Sector: Academia/Policy (collaboration governance).
- Dependencies: Cross-survey working groups; sustained support for mock production and validation.
- Industrial-grade “ShapeFit-like” model-agnostic compression libraries
- What: General-purpose software to decouple data compression from model inference, reducing prior sensitivity and compute; pluggable into Bayesian engines (Cobaya, Stan, NumPyro) and ML pipelines.
- Outcome: Products for multi-sensor data fusion in healthcare imaging, climate risk analytics, energy-grid monitoring, and industrial IoT.
- Sector: Software/Data, Healthcare, Energy, Geospatial/Climate, Manufacturing.
- Dependencies: Domain-specific summary-statistic design; explainability tooling; certification/regulatory validation in sensitive domains.
- Real-time, cross-instrument data assimilation with cross-covariance awareness
- What: Streaming pipelines that estimate and update cross-covariances for overlapping data sources on the fly, using compressed statistics and GPU/ASIC acceleration (e.g., scientific real-time alerting systems).
- Outcome: Faster, more reliable multi-probe inference; readiness for next-decade datasets (CMB-S4, SKA, Rubin).
- Sector: Software/Data (streaming analytics), Academia (time-domain astronomy).
- Dependencies: Robust incremental estimators; scalable GPU kernels for 3-point statistics; low-latency mock/emulator surrogates.
- AI/ML emulators and amortized inference for P+B
- What: Train emulators for GEO-FPT/RPT summaries and their covariances; use simulation-based inference to extend k-reach and speed up posteriors; integrate with normalizing flows or diffusion models for summary compression.
- Outcome: Order-of-magnitude speed-ups; better systematic control; feasibility of broader triangle sets in bispectrum.
- Sector: Software/Data, Academia (astrostatistics/ML).
- Dependencies: High-fidelity training sets; robust uncertainty quantification for emulators.
- Coordinated neutrino physics strategy
- What: Use joint cosmology+lab (KATRIN, Project 8, JUNO, DUNE, 0νββ) roadmaps informed by cosmological ∑mν sensitivity with P+B; align target sensitivities and timelines.
- Outcome: Efficient global investment; cross-validation between cosmology and terrestrial experiments.
- Sector: Policy (funding agencies, international labs), Academia (particle physics).
- Dependencies: Resolution of CMB likelihood/systematics tensions (e.g., lensing anomaly); agreement on priors and combinations.
- Robotics, 3D mapping, and geospatial analytics using 3-point spectral features
- What: Explore bispectrum-like features for point cloud SLAM, loop-closure robustness, and anomaly detection in LiDAR/SAR datasets; extend to urban-scale mapping.
- Outcome: Degeneracy-breaking features beyond pairwise correlations; improved resilience to noise and non-Gaussian artifacts.
- Sector: Robotics, Geospatial.
- Dependencies: Algorithmic adaptation to discrete, irregular point sets; real-time constraints; dataset benchmarks.
- Evidence-driven policy for dark energy and multi-probe combinations
- What: Encourage full Bayesian evidence calculations (beyond DIC) in official combinations; prioritize SNe calibration improvements and CMB systematics (e.g., lensing) to resolve model preferences.
- Outcome: More reliable claims about evolving dark energy; consistent public messaging.
- Sector: Policy (collaboration analysis standards).
- Dependencies: Compute resources; community consensus; robust, transparent likelihoods and priors.
Notes on assumptions and dependencies that affect feasibility
- Data availability and quality: Reliance on DESI DR1/DR2, Lyman-α FS, SNe (DES-Dovekie), and specific CMB likelihoods; future extensions depend on forthcoming releases and calibrations.
- Modeling validity: GEO-FPT and RPT accuracy holds to stated k-cuts; bispectrum model/systematics must be validated per tracer (e.g., ELG/QSO not yet robust for B).
- Likelihood form: Gaussian approximations in compressed space work within demonstrated regimes; departures may require alternative likelihoods or transformation.
- Mocks and systematics: Cross-covariance accuracy hinges on mock fidelity; systematic error budgets must be kept in step with model/estimator improvements.
- Compute and engineering: Scaling to real-time or broader triangle sets requires GPU/accelerator development and ML surrogates.
- Cross-survey governance: Standards and evidence practices need buy-in from collaborations and funding agencies to be effective.
Glossary
- ACT-DR6: The sixth data release of the Atacama Cosmology Telescope, providing CMB lensing and related measurements. Example: "the Atacama Cosmology Telescope Data Release 6 (ACT-DR6) [43-45]."
- Alcock–Paczynski (AP) effect: A geometric distortion in observed clustering due to assuming an incorrect cosmology when converting redshifts to distances. Example: "provide constraints on the Alcock-Paczynski (AP) effect rather than to constrain growth"
- Alcock–Paczynski anisotropy parameter qap: The parameter encoding anisotropic scaling between radial and transverse distances used in AP tests. Example: "OSF = {qiso, qap, dm, f, fos8}"
- BAO2: The analysis using DESI DR2 BAO data alone. Example: "When using DR2 BAO data alone, this is labeled as BAO2."
- Baryon Acoustic Oscillation (BAO): A periodic feature in the matter distribution from early-universe sound waves, used to measure cosmic distances. Example: "mapping the Baryon Acoustic Oscillation (BAO) feature in the clustering of each tracer."
- Big Bang Nucleosynthesis (BBN): The process that produced light elements in the early universe, used to constrain the baryon density. Example: "The wb prior is informed by Big Bang Nucleosynthesis (BBN) constraints from [38]"
- bispectrum: The three-point correlation in Fourier space, sensitive to non-Gaussianity and parameter degeneracies. Example: "The bispectrum, in particular, has long been recognized as a key statistic to break parameter degeneracies"
- Brass: A code used to sample the ShapeFit posterior including bispectrum data. Example: "we use the code Brass6 to sample the SF posterior when including the bispectrum."
- CamSpec: A Planck CMB likelihood suite (PR4) used for cosmological inference, particularly with extended models. Example: "we switch to the CamSpec likelihoods from Planck PR4 [40, 41]"
- CMB lensing: The deflection of CMB photons by large-scale structure, reconstructed to add information on matter distribution. Example: "we supplement the primary temperature/polarization likelihood with reconstructed CMB lensing information."
- compressed parameter space: A reduced set of summary statistics (e.g., qiso, qap, f, fos8) used instead of full spectra to simplify inference and covariance estimation. Example: "in the compressed parameter space."
- CPL parametrization: The Chevallier–Polarski–Linder model for dynamical dark energy, w(a)=w0+wa(1−a). Example: "When assuming a model with dynamical dark energy, we use the CPL [67, 68] parametrization."
- cross-covariance: Statistical covariance between different datasets or statistics (e.g., DR1 FS and DR2 BAO) that must be accounted for in joint analyses. Example: "The joint anal- ysis accounts for cross-covariance using mocks"
- DES-Dovekie: A reanalyzed DES Type Ia supernova sample with improved calibration and modeling. Example: "Additionally, we make use of the updated Type Ia supernova (SNe Ia) sample from the Dark Energy Survey, referred to as DES-Dovekie"
- DESI: The Dark Energy Spectroscopic Instrument, a large spectroscopic survey of galaxies and quasars. Example: "The Dark Energy Spectroscopic Instrument (DESI) [1-3] has surveyed the sky with unprecedented precision"
- desilike: A framework for sampling cosmological likelihoods, used for BAO parameter inference. Example: "We sample the posterior distribution of BAO parameters using the desilike framework3"
- Effective Field Theory (EFT): A perturbative approach to model large-scale structure beyond linear theory. Example: "the power spectrum is computed using the Renormalized Perturbation Theory (RPT) instead of EFT"
- EZmocks: Fast mock catalogues used to estimate covariances and test pipelines. Example: "we employ the DESI EZmock suite [33-35], which comprises one thousand mocks per galactic cap"
- full modeling (FM): Direct fitting of perturbation-theory predictions to two-point statistics, often requiring informative priors. Example: "employed a 'full modeling' (FM) approach, directly fitting perturbation-theory predictions"
- Full-Shape (FS): Use of the broadband shape of clustering statistics (power spectrum and/or correlation function) beyond the BAO peak. Example: "additional cosmological information resides in the Full-Shape (FS) of the galaxy power spectrum"
- GEO-FPT: A bispectrum model extending tree-level with triangle-shape dependence to improve accuracy. Example: "The bispectrum is modeled with the GEO-FPT approach [56]"
- hexadecapole: The ℓ=4 multipole of the power spectrum, adding angular information beyond monopole and quadrupole. Example: "the mono- quad- and hexadecapole of the power spectrum"
- Hubble distance DH: The radial distance defined as DH(z)=c/H(z), used in BAO dilation parameters. Example: "Equivalently, q can be expressed via the radial Hubble distance DH(z) = c/H(z)"
- k-bandpowers: Binned power spectrum measurements in Fourier space used in clustering analyses. Example: "computing cross covariances in the space of k-bandpowers"
- Lyman-α (Lya) forest: Absorption features in quasar spectra caused by intergalactic neutral hydrogen, probing large-scale structure at high redshift. Example: "the Lyman-a (Lya) forest, i.e. the pattern of absorption imprinted on quasar spectra"
- maximum a posteriori (MAP): The parameter point that maximizes the posterior probability. Example: "we overlay the maximum a-posteriori (MAP) estimates for each analysis variant."
- mock catalogues: Synthetic datasets simulating survey observations, used to estimate covariances and validate methods. Example: "extracting joint power spectrum and bispectrum measurements from the mock catalogues"
- monopole: The ℓ=0 multipole component of the correlation function/power spectrum. Example: "fitting its monopole and quadrupole moments"
- non-Gaussian contributions: Covariance terms beyond Gaussian assumptions, including cross-covariances like P(k)–B(k). Example: "which includes the non-Gaussian contributions i.e. the P(k)-B(k) cross covariance."
- Planck PR3: The 2018 Planck data release used for CMB TT/TE/EE likelihoods. Example: "Planck (2018) PR3 temperature and polarization power spectra (TT, TE, and EE) [39]."
- Planck PR4: A later Planck processing release (NPIPE) with updated likelihoods and lensing reconstruction. Example: "CamSpec likelihoods from Planck PR4 [40, 41]"
- Plik likelihood: A Planck high-ℓ TT/TE/EE likelihood used in CMB analyses. Example: "the Plik likelihood for l > 30."
- power spectrum: The Fourier-space two-point statistic of density fluctuations, central to large-scale structure analyses. Example: "the Full-Shape (FS) of the galaxy power spectrum"
- Renormalized Perturbation Theory (RPT): A perturbative scheme to compute the nonlinear power spectrum. Example: "the power spectrum is computed using the Renormalized Perturbation Theory (RPT)"
- SALT3: A light-curve model for Type Ia supernovae used to derive distances. Example: "a retrained SALT3 light-curve model (SALT3.DOV)"
- ShapeFit: A model-agnostic compression technique parameterizing clustering via dilation, growth, amplitude, and shape parameters. Example: "ShapeFit compression mitigates prior volume effects that hinder beyond-ΛCDM analyses."
- SimAll Commander likelihood: A Planck low-ℓ CMB likelihood for large-scale polarization/temperature. Example: "we adopt the SimAll Commander likelihood for multipoles l < 30"
- S8: A combination of σ8 and Ωm that captures the amplitude of matter fluctuations relevant to weak lensing. Example: "and S8 by 1.20, reducing their uncertainties by 26% and 28%, respectively."
- sound horizon at the drag epoch (rd): The comoving scale of the BAO feature set by baryon-photon decoupling. Example: "rd the sound horizon at the drag epoch"
- two-point correlation function (2PCF): The configuration-space statistic of galaxy clustering used for BAO fitting. Example: "the two-point correlation function (2PCF) template."
- fos8: The product of the growth rate f and σ8, capturing growth-amplitude degeneracy in two-point analyses. Example: "we keep only the f parameter which is effectively reinterpreted as fos8"
- qiso: The isotropic dilation parameter encoding overall BAO scale shifts. Example: "OSF = {qiso, qap, dm, f, fos8}"
- vwowaCDM: An extended cosmological model combining dynamical dark energy with varying neutrino mass sum. Example: "4.2.4 vwowaCDM constraints"
- w0waCDM: The ΛCDM extension with CPL dark energy parameters (w0, wa) allowing time-varying equation of state. Example: "For w0waCDM, DESI-only analyses with the bispectrum shift dark energy parameters toward ΛCDM"
Collections
Sign up for free to add this paper to one or more collections.