DESI DR2:

BAO Cosmological Constraints

Arnaud de Mattia

CEA Paris-Saclay, Irfu

IPhT, December 17th

Thanks to our sponsors and

72 Participating Institutions!

DESI DR1-5 galaxy samples

Bright Galaxies: 17M (SDSS: 600k)

0 < z < 0.4

LRG: 14M (SDSS: 1M)

0.4 < z < 1.1

ELG: 30M (SDSS: 200k)

0.6 < z < 1.6

QSO: 3.4M (SDSS: 500k)

Ly\(\alpha\) \(1.8 < z\)

Tracers \(0.8 < z < 2.1\)

8 years \(\sim 63\)M galaxy redshifts over 17k \(\mathrm{deg}^2\)

\(z = 0.4\)

\(z = 0.8\)

\(z = 0\)

\(z = 1.6\)

\(z = 2.0\)

\(z = 3.0\)

DESI data release 2 (DR2)

Observations from May 14th 2021 to April 9th 2024

approved

construction started

first light

survey started

DR1 data sample

DR1 results

DR2 sample secured

DR3

DR2 results

2015

DESI data release 2 (DR2)

30M galaxy and QSO redshifts in 3 years of operation
14M used in the DR2 analysis (6M in DR1)
Including 820,000 Ly\(\alpha\) QSO at \(z > 2.09\) (420,000 in DR1)
\(> 2\times\) increase in number of tracers

higher completeness (deeper)

extended mag cut

Release of DESI DR2 (BAO) results

March 19th 2025

First batch of DESI DR2 cosmological analyses: https://data.desi.lbl.gov/doc/papers /dr2

• DESI Collaboration et al. (2025), DESI DR2 Results I: Baryon Acoustic Oscillations from the Lyman Alpha Forest
• DESI Collaboration et al. (2025), DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

Companion supporting papers:

Lodha et al. (2025), Extended Dark Energy analysis

Elbers et al. (2025), Constraints on Neutrino Physics

Andrade et al. (2025), Validation of the DESI DR2 BAO mesurements

Casas et al. (2025), Validation of the DESI DR2 Lyα BAO analysis using synthetic datasets

Brodzeller et al. (2025), Construction of the Damped Lyα Absorber Catalog for DESI DR2 Lyα BAO

DR1 public!

BAO measurements

angle on the sky (transverse to the line-of-sight): \(\theta_\mathrm{BAO} = \orange{r_\mathrm{d}}/\green{D_\mathrm{M}(z)}\)
\(\Delta z\) (along the line-of-sight): \( \Delta z_\mathrm{BAO} = r_\mathrm{d} / D_\mathrm{H}(z) = \green{H(z)} \orange{r_\mathrm{d}} / c \)
at multiple redshifts \(z\)

Probes the expansion history (\(\green{D_\mathrm{M}, D_H}\)), hence the energy content (e.g. dark energy)

Absolute size at \(z = 0\): \(H_0 \orange{r_\mathrm{d}}\)

z_1

z_2

z_3

BAO measurements

correlation function

BAO peak

line of sight

monopole

BAO measurements

correlation function

\alpha_\mathrm{iso} \propto (D_{\mathrm{M}}^{2}(z) D_\mathrm{H}(z))^{1/3} / r_\mathrm{d}

BAO peak

line of sight

monopole

isotropic

comoving transverse distance

Hubble distance \(c/H(z)\)

sound horizon (standard ruler)

BAO measurements

isotropic

anisotropic

\propto D_{\mathrm{M}}(z) / D_\mathrm{H}(z)

BAO peak

line of sight

monopole

quadrupole

\propto (D_{\mathrm{M}}^{2}(z) D_\mathrm{H}(z))^{1/3} / r_\mathrm{d}

low S/N

BAO detection: \(14.7\sigma\)

0.1 < z < 0.4

0.4 < z < 0.6

0.6 < z < 0.8

0.8 < z < 1.1

1.1 < z < 1.6

Robustness tests

tracers / redshift bins

data vector

Robustness tests

tracers / redshift bins

BAO modelling

Robustness tests

tracers / redshift bins

imaging systematics

Robustness tests

tracers / redshift bins

data splits

Ly\(\alpha\) forest

Absorption in QSO spectra by neutral hydrogen in the intergalactic medium: \(\lambda_\mathrm{abs} = (1 + z_\mathrm{HI}) \times 1215.17 \; \AA \)

Transmitted flux fraction \(F = e^{-\tau}\) probes the fluctuation in neutral hydrogen density, \(\tau \propto n_\mathrm{HI} \)

credit: Andrew Pontzen

Correlation functions

Ly\(\alpha\) forest auto-correlation

\(\langle \delta_F(\mathbf{x}) \delta_F(\mathbf{x + s}) \rangle\)

Ly\(\alpha\) forest - QSO cross-correlation

\(\langle \delta_F(\mathbf{x}) Q(\mathbf{x + s}) \rangle\)

Robustness tests

data vector / covariance

Robustness tests

modelling choices

Robustness tests

continuum fitting

Robustness tests

data splits

DESI DR2 BAO

DESI DR2 BAO measurements

\propto (D_{\mathrm{M}}^{2}(z) D_\mathrm{H}(z))^{1/3} / r_\mathrm{d}

DESI DR2 BAO

DESI DR2 BAO measurements

\propto D_{\mathrm{M}}(z) / D_\mathrm{H}(z) = f(\Omega_\mathrm{m})

DESI DR2 BAO

DESI DR2 BAO measurements

DESI DR2 BAO

DESI DR2 BAO measurements

DESI DR2 BAO

DESI DR2 BAO measurements

DESI DR2 BAO

DESI DR2 BAO measurements

DESI DR2 BAO

DESI DR2 BAO measurements

Consistent with each other,

and complementary

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.2975 \pm 0.0086 & \mathbf{(3.0\%)} \\ H_{0} r_\mathrm{d} &= (101.54 \pm 0.73) \, [100 \, \mathrm{km} \, \mathrm{s}^{-1}] & \mathbf{(0.7\%)} \end{align*}}_{\textstyle \text{\color{black}{DESI}}}

DESI DR2 BAO

DESI DR2 BAO measurements

DESI DR2 BAO fully consistent with DESI DR1
Improvement of \(\simeq 40\%\)
\(2.3 \sigma\) discrepancy with primary CMB¹ + CMB lensing²

BAO vs CMB

1. Planck PR4 CamSpec

2. Planck PR4 + ACT DR6 lensing

DESI DR2 / DR1 vs Planck

\(\mathcal{D}_\parallel, \mathcal{D}_\perp = \mathrm{Rot}(D_\mathrm{H}/r_\mathrm{d}, D_\mathrm{M}/r_\mathrm{d})\) with \(\mathcal{D}_\perp\) best constrained by Planck

following Efstathiou+25

DESI DR2 / DR1 vs Planck

following Efstathiou+25

turned into \(\omega_\mathrm{bc}\) constraint

DR2 more consistent

DESI DR2 / DR1 vs Planck

\(\omega_\mathrm{bc}\)

\(2.3 \sigma\) discrepancy with primary CMB + CMB lensing

DESI DR2 / DR1 vs Planck

following Efstathiou+25

With CMB = low-\(\ell\) PR3 + CamSpec PR4 + (ACT+PR4) lensing

\(H_0r_\mathrm{d}, \Omega_\mathrm{m}\) space

BAO \(\alpha\) space

\(\mathcal{D}_\perp\)

\(\mathcal{D}_\parallel\)

\(\omega_\mathrm{bc}\)

DR2

DR1

\(2.3\sigma\)

\(2.2\sigma\)

\(1.8\sigma\)

\(1.9\sigma\)

\(2.1\sigma\)

\(0.8\sigma\)

\(2.6\sigma\)

\(2.7\sigma\)

\(1.3\sigma\)

\(2.1\sigma\)

\(2.3\sigma\)

no isotropic BAO

multiple counting of Planck uncertainty

where there is most discrepancy

DESI DR2 / DR1 vs Planck

following Efstathiou+25

With CMB = low-\(\ell\) PR3 + CamSpec PR4

\(H_0r_\mathrm{d}, \Omega_\mathrm{m}\) space

BAO \(\alpha\) space

\(\mathcal{D}_\perp\)

\(\mathcal{D}_\parallel\)

\(\omega_\mathrm{bc}\)

DR2

DR1

\(2.3\sigma\) \(1.9\sigma\)

\(2.2\sigma\) \(1.9\sigma\)

\(1.8\sigma\) \(1.6\sigma\)

\(1.9\sigma\) \(1.7\sigma\)

\(2.1\sigma\) \(2.0\sigma\)

\(0.8\sigma\)

\(2.6\sigma\) \(2.2\sigma\)

\(2.7\sigma\) \(2.3\sigma\)

\(1.3\sigma\)

\(2.1\sigma\) \(1.9\sigma\)

\(2.3\sigma\) \(2.1\sigma\)

no isotropic BAO

multiple counting of Planck uncertainty

where there is most discrepancy

BAO vs CMB

Camphuis+25

SPA = SPT+Planck+ACT

Curvature \(\Omega_\mathrm{k}\)

Chen+25

CMB \(\theta_\star\) constrains \(\Omega_\mathrm{m}h^3(1-7\Omega_\mathrm{k})\)

\(\Omega_\mathrm{k} = 0.0023 \pm 0.0011\) (DESI + CMB)

DESI 2025

\(\Lambda\mathrm{CDM}\) constraints

DESI \(\Omega_\mathrm{m}\) lower than the CMB (\(1.8\sigma\))
DESI \(\Omega_\mathrm{m}\) lower than SN:
- Pantheon+: \(1.7\sigma\)
- Union3: \(2.1\sigma\)
- DESY5: \(2.9\sigma\)

Dark energy fluid

No strong preference for dark energy evolution: \(1.7\sigma\) from DESI data alone

Dark Energy Equation of State

\(\Lambda\)

p / \rho = w = w_0 + w_a (1 - a)

pressure

density

CPL

Combining DESI + CMB:

Dark Energy Equation of State

\underbrace{ w_{0} = -0.42 \pm 0.21 \qquad w_{a} = -1.75 \pm 0.58 }_{\textstyle \textcolor{orange}{\text{DESI + CMB} \; \implies \; 3.1\sigma}}

CMB early-Universe priors: \(2.4\sigma\)
Without CMB lensing \(2.7\sigma\)

\(+0.5\sigma\) compared to DR1

Dark Energy Equation of State

Camphuis+25

constrained by CMB

Dark Energy EoS (with SN)

Combining all DESI + CMB + SN

\underbrace{ w_{0} = -0.838 \pm 0.055 \qquad w_{a} = -0.62^{+0.22}_{-0.19} }_{\textstyle \textcolor{blue}{\text{DESI + CMB + Pantheon+} \; \implies \; 2.8\sigma}}

\underbrace{ w_{0} = -0.667 \pm 0.088 \qquad w_{a} = -1.09^{+0.31}_{-0.27} }_{\textstyle \color{orange}{\text{DESI + CMB + Union3} \; \implies \; 3.8\sigma}}

\underbrace{ w_{0} = -0.752 \pm 0.057 \qquad w_{a} = -0.86^{+0.23}_{-0.20} }_{\textstyle \color{green}{\text{DESI + CMB + DES-SN5YR} \; \implies \; 4.2\sigma}}

\(+0.3\sigma\) compared to DR1

Combining all DESI + CMB + SN

\underbrace{ w_{0} = -0.838 \pm 0.055 \qquad w_{a} = -0.62^{+0.22}_{-0.19} }_{\textstyle \textcolor{blue}{\text{DESI + CMB + Pantheon+} \; \implies \; 2.8\sigma}}

\underbrace{ w_{0} = -0.667 \pm 0.088 \qquad w_{a} = -1.09^{+0.31}_{-0.27} }_{\textstyle \color{orange}{\text{DESI + CMB + Union3} \; \implies \; 3.8\sigma}}

\underbrace{ w_{0} = -0.752 \pm 0.057 \qquad w_{a} = -0.86^{+0.23}_{-0.20} }_{\textstyle \color{green}{\text{DESI + CMB + DES-SN5YR} \; \implies \; 4.2\sigma}}

Dovekie \(3.3\sigma\)

Dark Energy EoS (with SN)

Robustness tests

Removing low-\(z\) SN

"Replacing CMB": DESY3 \(3\times2\)pt

\(3.3\sigma\)

Understanding tensions

doesn't fit the SN!

Understanding tensions

doesn't fit the BAO!

Understanding tensions

\(w\mathrm{CDM}\) not flexible enough to fit all 3 datasets!

w = -0.970

Understanding tensions

\(w_0w_a\mathrm{CDM}\) fits all 3 datasets!

Understanding tensions

Dark Energy Evolution (\(w_0w_a\mathrm{CDM}\))

q(z)\equiv{-\frac{\ddot{a}a}{\dot{a}^2}}=\frac{d\ln H}{d\ln(1+z)}-1

Om(z)\equiv\frac{h^2(z)-1}{(1+z)^3-1}

f_{\rm DE}(z) \equiv \frac{\rho_\mathrm{DE}(z)}{\rho_\mathrm{DE,0}}

Lodha+25

phantom

Dark Energy Evolution

best described by CPL

\(4\sigma\)

Also considered: Gaussian Processes, similar evolution obtained

Lodha+25

Sum of neutrino masses

Internal CMB degeneracies limiting precision on the sum of neutrino masses

Broken by BAO

Sum of neutrino masses

Internal CMB degeneracies limiting precision on the sum of neutrino masses

Broken by BAO, which favors low \(\Omega_\mathrm{m}\)

\sum m_\nu < 0.064 \, \mathrm{eV} \; (95\%, \text{DESI + CMB})

Sum of neutrino masses

Internal CMB degeneracies limiting precision on the sum of neutrino masses

Broken by BAO, which favors low \(\Omega_\mathrm{m}\)

\sum m_\nu < 0.064 \, \mathrm{eV} \; (95\%, \text{DESI + CMB})

Limit relaxed for \(w_0w_a\mathrm{CDM}\):

DESI+CMB: \(\sum m_\nu < 0.163 \, \mathrm{eV} \; (95\%)\)

DESI+CMB+DESY5: \(< 0.129 \, \mathrm{eV} \; (95\%)\)

Summary

DESI already has the most precise BAO measurements ever (40% more precise than DR1)

DESI in mild, growing, tension with CMB (\(2 - 3.7\sigma\)) and SN \((\sim 2\sigma)\) when interpreted in the ΛCDM model

Evidence for time-varying Dark Energy equation of state has increased with the DR2 BAO data by \(0.3\sigma\): CMB: \(3.1\sigma\), SN: \(2.8 - 3.8\sigma\), resolves \(\sum m_\nu\) tension

Evolving DE?

Phantom crossing isn't very natural. Can be achieved with:

multifield \(\Rightarrow\) complex, fine-tuning
non-minimal coupling between scalar field and gravity (e.g. Wolf+25)

Evolving DE?

Phantom crossing isn't very natural. Can be achieved with:

multifield \(\Rightarrow\) tuning (time and amplitude)
non-minimal coupling between scalar field and gravity (e.g. Wolf+25)
- but the effect would be visible in structure growth

Evolving DE?

Phantom crossing isn't very natural. Can be achieved with:

multifield \(\Rightarrow\) tuning (time and amplitude)
non-minimal coupling between scalar field and gravity (e.g. Wolf+25)
- but the effect would be visible in structure growth
coupling between DE and DM? (e.g. Das+05)
- but shifting \(w_\mathrm{DE}^\mathrm{eff}\) requires shifting \(w_\mathrm{m}^\mathrm{eff}\) in the opposite direction \(\Rightarrow\) difficult for structure growth
- maybe tilting (sign of interaction changing with time) dark energy? see Linder 2025 for complete discussion