DESI DR2: Cosmological Constraints from the Baryon Acoustic Oscillations

Arnaud de Mattia

CEA Saclay, Irfu

Antony, May 12th

Thanks to our sponsors and

72 Participating Institutions!

DESI 3D Map

Physics program
- Galaxy and quasar clustering
- Lyman-alpha forest
- Clusters and cross-correlations
- Galaxy and quasar physics
- Milky Way Survey
- Transients and low-z

DESI 3D Map

Physics program
- Galaxy and quasar clustering
- Lyman-alpha forest
- Clusters and cross-correlations
- Galaxy and quasar physics
- Milky Way Survey
- Transients and low-z

DESI: a stage IV survey

Schlegel+22, arXiv:2209.03585

10 years = \(10 \times \)

DESI Y5 galaxy samples

Bright Galaxies: 14M (SDSS: 600k)

0 < z < 0.4

LRG: 8M (SDSS: 1M)

0.4 < z < 1.1

ELG: 16M (SDSS: 200k)

0.6 < z < 1.6

QSO: 3M (SDSS: 500k)

Lya \(1.8 < z\)

Tracers \(0.8 < z < 2.1\)

Y5 (DR1-DR2-DR3) \(\sim 40\)M galaxy redshifts!

\(z = 0.4\)

\(z = 0.8\)

\(z = 0\)

\(z = 1.6\)

\(z = 2.0\)

\(z = 3.0\)

From images to redshifts

imaging surveys (2014 - 2019) + WISE (IR)

target selection

spectroscopic observations

spectra and redshift measurements

Mayall Telescope

focal plane 5000 fibers

wide-field corrector

6 lenses, FoV \(\sim 8~\mathrm{deg}^{2}\)

Kitt Peak, AZ

4 m mirror

Mayall Telescope

focal plane 5000 fibers

fiber view camera

ten 3-channel spectrographs

49 m, 10-cable fiber run

Kitt Peak, AZ

Focal plane: 5000 robotic positioners

86 cm

Focal plane: 5000 robotic positioners

Exposure time (dark): 1000 s

Configuration of the focal plane
CCD readout
Go to next pointing

140 s

0.1 mm

Spectroscopic pipeline

wavelength

fiber number

\(z = 2.1\) QSO

\(z = 0.9\) ELG

Ly\(\alpha\)

CIV

CIII

[OII] doublet at \(3727 \AA\) up to \(z = 1.6\)

[OII]

Ly\(\alpha\) at \(1216 \AA\) down to \(z = 2.0\)

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

Final survey

- dark time (LRG, ELG, QSO): 7 visits

- bright time (BGS): 5 visits

- 14,000 \(\mathrm{deg}^2\)

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!

Baryon Acoustic Oscillations

Sound waves in primordial plasma

At recombination (\(z \simeq 1100\))

plasma changes to optically thin
baryons decouple from photons
sound wave stalls after travelling \(r_\mathrm{d}\)

Sound horizon scale at the drag epoch

\(r_\mathrm{d} \simeq 150\; \mathrm{Mpc}\)

standard ruler

Baryon Acoustic Oscillations

CMB (\(z \simeq 1100\))

Sound waves in primordial plasma

At recombination (\(z \simeq 1100\))

plasma changes to optically thin
baryons decouple from photons
sound wave stalls after travelling \(r_\mathrm{d}\)

Sound horizon scale at the drag epoch

\(r_\mathrm{d} \simeq 150\; \mathrm{Mpc}\)

standard ruler

CMB (\(z \simeq 1100\))

LSS

Baryon Acoustic Oscillations

BAO measurements

distribution of galaxies (cartoonish)

\theta_\mathrm{BAO} = r_\mathrm{d} / D_\mathrm{M}(z)

transverse comoving distance

sound horizon \(r_\mathrm{d}\)

BAO measurements

distribution of galaxies (cartoonish)

\Delta z_\mathrm{BAO} = r_\mathrm{d} / D_\mathrm{H}(z)

Hubble distance

sound horizon \(r_\mathrm{d}\)

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

What's new in the analyses?

Analysis pipelines mostly the same as DR1

Again, blind analyses:

- discrete tracers: catalog-level blinding

- Ly\(\alpha\): data vector-level blinding

Specifics:

- discrete tracers: more robustness tests, increased BGS density

- Ly\(\alpha\): improved mocks / modelling (DLA, metals, continuum fitting)

Some updates in BAO fitting

Subdominant systematics: \(\sigma_\mathrm{stat+syst} < 1.09 \sigma_\mathrm{stat}\) for discrete tracers, \(<1.06 \sigma_\mathrm{stat}\) for Ly\(\alpha\)

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

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

Consistency with other data

1. Planck PR4 CamSpec

2. Planck PR4 + ACT DR6 lensing

BAO constrains \(\Omega_\mathrm{m}\), \(h \times r_d(\Omega_\mathrm{b}h^2, \Omega_\mathrm{bc}h^2)\)
Calibrating BAO relative distance measurements using BBN \(\Omega_\mathrm{b} h^2\)

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

\underbrace{ H_0 = (68.51 \pm 0.58) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \text{BBN}}}

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

\underbrace{ H_0 = (68.45 \pm 0.47) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{orange}{\text{DESI} + \theta_\ast + \text{BBN}}}

BAO constrains \(\Omega_\mathrm{m}\), \(h \times r_d(\Omega_\mathrm{b}h^2, \Omega_\mathrm{bc}h^2)\)
Calibrating BAO relative distance measurements using BBN \(\Omega_\mathrm{b} h^2\)

\underbrace{ H_0 = (68.51 \pm 0.58) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \text{BBN}}}

Adding very precise CMB acoustic angular scale

\(\sim \Omega_\mathrm{m} h^3\)

\(\sim \Omega_\mathrm{m} h^2\)

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

In \(4.5\sigma\) tension with SH0ES (Breuval+24) (independently of the CMB)

BAO constrains \(\Omega_\mathrm{m}\), \(h \times r_d(\Omega_\mathrm{b}h^2, \Omega_\mathrm{bc}h^2)\)
Calibrating BAO relative distance measurements using BBN \(\Omega_\mathrm{b} h^2\)

\underbrace{ H_0 = (68.51 \pm 0.58) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \text{BBN}}}

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

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

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!

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

Neutrino mass oscillations constrain \(\Delta m_{21}^2\) and \(\vert \Delta m_{31}^2\vert\)

\(\sum m_\nu = m_1 + \sqrt{m_1^2 + \Delta m_{21}^2} + \sqrt{m_1^2 + \Delta m_{31}^2}\)

\(m_3 + \sqrt{m_3^2 - \Delta m_{31}^2} + \sqrt{m_3^2 + \Delta m_{32}^2}\)

prior NO/IO: 0.5/0.5

\sum m_\nu < 0.101 \, \mathrm{eV} \; (95\%, \text{NO})

\sum m_\nu < 0.133 \, \mathrm{eV} \; (95\%, \text{IO})

Elbers+25

Normal Ordering (NO)

Inverted Ordering (IO)

\Rightarrow P(\mathrm{NO}) = 1 - P(\mathrm{IO}) = 0.91

Sum of neutrino masses

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

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

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

\(w_0w_a\) shifts to positive \(\sum m_\nu\)

profile likelihood

adding SN shifts the minimum back towards negative \(\sum m_\nu\)

Summary

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

DESI in mild, growing, tension with Planck (\(2.3\sigma\)) and SN \((\sim 2\sigma)\) when interpreted in the ΛCDM model

Tightest upper bound on \(\sum m_\nu\), increasing tension with neutrino oscillations

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: \(2.8 - 4.2\sigma\), resolves \(\sum m_\nu\) tension

What's next in DESI?

In November 2024: DR1 Full-Shape results (probing the growth of structure)

\(S_8 = \sigma_8(\Omega_\mathrm{m} / 0.3)^{0.5}\)

General Relativity

What's next in DESI?

In November 2024: DR1 Full-Shape results (probing the growth of structure)

With DR2 - stay tuned!

Full-Shape from power spectrum
Bispectrum
Primordial non-Gaussianity
x CMB lensing
Low-\(z\) growth of structure with peculiar velocities

What's next in DESI?

~6 months ahead of schedule \(\Rightarrow\) DR1-DR2-DR3 to finish in Nov. 2025
DR4-DR5: ~ 3.5 year transition period
DESI-II: Dark Matter, high-density and high-z programs