Cosmological constraints from the galaxy power spectrum with the Dark Energy Spectroscopic Instrument (DESI)

DESI constraints on gravity

prediction from general relativity

growth rate of structure

$\Rightarrow$ Similar precision on $f\sigma_8$ at $z < 1.5$ between

DESI DR1 (1 year of observations) and SDSS (20 years of observations)

DESI constraints on gravity

general relativity is here

Galaxy Full Shape in a nutshell

observed redshift = Hubble flow

and peculiar velocities (RSD = "redshift space distortions")

Galaxy Full Shape in a nutshell

Modelling of the full-shape of the galaxy power spectrum enables to:

• probe the growth of structures $f\sigma_8$
• test the theory of gravity and dark energy
• constrain the sum of neutrino masses

observed redshift = Hubble flow

and peculiar velocities (RSD = "redshift space distortions")

RSD

Growth of cosmic structure

Through gravity

Credit: Claire Lamman and Michael Rashkovetskyi / DESI collaboration

The new DESI analysis in details

Thanks to our sponsors and

72 Participating Institutions!

The DESI instrument

Credit: NSF

DESI: a stage IV survey

Schlegel et al. 2022, 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 < 0.8

ELG: 16M (SDSS: 200k)

0.6 < z < 1.6

QSO: 3M (SDSS: 500k)

Lya $1.8 < z$

Tracers $0.8 < z < 2.1$

Y5 $\sim 40$M galaxy redshifts!

$z = 0.4$

$z = 0.8$

$z = 0$

$z = 1.6$

$z = 2.0$

$z = 3.0$

DESI data release 1 (DR1)

Observations from May 14th 2021 to June 12th 2022

Final survey (5 years)

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

- bright time (BGS): 5 layers

- 14,000 $\mathrm{deg}^2$

DESI data release 1 (DR1)

Observations from May 14th 2021 to June 12th 2022

5.7 million unique redshifts at z < 2.1 and > 420,000 Ly$\alpha$ QSO at z > 2.1

used for BAO and Full Shape

used for BAO

Release of DESI DR1 (BAO) results

April 4th 2024

Previously...

Release of DESI DR1 (BAO) results

April 4th 2024

Previously...

BAO-only

$\Lambda$CDM is here

Release of DESI DR1 (FS) results

November 19th 2024

• DESI 2024 I: First year data release
• DESI 2024 II: Sample definitions and two-point clustering statistics
• DESI 2024 III: BAO from Galaxies and Quasars
• DESI 2024 IV: BAO from the Lyman-Forest
• DESI 2024 V: Full Shape measurements from Galaxies and Quasars
• DESI 2024 VI: Cosmological constraints from BAO measurements
• DESI 2024 VII: Cosmological constraints from Full Shape measurements

Ashley Ross

Cheng Zhao

Rongpu Zhou

Hector Gil-Marin

Pauline Zarrouk

Dragan Huterer

Mustapha Ishak

Eva Mueller

KP leads

Second batch of DESI DR1 cosmological analyses
https://data.desi.lbl.gov/doc/papers/

Extract cosmological constraints from the galaxy power spectrum

galaxy 3D map

galaxy power spectrum

cosmological model constraints ($\Lambda$CDM)

BAO

Full Shape

Joint

Extract cosmological constraints from the galaxy power spectrum

galaxy 3D map

galaxy power spectrum

cosmological model constraints ($\Lambda$CDM)

Full-Modelling

(direct fitting approach)

BAO

Full Shape

Joint

Extract cosmological constraints from the galaxy power spectrum

galaxy 3D map

galaxy power spectrum

Extract cosmological constraints from the galaxy power spectrum

galaxy 3D map

galaxy power spectrum

cosmological model constraints ($\Lambda$CDM)

BAO

Full Shape

Joint

Extract cosmological constraints from the galaxy power spectrum

galaxy 3D map

galaxy power spectrum

ShapeFit

(compressed approach)

Comparison of both approaches

Maus et al. 2024a

Modelling the galaxy power spectrum

Three power spectrum Effective Field Theory models considered:

- velocileptors Maus et al. 2024

- folps Noriega et al. 2024

- pybird Lai et al. 2024

credit: Mark Maus, Hernan Noriega, Yan Lai

One comparison paper:

Maus et al. 2024

One configuration-space model:

- EFT-GSM Ramirez et al. 2024

Modelling the galaxy power spectrum

The Effective Field Theory in a nutshell

• model for the multipoles of the power spectrum
• perturbation theory model + counter-terms and stochastic terms
• for the baseline analysis (monopole & quadrupole): 3 galaxy bias parameters, 2 counter-terms, 2 stochastic parameters
• dependence on cosmology into $P_\mathrm{lin}$, $f$ and Alcock-Paczynski parameters

perturbation theory term

linear and quasi-linear physics

counter-terms contribution

truncation of perturbative series

stochastic-terms contribution

small-scale galaxy physics

Blind analysis

• DESI represents the first galaxy redshift survey data that has been analyzed in a catalogue-based blinded way

• Allow us to mitigate confirmation bias

1. geometrical AP-like shift

2. density-dependent RSD-like shift

Density-dependent shift

Imprints a new RSD shift

Same as the BAO blinding

Changes the z-to-distance conversion

Projection effects

2 types of projection effects:

• prior volume effect when data not constraining enough for the parameter space

mean and 95% of the marginalised posterior  $\neq$  maximum of the posterior (MAP)

Projection effects

2 types of projection effects:

• prior volume effect when data not constraining enough for the parameter space

• prior weight effect when the prior on a parameter differs from the true value of the data

$\Rightarrow$ Difference in MAP values (crosses) between uninformative flat priors and physically-motivated Gaussian priors: prior weight effect

Systematic effects

Study of several potential sources of systematic effects using realistic simulations:

• Theoretical modelling (Maus et al. 2024ab, Lai et al. 2024, Noriega et al. 2024, Ramirez et al. 2024)

• Galaxy-halo connection (Findlay et al. 2024)

• Fiducial cosmology (Gsponer et al. 2024)

• Fibre assignment (Pinon et al. 2024)

• Inhomogeneities in the target selection (Zhao et al. 2024)

• Spectroscopic redshift failures/uncertainties (Yu et al. 2024, Krowleski et al. 2024)

• Covariance matrix: mock-based vs analytic (Forero-Sanchez et al. 2024, Alves et al. 2024, Rashkovetskyi et al. 2024)

Galaxy-halo connection

How well do theoretical models capture galaxy clustering under different assumptions about galaxy formation?

dark matter halo

satellite galaxy

central galaxy

Galaxy-halo connection

How well do theoretical models capture galaxy clustering under different assumptions about galaxy formation?

dark matter halo

satellite galaxy

central galaxy

Findlay et al. 2024

Galaxy-halo connection

How well do theoretical models capture galaxy clustering under different assumptions about galaxy formation?

Findlay et al. 2024

Fiber assignment

Groups of galaxies too close to each other cannot all receive a fiber

$0.05^\circ \simeq$ positioner patrol diameter

Pinon et al. 2024

Fiber assignment

Impacts power spectrum measurements (altMTL vs complete)

Solution: $\theta$-cut = remove all pairs $< 0.05^\circ$, new window matrix

Pinon et al. 2024

Systematic effects

Study of several potential sources of systematic effects using realistic simulations:

• Theoretical modelling (Maus et al. 2024ab, Lai et al. 2024, Noriega et al. 2024, Ramirez et al. 2024)

• Galaxy-halo connection (Findlay et al. 2024)

• Fiducial cosmology (Gsponer et al. 2024)

• Fibre assignment (Pinon et al. 2024)

• Inhomogeneities in the target selection (Zhao et al. 2024)

• Spectroscopic redshift failures/uncertainties (Yu et al. 2024, Krowleski et al. 2024)

• Covariance matrix: mock-based vs analytic (Forero-Sanchez et al. 2024, Alves et al. 2024, Rashkovetskyi et al. 2024)

Total systematic error = ⅖ of DR1 statistical error

Full Shape pipeline - summary

• Observable: power spectrum monopole and quadrupole

• Model: Effective Field Theory

• Covariance: mock-based

• Fitting range: $0.02 < k\, [h/\mathrm{Mpc}] < 0.2$

• Fitting parameters:

  • 5 $\Lambda$CDM parameters (FM)

  • 4 compressed parameters (SF)

  • 7 non-cosmological parameters

Full Shape pipeline - summary

• Observable: power spectrum monopole and quadrupole

• Model: Effective Field Theory

• Covariance: mock-based

• Fitting range: $0.02 < k\, [h/\mathrm{Mpc}] < 0.2$

• Fitting parameters:

  • 5 $\Lambda$CDM parameters (FM)

  • 4 compressed parameters (SF)

  • 7 non-cosmological parameters

• ​Systematic error: at the data vector level

Full Shape pipeline: what's new!

• Biggest ever spectroscopic dataset ($N_\mathrm{tracer}$ and $V$)
• Blind analysis to mitigate observer / confirmation biases (catalogue-level blinding)
• Effective Field Theory models
• Full-Modelling ($\Omega_\mathrm{cosmo}$) and updated compression approach (ShapeFit)
• Improvements in the treatment of observational systematics (e.g. fiber assignment)
• Unified Full Shape pipeline applied to all (discrete) tracer / redshift bins consistently

(compared to SDSS)

The cosmological measurements!

Full Shape + BAO measurements

$\Omega_\mathrm{b} h^2$: BBN from Schöneberg 2024

$n_\mathrm{s} \sim \mathcal{G}(0.9649, 0.042^2)$: "$n_{\mathrm{s}10}$"*

*$10\times$ wider than Planck posterior

$\Omega_\mathrm{b} h^2$: BBN from Schöneberg 2024

$n_\mathrm{s} \sim \mathcal{G}(0.9649, 0.042^2)$

Full Shape + BAO measurements

$\Omega_\mathrm{b} h^2$: BBN from Schöneberg 2024

$n_\mathrm{s} \sim \mathcal{G}(0.9649, 0.042^2)$

Full Shape + BAO measurements

$\Omega_\mathrm{b} h^2$: BBN from Schöneberg 2024

$n_\mathrm{s} \sim \mathcal{G}(0.9649, 0.042^2)$

Full Shape + BAO measurements

$\Omega_\mathrm{b} h^2$: BBN from Schöneberg 2024

$n_\mathrm{s} \sim \mathcal{G}(0.9649, 0.042^2)$

Full Shape + BAO measurements

$\Omega_\mathrm{b} h^2$: BBN from Schöneberg 2024

$n_\mathrm{s} \sim \mathcal{G}(0.9649, 0.042^2)$

Full Shape + BAO measurements

Full Shape + BAO measurements

$S_8$ constraints

$S_8 = \sigma_8 (\Omega_\mathrm{m} / 0.3)^{0.5}$ best constrained by weak lensing surveys

$S_8$ constraints

• ​Consistency with SDSS
• In agreement with CMB*

*Primary CMB (CMB-nl): Planck Collaboration, 2018
Lensing: Planck PR4 + ACT DR6 lensing ACT Collaboration, 2023, Carron et al., 2022​

$S_8 = \sigma_8 (\Omega_\mathrm{m} / 0.3)^{0.5}$ best constrained by weak lensing surveys

$S_8$ constraints

• ​Consistency with SDSS
• In agreement with CMB
• Weak lensing prefers lower $S_8$, but still consistent

$S_8 = \sigma_8 (\Omega_\mathrm{m} / 0.3)^{0.5}$ best constrained by weak lensing surveys

Combined constraints

• Adding DESI to DESY3 6x2pt* improves $\sigma_8$ and $\Omega_\mathrm{m}$ precision by $\times 2$ ($S_8$ by $20\%$)

*DES and SPT collaborations 2022
6x2pt = galaxy-galaxy, galaxy-shear, shear-shear, galaxy-CMB lensing, shear-CMB lensing, CMB lensing-CMB lensing

Combined constraints

• Adding DESI to DESY3 6x2pt improves $\sigma_8$ and $\Omega_\mathrm{m}$ precision by $\times 2$ ($S_8$ by $20\%$)
• Adding DESI to CMB improves $\Omega_\mathrm{m}$, $H_{0}$ and $S_{8}$ precision by $30\%$

Combined constraints

• Adding DESI to DESY3 6x2pt improves $\sigma_8$ and $\Omega_\mathrm{m}$ precision by $\times 2$ ($S_8$ by $20\%$)
• Adding DESI to CMB improves $\Omega_\mathrm{m}$, $H_{0}$ and $S_{8}$ precision by $30\%$

Dark Energy fluid, pressure $p$, density $\rho$

Equation of State parameter $w = p / \rho$

Linked to the evolution of Dark Energy $w(z) = -1 + \frac{1}{3}\frac{d \ln f_\mathrm{DE}(z)}{d \ln (1 + z)}$

Let's assume the CPL parameterization

Dynamical Dark Energy - $(w_{0}, w_{a})$

Dynamical Dark Energy - $(w_{0}, w_{a})$

($\Omega_\mathrm{m}, \sigma_{8})$ constraints remain stable in $w_0w_a\text{CDM}$

SN (uncalibrated):

• Pantheon+​ Scolnic, Brout, Carr et al. 2022; Brout, Scolnic, Popovic et al. 2022
• Union3 Rubin, Aldering, Betoule et al. 2023
• DES-SN5YR DES Collaboration et al. 2024

Dynamical Dark Energy - $(w_{0}, w_{a})$

Dynamical Dark Energy - $(w_{0}, w_{a})$

Combining all DESI + CMB + SN

MAP

DESI + CMB + Pantheon+: $2.5\sigma$

DESI + CMB + Union3: $3.4\sigma$

DESI + CMB + DES-SNY5R: $3.8\sigma$

Dynamical Dark Energy - $(w_{0}, w_{a})$

Combining all DESI + CMB + SN

DESI + CMB + Pantheon+: $2.5\sigma$

DESI + CMB + Union3: $3.4\sigma$

DESI + CMB + DES-SNY5R: $3.8\sigma$

Dynamical Dark Energy - $(w_{0}, w_{a})$

Combining all DESI + CMB + SN

DESI + CMB + Pantheon+: $2.5\sigma$

DESI + CMB + Union3: $3.4\sigma$

DESI + CMB + DES-SNY5R: $3.8\sigma$

• $20\%$ better constraints in $(w_0, w_a)$ than without FS
• same preference for $w_{0} > -1, w_{a} < 0$
• similar significance for $w_0w_a$CDM vs $\Lambda$CDM

Massive neutrinos impact:

i) the expansion history

ii) the growth of structure: $\Delta P(k)/P(k) \propto -\sum m_\nu / \omega_\mathrm{m}$

Sum of neutrino masses

the $k$-fitting range

Massive neutrinos impact:

i) the expansion history

ii) the growth of structure: $\Delta P(k)/P(k) \propto -\sum m_\nu / \omega_\mathrm{m}$

Taking $n_\mathrm{s}$ prior from Planck:

Sum of neutrino masses

Sum of neutrino masses

Internal CMB degeneracies limiting precision on the sum of neutrino masses

Sum of neutrino masses

Internal CMB degeneracies limiting precision on the sum of neutrino masses

($15\%$ better than BAO + CMB: $0.082 \, \mathrm{eV}$)

Low preferred value of $H_{0}$ yields

Sum of neutrino masses

Impact of the CMB likelihood:

CamSpec and HiLLiPoP-LoLLiPoP based on Planck PR4

Sum of neutrino masses

Limit relaxed for more flexible expansion model

e.g. $\sim 0.2\, \mathrm{eV} \; (95\%)$ in $w_0w_a\mathrm{CDM}$, with DES-SN5YR

Perturbed FLRW metric

$ds^2=a(\tau)^2[-(1+2\orange{\Psi})d\tau^2+(1-2\orange{\Phi})\delta_{ij}dx^i dx^j]$

At late times:

(mass) $k^2\orange{\Psi} = -4\pi G a^2 \green{\mu(a,k)} \blue{\sum_i\rho_i\Delta_i}$

(light)  $k^2(\orange{\Phi} + \orange{\Psi})=-8\pi G a^2 \green{\Sigma(a,k)} \blue{\sum_i\rho_i\Delta_i}$

gravitational potentials

In general relativity, $\green{\mu(a, k)} = \green{\Sigma(a, k)} = 1$

density perturbations

Modified gravity

In general relativity, $\green{\mu(a, k)} = \green{\Sigma(a, k)} = 1$

To test GR, introduce $\green{\mu_0, \Sigma_0}$

Modified gravity

Perturbed FLRW metric

$ds^2=a(\tau)^2[-(1+2\orange{\Psi})d\tau^2+(1-2\orange{\Phi})\delta_{ij}dx^i dx^j]$

At late times:

(mass) $k^2\orange{\Psi} = -4\pi G a^2 \green{\mu(a,k)} \blue{\sum_i\rho_i\Delta_i}$

(light)  $k^2(\orange{\Phi} + \orange{\Psi})=-8\pi G a^2 \green{\Sigma(a,k)} \blue{\sum_i\rho_i\Delta_i}$

gravitational potentials

density perturbations

DESI constrains

GR

Modified gravity

$\Sigma_0$ constrained by

- CMB (ISW and lensing)

- galaxy lensing

Modified gravity

DESI constrains

$\Sigma_0$ constrained by

- CMB (ISW and lensing)

- galaxy lensing

Modified gravity

compared to CMB-nl + DESY3 (3x2pt) only: $\sigma(\mu_0) / 2.5$, $\sigma(\Sigma_0) / 2$

DESI constrains

Conclusions

Adding Full Shape information to BAO: sensitivity to structure growth

DESI Full Shape favors $\sigma_8, S_8$ consistent with Planck

Expansion history: in agreement with previous DESI BAO and CMB results

Still hint of dynamical dark energy, $w_0, w_a$ constraints improved by $20\%$

Still low $\sum m_\nu$, improved by $15\%$

Modified gravity $\mu_0$ parameter to be consistent with the zero GR value

Conclusions

Adding Full Shape information to BAO: sensitivity to structure growth

DESI Full Shape favors $\sigma_8, S_8$ consistent with Planck

Expansion history: in agreement with previous DESI BAO and CMB results

Still hint of dynamical dark energy, $w_0, w_a$ constraints improved by $20\%$

Still low $\sum m_\nu$, improved by $15\%$

Modified gravity $\mu_0$ parameter to be consistent with the zero GR value

Conclusions

Adding Full Shape information to BAO: sensitivity to structure growth

DESI Full Shape favors $\sigma_8, S_8$ consistent with Planck

Expansion history: in agreement with previous DESI BAO and CMB results

Still hint of dynamical dark energy, $w_0, w_a$ constraints improved by $20\%$

Still low $\sum m_\nu$, improved by $15\%$

Modified gravity $\mu_0$ parameter to be consistent with the zero GR value

DR2 data (Y3 > Y1) on disk, BAO analysis on-going... stay tuned!

https://data.desi.lbl.gov/doc/papers/

Back Up

Imaging systematics

variations of angular galaxy density

stellar redening map from DESI data

Zhou et al. 2024

Imaging systematics

• Imaging weights (linear for BGS and LRG, Sysnet for ELG, RF for QSO)

• Polynomial correction and mode removal for ELG and QSO

Zhao et al. 2024

Other datasets

• SDSS (for comparisons only): eBOSS Collaboration, 2020
• Primary CMB: Planck Collaboration, 2018
• CMB lensing: Planck PR4 + ACT DR6 lensing ACT Collaboration, 2023, Carron, Mirmelstein, Lewis, 2022
• BBN: Schöneberg, 2024
• SN: Pantheon+ Brout, Scolnic, Popovic et al., 2022, Union3 Rubin, Aldering, Betoule et al. 2023, DES-SN5YR DES Collaboration
• DESY3 3x2pt DES collaboration 2021, 6x2pt DES and SPT collaborations 2022

From images to redshifts

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

target selection

spectroscopic observations

spectra and redshift measurements

Mayall Telescope

focal plane 5000 fibers

fiber view camera

wide-field corrector FoV $\sim 8~\mathrm{deg}^{2}$

ten 3-channel spectrographs

49 m, 10-cable fiber run

Kitt Peak, AZ

Focal plane

86 cm

0.1 mm

Exposure time (dark): 1000 s

Configuration of the focal plane
CCD readout
Go to next pointing

140 s

5000 robotic fiber positioners!

Spectroscopic pipeline

fiber number

$z = 2.1$ QSO

$z = 0.9$ ELG

Ly$\alpha$

CIV

CIII

[OII] doublet at $2727 \AA$ up to $z = 1.6$

[OII]

Ly$\alpha$ at $1216 \AA$ down to $z = 2.0$

Impact of neutrinos

Euclid Collaboration 2024,

https://arxiv.org/pdf/2405.06047