DESI 2024: Cosmological Parameters from the Baryon Acoustic Oscillations

Arnaud de Mattia

on behalf of the DESI collaboration

Key Project led by Eva Mueller and Dragan Huterer

Moriond, April 4th

Thanks to our sponsors and

72 Participating Institutions!

  • transverse to the line-of-sight: \(D_\mathrm{M}(z) / r_\mathrm{d}\)

BAO measures ratios of distances over the sound horizon scale at the drag epoch ["standard ruler"] \(r_\mathrm{d}\)

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

BAO measurements

  • transverse to the line-of-sight: \(D_\mathrm{M}(z) / r_\mathrm{d}\)
  • along the line-of-sight: \(D_\mathrm{H}(z) / r_\mathrm{d} = c / (H(z) r_\mathrm{d}) \)
z
\Delta z_\mathrm{BAO} = r_\mathrm{d} / D_\mathrm{H}(z)

BAO measurements

BAO measures ratios of distances over the sound horizon scale at the drag epoch ["standard ruler"] \(r_\mathrm{d}\)

  • transverse to the line-of-sight: \(D_\mathrm{M}(z) / r_\mathrm{d}\)
  • along the line-of-sight: \(D_\mathrm{H}(z) / r_\mathrm{d} = c / (H(z) r_\mathrm{d}) \)
  • isotropic average: \( D_\mathrm{V}(z) / r_\mathrm{d} = (z D_{\mathrm{M}}^{2}(z) D_\mathrm{H}(z))^{1/3} / r_\mathrm{d}\)

BAO measurements

BAO measures ratios of distances over the sound horizon scale at the drag epoch ["standard ruler"] \(r_\mathrm{d}\)

Let's factor out the \(h\) terms:

  • ​\(\color{blue}{[D_\mathrm{M}(z) h] (\Omega_\mathrm{m}, \Omega_\mathrm{K}, ...)} \color{black}{/} \color{orange}{[r_\mathrm{d}(\Omega_\mathrm{m} h^{2}, \Omega_\mathrm{b} h^{2}) h]} \)
  • \( \color{blue}{[D_\mathrm{H}(z) h] (\Omega_\mathrm{m}, \Omega_\mathrm{K}, ...)} \color{black}{/} \color{orange}{[r_\mathrm{d}(\Omega_\mathrm{m} h^{2}, \Omega_\mathrm{b} h^{2}) h]} \)

BAO measurements at different \(z\) constrain:

  • energy content \( \color{blue}{(\Omega_\mathrm{m}, \Omega_\mathrm{K}, ...)} \)
  • constant-over-\(z\) product \(\color{orange}{r_\mathrm{d} h}\) i.e. \(\color{orange}{H_{0} r_\mathrm{d}}\)

These quantities directly relate to base cosmological parameters

BAO measurements

Dark energy equation of state:

\(P = w \rho\)

  • \(w\) = constant

BAO measurements: dark energy

Dark energy equation of state:

\(P = w \rho\)

  • CPL parameterization: \(w(a) = w_0 + (1 - a) w_a\)

BAO measurements: dark energy

DESI Y1 BAO

DESI BAO measurements

DESI Y1 BAO

DESI BAO measurements

DESI Y1 BAO

DESI BAO measurements

DESI Y1 BAO

DESI BAO measurements

DESI Y1 BAO

DESI BAO measurements

DESI Y1 BAO

DESI BAO measurements

DESI Y1 BAO

DESI BAO measurements

Consistent with each other,

and complementary

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.295 \pm 0.015 & \mathbf{(5.1\%)} \\ H_{0} r_\mathrm{d} &= (101.8 \pm 1.3) \, [100 \, \mathrm{km} \, \mathrm{s}^{-1}] & \mathbf{(1.3\%)} \end{align*}}_{\textstyle \text{\color{black}{DESI}}}

Consistency with other probes

DESI Y1 BAO consistent with:

Consistency with other probes

DESI Y1 BAO consistent with:

Consistency with other probes

DESI Y1 BAO consistent with:

Consistency with other probes

DESI Y1 BAO consistent with:

\underbrace{ \Omega_\mathrm{m} = 0.3069 \pm 0.0050 \; \mathbf{(1.6\%)} }_{\textstyle \text{\green{DESI + CMB}}}
  • BAO constrains \( r_\mathrm{d}(\Omega_\mathrm{m} h^{2}, \Omega_\mathrm{b} h^{2}) h \)

Hubble constant

  • BAO constrains \( r_\mathrm{d}(\blue{\Omega_\mathrm{m}} h^{2}, \Omega_\mathrm{b} h^{2}) h \)
  • \( \blue{\Omega_\mathrm{m}} \) constrained by BAO at different \(z\)

Hubble constant

  • BAO constrains \( r_\mathrm{d}(\blue{\Omega_\mathrm{m}} h^{2}, \orange{\Omega_\mathrm{b} h^{2}}) h \)
  • \( \blue{\Omega_\mathrm{m}} \) constrained by BAO at different \(z\)
  • \(\orange{\Omega_\mathrm{b}h^2}\)  can be constrained by BBN: Schöneberg et al., 2024

Hubble constant

  • BAO constrains \( r_\mathrm{d}(\blue{\Omega_\mathrm{m}} h^{2}, \orange{\Omega_\mathrm{b} h^{2}}) h \)
  • \( \blue{\Omega_\mathrm{m}} \) constrained by BAO at different \(z\)
  • \(\orange{\Omega_\mathrm{b}h^2}\)  can be constrained by BBN: Schöneberg et al., 2024

\(\implies\) constraints on \(h\) i.e. \(H_0\)

Hubble constant

\underbrace{ H_0 = (68.53 \pm 0.80) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \text{BBN}}}

Hubble constant

\underbrace{ H_0 = (68.52 \pm 0.62) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \theta_\ast + \text{BBN}}}

\(\theta_\ast\) CMB angular acoustic scale

 

​

 

  • Consistency with SDSS
\underbrace{ H_0 = (68.53 \pm 0.80) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \text{BBN}}}

Hubble constant

\underbrace{ H_0 = (68.52 \pm 0.62) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \theta_\ast + \text{BBN}}}

 

​

 

  • Consistency with SDSS
  • In agreement with CMB
\underbrace{ H_0 = (68.53 \pm 0.80) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \text{BBN}}}

Hubble constant

\underbrace{ H_0 = (68.52 \pm 0.62) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \theta_\ast + \text{BBN}}}

 

​

 

  • Consistency with SDSS
  • In agreement with CMB
  • In \(3.7 \sigma\) tension with SH0ES
\underbrace{ H_0 = (68.53 \pm 0.80) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \text{BBN}}}

Hubble constant

\underbrace{ H_0 = (68.52 \pm 0.62) \, {\rm km\,s^{-1}\,Mpc^{-1}} }_{\textstyle \color{darkblue}{\text{DESI} + \theta_\ast + \text{BBN}}}

DESI + CMB measurements favor a flat Universe

\Omega_\mathrm{K} = 0.0024 \pm 0.0016 \; \green{(\text{DESI} + \text{CMB})}

Spatial curvature

Dark Energy Equation of State

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.293 \pm 0.015 & \mathbf{(5.1\%)} \\ w &= -0.99^{+0.15}_{-0.13} & \mathbf{(15\%)} \end{align*}}_{\textstyle \text{\color{darkblue}{DESI}}}

Constant EoS parameter \(w\)

Dark Energy Equation of State

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.293 \pm 0.015 & \mathbf{(5.1\%)} \\ w &= -0.99^{+0.15}_{-0.13} & \mathbf{(15\%)} \end{align*}}_{\textstyle \text{\color{darkblue}{DESI}}}

Constant EoS parameter \(w\)

Dark Energy Equation of State

SNe:

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.293 \pm 0.015 & \mathbf{(5.1\%)} \\ w &= -0.99^{+0.15}_{-0.13} & \mathbf{(15\%)} \end{align*}}_{\textstyle \text{\color{darkblue}{DESI}}}

Constant EoS parameter \(w\)

Dark Energy Equation of State

SNe:

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.293 \pm 0.015 & \mathbf{(5.1\%)} \\ w &= -0.99^{+0.15}_{-0.13} & \mathbf{(15\%)} \end{align*}}_{\textstyle \text{\color{darkblue}{DESI}}}

Constant EoS parameter \(w\)

Dark Energy Equation of State

SNe:

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.293 \pm 0.015 & \mathbf{(5.1\%)} \\ w &= -0.99^{+0.15}_{-0.13} & \mathbf{(15\%)} \end{align*}}_{\textstyle \text{\color{darkblue}{DESI}}}

Constant EoS parameter \(w\)

Dark Energy Equation of State

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.3095 \pm 0.0065 & \mathbf{(2.1\%)} \\ w &= -0.997 \pm 0.025 & \mathbf{(2.5\%)} \end{align*}}_{\textstyle \text{\color{orange}{DESI + CMB + Pantheon+}}}

Assuming a constant EoS, DESI BAO fully compatible with a cosmological constant...

\underbrace{\begin{align*} \Omega_\mathrm{m} &= 0.293 \pm 0.015 & \mathbf{(5.1\%)} \\ w &= -0.99^{+0.15}_{-0.13} & \mathbf{(15\%)} \end{align*}}_{\textstyle \text{\color{darkblue}{DESI}}}

Constant EoS parameter \(w\)

w(a) = w_{0} + (1 - a) w_{a} \qquad \text{(CPL)}
\left. \begin{align*} w_{0} &= -0.55^{+0.39}_{-0.21} \\ w_{a} &< -1.32 \end{align*} \right\rbrace {\text{\color{black}{DESI}}}

Dark Energy Equation of State

Varying EoS

\Lambda

Dark Energy Equation of State

\underbrace{ w_{0} = -0.45^{+0.34}_{-0.21} \qquad w_{a} = -1.79^{+0.48}_{-1.00} }_{\textstyle \purple{\text{DESI + CMB} \; \implies \; 2.6\sigma}}
w(a) = w_{0} + (1 - a) w_{a} \qquad \text{(CPL)}

Varying EoS

Dark Energy Equation of State

\underbrace{ w_{0} = -0.45^{+0.34}_{-0.21} \qquad w_{a} = -1.79^{+0.48}_{-1.00} }_{\textstyle \purple{\text{DESI + CMB} \; \implies \; 2.6\sigma}}
w(a) = w_{0} + (1 - a) w_{a} \qquad \text{(CPL)}

Varying EoS

Dark Energy Equation of State

\underbrace{ w_{0} = -0.45^{+0.34}_{-0.21} \qquad w_{a} = -1.79^{+0.48}_{-1.00} }_{\textstyle \purple{\text{DESI + CMB} \; \implies \; 2.6\sigma}}
w(a) = w_{0} + (1 - a) w_{a} \qquad \text{(CPL)}

Varying EoS

Dark Energy Equation of State

\underbrace{ w_{0} = -0.45^{+0.34}_{-0.21} \qquad w_{a} = -1.79^{+0.48}_{-1.00} }_{\textstyle \purple{\text{DESI + CMB} \; \implies \; 2.6\sigma}}
w(a) = w_{0} + (1 - a) w_{a} \qquad \text{(CPL)}

Varying EoS

Dark Energy Equation of State

Combining all DESI + CMB + SN

\underbrace{ w_{0} = -0.827 \pm 0.063 \qquad w_{a} = -0.75^{+0.29}_{-0.25} }_{\textstyle \blue{\text{DESI + CMB + Pantheon+} \; \implies \; 2.5\sigma}}

Dark Energy Equation of State

Combining all DESI + CMB + SN

\underbrace{ w_{0} = -0.827 \pm 0.063 \qquad w_{a} = -0.75^{+0.29}_{-0.25} }_{\textstyle \blue{\text{DESI + CMB + Pantheon+} \; \implies \; 2.5\sigma}}
\underbrace{ w_{0} = -0.64 \pm 0.11\qquad w_{a} = -1.27^{+0.40}_{-0.34} }_{\textstyle \color{orange}{\text{DESI + CMB + Union3} \; \implies \; 3.5\sigma}}

Dark Energy Equation of State

Combining all DESI + CMB + SN

\underbrace{ w_{0} = -0.827 \pm 0.063 \qquad w_{a} = -0.75^{+0.29}_{-0.25} }_{\textstyle \blue{\text{DESI + CMB + Pantheon+} \; \implies \; 2.5\sigma}}
\underbrace{ w_{0} = -0.64 \pm 0.11\qquad w_{a} = -1.27^{+0.40}_{-0.34} }_{\textstyle \color{orange}{\text{DESI + CMB + Union3} \; \implies \; 3.5\sigma}}
\underbrace{ w_{0} = -0.727 \pm 0.067 \qquad w_{a} = -1.05^{+0.31}_{-0.27} }_{\textstyle \color{green}{\text{DESI + CMB + DES-SN5YR} \; \implies \; 3.9\sigma}}

Dark Energy Equation of State

Combining all DESI + CMB + SN

\(w_{0} > -1, w_{a} < 0\) favored, level varying on the SN dataset

\underbrace{ w_{0} = -0.827 \pm 0.063 \qquad w_{a} = -0.75^{+0.29}_{-0.25} }_{\textstyle \blue{\text{DESI + CMB + Pantheon+} \; \implies \; 2.5\sigma}}
\underbrace{ w_{0} = -0.64 \pm 0.11\qquad w_{a} = -1.27^{+0.40}_{-0.34} }_{\textstyle \color{orange}{\text{DESI + CMB + Union3} \; \implies \; 3.5\sigma}}
\underbrace{ w_{0} = -0.727 \pm 0.067 \qquad w_{a} = -1.05^{+0.31}_{-0.27} }_{\textstyle \color{green}{\text{DESI + CMB + DES-SN5YR} \; \implies \; 3.9\sigma}}

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

Broken by BAO, especially through \(H_{0}\)

Low preferred value of \(H_{0}\) yields

\(\sum m_\nu < 0.072 \, \mathrm{eV} \; (95\%, \color{green}{\text{DESI + CMB})}\)

Limit relaxed for extensions to \(\Lambda\mathrm{CDM}\)

\(\sum m_\nu < 0.195 \, \mathrm{eV}\) for \(w_0w_a\mathrm{CDM}\)

Neutrino mass hierarchies

\sum m_\nu < 0.113 \, \mathrm{eV} \; (95\%, \color{green}{\text{DESI + CMB})}

With \(> 0.059 \, \mathrm{eV}\) prior (NH)

Neutrino mass hierarchies

\sum m_\nu < 0.113 \, \mathrm{eV} \; (95\%, \color{green}{\text{DESI + CMB})}
\sum m_\nu < 0.145 \, \mathrm{eV} \; (95\%, \color{green}{\text{DESI + CMB})}

With \(> 0.059 \, \mathrm{eV}\) prior (NH)

With \(> 0.1 \, \mathrm{eV}\) prior (IH)

Neutrino mass hierarchies

\sum m_\nu < 0.113 \, \mathrm{eV} \; (95\%, \color{green}{\text{DESI + CMB})}
\sum m_\nu < 0.145 \, \mathrm{eV} \; (95\%, \color{green}{\text{DESI + CMB})}

With \(> 0.059 \, \mathrm{eV}\) prior (NH)

With \(> 0.1 \, \mathrm{eV}\) prior (IH)

Current constraints do not strongly favor normal over inverted hierarchy (\(\simeq 2 \sigma\))

Summary

DESI + BBN (+ \(\theta_\ast\)) constraints \(H_{0}\) to ~1%, tension w/ SH0ES

Summary

DESI + BBN (+ \(\theta_\ast\)) constraints \(H_{0}\) to ~1%, tension w/ SH0ES


DESI, in combination with CMB data, favors zero spatial curvature

Summary

DESI + BBN (+ \(\theta_\ast\)) constraints \(H_{0}\) to ~1%, tension w/ SH0ES


DESI, in combination with CMB data, favors zero spatial curvature


DESI is consistent with \(w = -1\) when assumed constant


When allowing \(w\) to vary, DESI combined with CMB: \(2.6 \sigma\) and SN: \(2.5\) to \(3.9 \sigma\) tension with \((w_{0}, w_{a}) = (-1, 0)\)

Summary

DESI + BBN (+ \(\theta_\ast\)) constraints \(H_{0}\) to ~1%, tension w/ SH0ES


DESI, in combination with CMB data, favors zero spatial curvature


DESI is consistent with \(w = -1\) when assumed constant


When allowing \(w\) to vary, DESI combined with CMB: \(2.6 \sigma\) and SN: \(2.5\) to \(3.9 \sigma\) tension with \((w_{0}, w_{a}) = (-1, 0)\)


Limit on \(\sum m_\nu\) improves to \(< 0.072 \, \mathrm{eV} \; (95\%, \Lambda\mathrm{CDM})\), \(< 0.195 \, \mathrm{eV} \; (95\%, w_{0}w_{a}\mathrm{CDM}) \)

Other datasets

Hubble tension

\(w(z)\)

\(w(z)\)

Full tables

Full tables

Full tables

Full tables

Dark Energy Equation of State

Preference for \(w_{0} > -1, w_{a} < 0\) persists when curvature is left free