Cosmological Tension? Space Administration Jet Propulsion Laboratory - - PowerPoint PPT Presentation

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

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Cosmological Tension?

DES collaboration (2017) Freedman (2017)

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

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DKL(P||Q) = Z dx p(x) log p(x) q(x)

S = D hDidata

Surprise

• Distance metric between probability distributions
• Quantifies how much the parameter constraints

change due to the data

• Invariant to invertible transformations in x
• Unwieldy when data generating p and q are

correlated

hDi = 1 2 det Σnew det Σold

(Gaussian limit)

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

Bayes Factor

R = p(d1, d2|M) p(d1|M1) p(d2|M)

• Is each data set (or slice of a data set) measuring

consistent parameters?

• Prior-dependent (in general, tension can be reduced

if the prior range is wider)

• Easy to compute
• R>1 implies consistency;
• 3.1 < R < 10 is substantial evidence for consistency;
• R>10 is strong evidence for consistency

0.24 0.30 0.36 0.42

Ωm

0.72 0.78 0.84 0.90 0.96

S8 DES Y1 Planck DES Y1 + Planck

R=4.2

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

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Posterior Predictive Distribution

PPD = p(d2|d1) = Z dθ p(d2|θ)p(θ|d1)

• Assess consistency in data space (highlight sources
• f tension)
• Naturally handles correlated data

Feeney et al (2018)

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

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Practical Tension Resolution

0.65 0.70 0.75 0.80 0.85 0.90 S8 ≡ σ8(Ωm/0.3)0.5 0.1 0.2 0.3 0.4 0.5 Ωm H17 analysis configuration

KiDS-450 (θ+Cov corr.) KiDS-450 (θ corr.) KiDS-450 (original) Planck

0.1 0.2 0.3 0.4 0.5 Ωm T17 analysis configuration

DES Y1 KiDS-450 Planck

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

Tension Metric Metrics

time parameter consensus value Truth We want this.

collect data choose and fit systematics + physical model measure tension between experiments, internal goodness of fit if tension, force loser to update systematics model if agreement and good fits, update “consensus”

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

Tension Metric Metrics

time parameter consensus value Truth We’d like to avoid this

collect data choose and fit systematics + physical model measure tension between experiments, internal goodness of fit if tension, force loser to update systematics model if agreement and good fits, update “consensus”

National Aeronautics and 
 Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

Tension Metric Metrics

collect data choose and fit systematics + physical model measure tension between experiments, internal goodness of fit if tension, force loser to update systematics model if agreement and good fits, update “consensus”

time parameter consensus value Truth And we want to be sure we’re not doing this.