The posterior predictive distribution as a measure of tension - PowerPoint PPT Presentation

The posterior predictive distribution as a measure of tension Hiranya V. Peiris 
 UCL and Oskar Klein Centre Stockholm

Cosmic Consistency Efstathiou, Bond, White (1992)

Cosmic Consistency Bahcall, Ostriker, Perlmutter, Steinhardt (1999)

Cosmic Consistency lines: Planck prediction from primary CMB Baryon acoustic scale (standard ruler) and amplitude 
 as a function of redshift in galaxy survey data BOSS Collaboration (Auborg et al 2015)

Cosmic Consistency Planck prediction from primary CMB CMB lensing amplitude and scale dependence ACTPol Collaboration (Sherwin et al 2017)

Cosmic (in)consistency? growth of structure Amplitude of fluctuations Matter density weak gravitational lensing measurements (450 sq. deg.) KiDS Collaboration (Hildebrandt et al 2017)

Cosmic (in)consistency? watch this space! Amplitude of fluctuations Matter density weak gravitational lensing + galaxy clustering measurements 
 (1321 sq. deg.) DES Collaboration (2017)

Cosmic (in)consistency? expansion history Planck prediction from primary CMB H0 measurement (Riess et al. 2016) DR12 BOSS Galaxy BAO (Alam et al. 2016) DR12 BOSS Lyman alpha forest BAO (du-Mas-des-Bourboux et al. 2017) Figure: Andreu Font-Ribera

Watch this space! DESI (first light 2019) Forecasts: Font-Ribera et al (2014)

H 0: Cosmological vs distance ladder measurements Figure: Science Magazine

Cosmic (in)consistency: real or “tension in a teapot”? Systematics? astrophysics? (new) physics? Freedman (2017) adapted from Beaton et al (2016)

“No one trusts a model except the person who wrote it; everyone trusts an observation, except the person who made it”. paraphrasing H. Shapley

Prospects for Resolving the H 0 Tension with Standard Sirens arXiv:1802:03404 Stephen M. Feeney, Hiranya V. Peiris, Andrew R. Williamson, Samaya M. Nissanke, Daniel Mortlock, Justin Alsing, Dan Scolnic

H 0 : why care, and how? • Cosmological parameter that can be measured locally, assuming minimal physical model. • “Simplest” method: measure robust distance and redshift • Use distance ladders assuming minimal cosmology - “local”: use nearby Cepheids w/ known distances to calibrate supernovae @ z ≃ 0.2 - “inverse”: use supernovae and BAOs to extrapolate CMB sound horizon @ radiation drag scale from z=1100 to ~0 • Use CMB anisotropies assuming complete cosmology

Standard Bayesian tension metrics • Marshall++ (1404.5950) , DES Yr1 (1708.01530), Feeney++ (1707.00007) use model comparison to assess tension. • Is it more likely that each dataset is measuring its own parameter set or that both datasets are measuring the same? • Need alternate non-physical “designer” model w/ extra parameter(s). Not obvious what alternative to use. • Answer depends linearly on volume of extra parameter space: more volume, less tension!

Model Assessment: posterior predictive distribution • Sampling distribution of new data d’ given old data d and model I with parameters 𝜾 Z Pr( d 0 | d , I ) = Pr( d 0 | θ , I ) Pr( θ | d , I ) d θ • “Convolution” of likelihood of new data w/ posterior of old • Compare measured values to PPD: are new data consistent with being a draw from the model? • Model assessment (no need for alternative model), weak dependence on prior

Quantifying tension with PPD • Treat Cepheid distance ladder H 0 as data: H 0 posterior given Planck, LCDM • PPD: predicted sampling Cepheid distribution of given distance ladder prediction given Planck CMB data, LCDM Planck, LCDM Measured • Is SH 0 ES measurement cepheid distance ladder consistent with draw from H 0 PPD? • Summarize tension using PPD(observed H 0 ) / max(PPD) = 1/45

Can other data arbitrate? Pantheon SN sample Cepheid distance BOSS DR12 BAO ladder H 0 post measurements Inverse distance Inverse distance ladder expansion ladder H 0 post history Planck LCDM Planck LCDM H 0 posterior expansion history • Inverse distance ladder: BOSS BAOs + Pantheon SNe (Scolnic+:1710.00845) + CMB drag scale from Planck • Assume smooth expansion & pre-recombination physics only Feeney, Peiris et al (2018)

H 0 tension and inverse distance ladder Pantheon SN sample Cepheid distance BOSS DR12 BAO ladder H 0 post measurements Inverse distance Inverse distance ladder expansion ladder H 0 post history Planck LCDM Planck LCDM H 0 posterior expansion history • Inverse distance ladder H 0 posterior agrees with Planck LCDM • Distance ladders are in significant tension Feeney, Peiris et al (2018)

Inverse distance ladder with WMAP Pantheon SN sample BOSS DR12 BAO Cepheid distance measurements ladder H 0 post Inverse distance Inverse distance ladder expansion ladder H 0 post history WMAP LCDM WMAP LCDM H 0 posterior expansion history • Inverse distance ladder H 0 posterior using WMAP9’s drag scale estimate is consistent with Planck Feeney, Peiris et al (2018)

Quantifying tension: inverse distance ladder Prediction given inverse distance ladder, smooth exp Measured Cepheid Prediction given distance ladder H 0 Planck, LCDM Measured cepheid Prediction given distance ladder H 0 inverse distance ladder, smooth exp. Prediction given Planck, LCDM • Compute sampling distribution of given inverse distance ladder observations, assuming smooth expansion • Summarize tension using PPD(observed H 0 ) / max(PPD) = 1/17

The story so far • Two distance ladder measurements inconsistent with draw from same model • But supernovae in common… • New independent data to arbitrate tension? GW standard sirens!

Arbitrating H 0 tension with GW standard sirens • Simulate binary neutron star mergers Luminosity distance posteriors w/ EM counterparts (angular position and redshift known) • Four years of LIGO/ Virgo, assuming R BNS =1500/Gpc 3 /yr • Waveforms injected in coloured noise, analysed with lalinference_mcmc (Veitch+:1409.7215) • 51 detectable events Feeney, Peiris et al (2018)

Arbitrating H 0 tension with GW standard sirens • Compute H 0 posterior assuming perfect redshift measurements + Gaussian peculiar velocity likelihoods • Sample of 51 mergers sufficient to arbitrate tension (though sample variance important) Feeney, Peiris et al (2018)

Arbitrating tension using standard sirens SH 0 ES Planck PPD Ratios correct correct Planck Cepheid True H 0 Planck CDL Obs. H 0 PPDs for Cepheid H 0 1/2 1/10 Planck PPDs for CMB H 0 Standard siren H 0 uncertainty 1/300 1/2 CDL • Plotting PPD for CMB and Cepheid distance ladder given simulated standard siren sample and assumed H 0 • Sample of 51 mergers sufficient to arbitrate tension (though sample variance important)

Impact of realization noise Planck SH0ES correct correct Planck Cepheid PPDs for Cepheid H 0 PPDs for CMB H 0 • PPD variations from 1000 bootstrapped samples • Negligible realization noise w/ ~80/3000 events if SH0ES/Planck correct (PPD dominated by siren posterior/SH0ES likelihood)

Conclusions • Posterior prediction distribution provides powerful tool for model assessment. • “H0 tension” example illustrates utility in cosmology: - support for “Planck” H0 from inverse distance ladder (but same SNe as Cepheid ladder, some CMB info used); - completely independent GW data will arbitrate within decade.

G.R.E.A.T. @ Stockholm 
 Gravitational Radiation and Electromagnetic Astrophysical Transients • 6 year programme. • Create end-to-end simulations of EM signals from compact object mergers. • Use to optimize search strategies and perform searches for electromagnetic counterparts of GW events in ZTF and LSST. • Join us! https://www.great.cosmoparticle.com H IRANYA P EIRIS , J ESPER S OLLERMAN , S TEPHAN R OSSWOG , AND A RIEL G OOBAR

C OSMOPARTICLE , WWW.PENELOPEROSECOWLEY.COM