Cosmic Calibration - Statistical Modeling for Dark Energy

1. Cosmic Calibration - Statistical Modeling for Dark Energy UCSC Tracy Holsclaw, Bruno Sanso, and Herbie Lee LANL Ujjaini Alam, Katrin Heitmann, David Higdon and Salman Habib LA-UR-09-05891

2. Overview -The Universe is expanding (1920s) -Observations have been made that the Universe is expanding at an accelerating pace (1998) -Ordinary matter would mean the Universe is decelerating -Dark energy is the unknown driver of this acceleration -Dark energy has an equation of state relating its pressure to density; this equation is our focus to understand more about the nature of dark energy -Our current method is based on Bayesian analysis of a differential equation by modeling w(z) directly, where w(z) is the equation of state parameter

3. Data of Interest We want to know whether w(z), the equation of state for Dark Energy, is constant or not BAO – Baryon Acoustic CMB- Cosmic Microwave Oscillation Background large scale matter clusteringprobes the oldest light in the Universe 0 2 1000 Redshift (z) SNe – Supernovae Stars 397 measurements Photos provided by NASA

4. Likelihood Equation • -The main parameter of interest is w(z); we need to specify a form for w(z) • -Three other unknown parameters also have to be estimated H0, Ωm, M, and σ2 • This leads to the following likelihood equation: CMB SNe BAO

5. Overview of the Models Model 1: w(u) = α Model 2: w(u) = α-βu/(1+u) Gaussian Process: w(ui) ~ GP(-1, k2ρ|u-u’|2) -Prior sensitivity was examined and thus far it seems that the prior does not change the outcome of the estimations Ωr=0.247/ Ho2 π(Ho) ~ N(71.9, 2.72) π(σ2) ~ IG(10,9) π(Ωm| Ho) ~ N(0.1326(100/ Ho)2, (0.0063(100/ Ho)2) 2) π(α) ~ U(-25,1) π(β) ~ U(-25,25)

6. Model 1: w(u) = α SNe SNe+BAO SNe+CMB SNe+BAO+CMB

7. Model 2:w(u) = α – βu/(1+u) SNe SNe+BAO SNe+CMB SNe+BAO+CMB

8. Gaussian Process Model SNe SNe+BAO SNe+CMB SNe+BAO+CMB

9. Extended Model Model 1 Model 2 Gaussian Process Model -The parametric Model 2 does not extend well to a larger domain, whereas the Gaussian process model does

10. Conclusions • The Gaussian process method provides a non-parametric fit to the equation of state • The Gaussian process analysis has tighter estimated bands than one of the commonly used parametric forms • Unlike the parametric models the fit presented here is coherent even when extended to z=1000 • All methods presented here have been tested with simulated datasets and correct results have been obtained

11. Future Work • We would like to explore a new set of real data with nearly 600 Supernovae observations • We want to show that this work will extend to future data sets with 2000 SNe points and 20 BAO points. And how this new data could shrink the uncertainty of the parameters • The cosmologists would like to know where more observations (on the z axis) are needed to shrink uncertainty • We want to understanding how measurement error in the Supernovae data affects the analysis

12. Cosmic Calibration - Statistical Modeling for Dark Energy UCSC Tracy Holsclaw, Bruno Sanso, and Herbie Lee LANL Ujjaini Alam, Katrin Heitmann, David Higdon and Salman Habib