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Falsifying Paradigms for Cosmic Acceleration Michael Mortonson Kavli Institute for Cosmological Physics University of Chicago January 22, 2009

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Outline Cosmic acceleration Observables and fiducial data for forecasts (SNAP, Planck) Dark energy models – principal components of w(z) Predictions for growth and expansion observables from distances January 22, 20092Michael Mortonson KICP/UChicago

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Dark Energy Consistency Tests 1.Find the range of possible growth histories (and other observables) for a given set of distance measurements for all dark energy models in a particular class (e.g. quintessence) 2.Test the dark energy model class by measuring the growth history directly and comparing with the growth predicted from distances January 22, 20093Michael Mortonson KICP/UChicago

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Cosmic Expansion and Acceleration Friedmann equation: Acceleration: January 22, 20094Michael Mortonson KICP/UChicago

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Evidence for Acceleration Type Ia Supernovae “Union” compilation (Kowalski et al. 2008) January 22, 20095Michael Mortonson KICP/UChicago

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Acceleration Paradigms Cosmological constant/vacuum energy ( ): Scalar field (quintessence): Dark energy beyond quintessence (e.g., non-canonical kinetic term) Modified gravity Violation of spatial homogeneity January 22, 20096Michael Mortonson KICP/UChicago

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Dark Energy Phenomenology Time-varying w(z): Early dark energy (e.g. tracking models) CMB acoustic peaks: (Doran, Robbers, & Wetterich 2007) Big Bang nucleosynthesis: (Bean, Hansen, & Melchiorri 2001) January 22, 20097Michael Mortonson KICP/UChicago

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Flat CDM Observables m =0.24, K =0, h=0.73 Expansion rate: January 22, 20098Michael Mortonson KICP/UChicago

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Distance: m =0.24, K =0, h=0.73 Flat CDM Observables January 22, 20099Michael Mortonson KICP/UChicago

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m =0.24, K =0, h=0.73 Growth: Flat CDM Observables January 22, 200910Michael Mortonson KICP/UChicago

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Dark Energy Consistency Tests 1.Find the range of possible growth histories (and other observables) for a given set of distance measurements for all dark energy models in a particular class (e.g. quintessence) 2.Test the dark energy model class by measuring the growth history directly and comparing with the growth predicted from distances January 22, 200911Michael Mortonson KICP/UChicago

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Dark Energy Consistency Tests 1.Find the range of possible growth histories (and other observables) for a given set of distance measurements for all dark energy models in a particular class (e.g. quintessence) SNAP SNe, Planck CMB, priors based on current data Measure distances: Choose class of DE models: + priors on w(z) Find models that fit distances: MCMC Compute observables (e.g. growth) for models that fit distance data January 22, 200912Michael Mortonson KICP/UChicago

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Planck SNAP SNe, Planck CMB, priors based on current data Measure distances: January 22, 200913Michael Mortonson KICP/UChicago

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Planck SNAP SNe, Planck CMB, priors based on current data Measure distances: Priors BAO: D V (z=0.35) [SDSS] H 0 [HST Key Project] Early DE fraction [WMAP] January 22, 200914Michael Mortonson KICP/UChicago

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Choose class of DE models: + priors on w(z) January 22, 200915Michael Mortonson KICP/UChicago

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or w(z)? Principal components of w(z) at z < 1.7 Choose class of DE models: + priors on w(z) January 22, 200916Michael Mortonson KICP/UChicago

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Dark Energy Principal Components Eigenfunctions of SN+CMB Fisher matrix Principal components of w(z) PCs ordered by eigenvalues of F = (variance) -1 from distance data, so higher variance PCs affect observables less January 22, 200917Michael Mortonson KICP/UChicago

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Dark Energy Principal Components January 22, 200918Michael Mortonson KICP/UChicago N ~ 10-15 PCs for completeness

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Dark Energy Principal Components January 22, 200919Michael Mortonson KICP/UChicago Use PC basis functions to span the model space within a class of DE models These are not physically-motivated models, but any particular w(z) can be represented by PCs Reconstruction of w(z) is not the goal (PCs are complete in observables, not w)

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Large fraction of DE at early times (EDE)? w(z > 1.7) = w ∞ Choose class of DE models: + priors on w(z) January 22, 200920Michael Mortonson KICP/UChicago

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Flat, or nonzero spatial curvature? KK Choose class of DE models: + priors on w(z) January 22, 200921Michael Mortonson KICP/UChicago

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January 22, 2009Michael Mortonson KICP/UChicago 22 Find models that fit distances: MCMC w(z), w ∞, K H(z)H(z) D(z)D(z)G(z)G(z)

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January 22, 2009Michael Mortonson KICP/UChicago 23 Find models that fit distances: MCMC w(z), w ∞, K H(z)H(z) D(z)D(z)G(z)G(z) SN+CMB data Predictions

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Compute observables (e.g. growth) for models that fit distance data January 22, 200924Michael Mortonson KICP/UChicago

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Compute observables (e.g. growth) for models that fit distance data January 22, 200925Michael Mortonson KICP/UChicago

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Compute observables (e.g. growth) for models that fit distance data January 22, 200926Michael Mortonson KICP/UChicago

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Compute observables (e.g. growth) for models that fit distance data January 22, 200927Michael Mortonson KICP/UChicago

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January 22, 200928Michael Mortonson KICP/UChicago CDM

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Michael Mortonson KICP/UChicago CDM pivot H 2 ≈ m H 0 2 (1+z) 3 H ≈ H 0 January 22, 200929

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Quintessence: -1<w<1 (flat, no early DE) January 22, 200930Michael Mortonson KICP/UChicago

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Quintessence + early DE or curvature flat, early dark energy w < –1 January 22, 200931Michael Mortonson KICP/UChicago

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Quintessence + early DE or curvature closed, no early dark energy w < –1 January 22, 200932Michael Mortonson KICP/UChicago

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Quintessence + early DE or curvature January 22, 200933Michael Mortonson KICP/UChicago

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Quintessence + early DE and curvature January 22, 200934Michael Mortonson KICP/UChicago

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Smooth DE: -5<w<3 (flat, no early DE) January 22, 200935Michael Mortonson KICP/UChicago

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January 22, 200936Michael Mortonson KICP/UChicago Smooth DE with early DE and curvature

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January 22, 200937Michael Mortonson KICP/UChicago Smooth DE with early DE and curvature

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Smooth DE with early DE and curvature January 22, 200938Michael Mortonson KICP/UChicago

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Growth Index Growth rate: Growth index: January 22, 200939Michael Mortonson KICP/UChicago

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January 22, 200940Michael Mortonson KICP/UChicago Growth Index CDM Quintessence Smooth dark energy

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Summary Combinations of distance and growth observables can falsify classes of dark energy models With SNAP + Planck data, CDM predictions for growth and expansion histories are very strong More general w(z) have strong distance-growth relations for flat geometry and small early DE fraction Allowing freedom in curvature and early DE, quintessence makes one-sided predictions, and more general w(z) can be tested by checking consistency of observations across multiple redshifts Mortonson, Hu, & Huterer (2009), PRD (in press) [arXiv:0810.1744] January 22, 200941Michael Mortonson KICP/UChicago

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