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

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

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

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

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

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

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

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

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

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

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, Michael Mortonson KICP/UChicago

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, Michael Mortonson KICP/UChicago

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

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, Michael Mortonson KICP/UChicago

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

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

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, Michael Mortonson KICP/UChicago

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

Dark Energy Principal Components January 22, Michael 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)

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

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

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)

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

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

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

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

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

January 22, Michael Mortonson KICP/UChicago  CDM

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

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

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

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

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

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

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

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

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

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

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

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

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: ] January 22, Michael Mortonson KICP/UChicago