Falsifying Paradigms forCosmic Acceleration

Michael Mortonson

Kavli Institute for Cosmological PhysicsUniversity 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

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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

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Cosmic Expansion and Acceleration

Friedmann equation:

Acceleration:

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Evidence for Acceleration

Type Ia Supernovae

“Union”compilation(Kowalskiet al. 2008)

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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

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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)

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Flat CDM Observablesm=0.24, K=0, h=0.73

Expansion rate:

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Distance:

m=0.24, K=0, h=0.73

Flat CDM Observables

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m=0.24, K=0, h=0.73

Growth:

Flat CDM Observables

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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

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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

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Planck

SNAP SNe, Planck CMB,priors based on current data

Measure distances:

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Planck

SNAP SNe, Planck CMB,priors based on current data

Measure distances:

PriorsBAO: DV(z=0.35) [SDSS]

H0 [HST Key Project]Early DE fraction

[WMAP]

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Choose class of DE models:+ priors on w(z)

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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)

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Dark Energy Principal Components

Eigenfunctions ofSN+CMB Fisher matrix

Principalcomponentsof w(z)

PCs ordered by eigenvalues of F = (variance)-1 from distance data,so higher variance PCs affect observables less

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Dark Energy Principal Components

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N ~ 10-15 PCsfor completeness

Dark Energy Principal Components

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• Use PC basis functions to span the model spacewithin a class of DE models

• These are not physically-motivated models, but anyparticular 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)

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Flat, or nonzerospatial curvature?

K

Choose class of DE models:+ priors on w(z)

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Find models that fit distances: MCMC

w(z), w∞, K

H(z)

D(z) G(z)

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Find models that fit distances: MCMC

w(z), w∞, K

H(z)

D(z) G(z)SN+CMB data Predictions

Compute observables (e.g. growth) for models that fit distance data

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Compute observables (e.g. growth) for models that fit distance data

January 22, 2009 25Michael Mortonson KICP/UChicago

Compute observables (e.g. growth) for models that fit distance data

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Compute observables (e.g. growth) for models that fit distance data

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CDM

Michael Mortonson KICP/UChicago

CDM

pivot

H2 ≈ mH02

(1+z)3H ≈ H0

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Quintessence: -1<w<1(flat, no early DE)

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Quintessence + early DE or curvature

flat, early dark energy

w < –1

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Quintessence + early DE or curvature

closed, no early dark energy

w < –1

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Quintessence + early DE or curvature

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Quintessence +early DE and curvature

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Smooth DE: -5<w<3(flat, no early DE)

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Smooth DE withearly DE and curvature

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Smooth DE withearly DE and curvature

Smooth DE withearly DE and curvature

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Growth Index

Growth rate:

Growth index:

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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:0810.1744]

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