Can we detect tracking dark energy dynamics?

Can we detect tracking dark energy dynamics?

Bruce Bassett, Mike Brownstone, Antonio Cardoso, Marina Côrtes,

Yabebal Fantaye, Renee Hlozek, Jacques Kotze, Patrice Okouma

Bruce Bassett, Mike Brownstone, Antonio Cardoso, Marina Côrtes,

Yabebal Fantaye, Renee Hlozek, Jacques Kotze, Patrice Okouma

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Big Bang NucleosynthesisBig Bang Nucleosynthesis• Hence we can constrain the amount of dark energy

at BBN. Bean et al. (2001) find

at 2

• CMB constraints (Doran et al. 2005, 2006) from the power spectrum give

• Hence we can constrain the amount of dark energy at BBN. Bean et al. (2001) find

at 2

• CMB constraints (Doran et al. 2005, 2006) from the power spectrum give

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Tracking ModelsTracking Models

DE Dominated

Matter dominated

Radiation dominated

Perfect scalingSlow transition

Where the field stops Where the field stops tracking and starts to tracking and starts to dominatedominate

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Linking BBN to late timesLinking BBN to late times• Tracking Dark Energy models link the

constraints on DE at z = 1010 to today via the energy density of DE

• Tracking Dark Energy models link the constraints on DE at z = 1010 to today via the energy density of DE

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Hubble ParameterHubble Parameter

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as zas zt t →∞, r → 0 →∞, r → 0

Specific late-time modelsSpecific late-time models• Two broad classes of tracking models

considered – polynomial w(z) and scalar field φ in a double exponential potential

• Polynomial:

• Linear case (w2=0) → zt≈ 6.2

• Two broad classes of tracking models considered – polynomial w(z) and scalar field φ in a double exponential potential

• Polynomial:

• Linear case (w2=0) → zt≈ 6.2

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Quadratic CaseQuadratic Case• If w2≠0 then w(zt)=0 → • If w2≠0 then w(zt)=0 →

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w(0) = -1w(0) = -1zztt > 4.02 > 4.02

to ensure to ensure w(z) ≥-1 w(z) ≥-1

w< -0.8 for all w< -0.8 for all z< 1z< 1

Dark Energy DensityDark Energy Density

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H(z) - quadraticH(z) - quadratic

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2.7%2.7%

Δμ(z) - quadraticΔμ(z) - quadratic

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DETF Stage DETF Stage IIIIIIerrors between errors between 0.02 and 0.3 0.02 and 0.3 magmag

DETF DETF Stage IV Stage IV (SNAP-like)(SNAP-like)Errors ~ Errors ~ 0.01mag0.01mag

Deviation →0.03 mag as z →∞Deviation →0.03 mag as z →∞

Double Exponential PotentialDouble Exponential Potential

• Not perfect scaling: the BBN constraint is now• Not perfect scaling: the BBN constraint is now

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Double Exponential PotentialDouble Exponential Potential

• Two cases: – → smooth w(z) at low

redshift

– → oscillating w(z)

• Two cases: – → smooth w(z) at low

redshift

– → oscillating w(z)

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Double Exponential PotentialDouble Exponential Potential

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Double Exponential PotentialDouble Exponential Potential

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Double Exponential PotentialDouble Exponential Potential

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Field Field φφ oscillates oscillates around around minimumminimum

Double Exponential PotentialDouble Exponential Potential

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Double Exponential PotentialDouble Exponential Potential

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Double Exponential PotentialDouble Exponential Potential

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Early Early scalingscaling

Late-timeLate-timeAcceleration Acceleration with smooth with smooth w(z)w(z)

Derived w(z) from Double Exponential V(φ)

Derived w(z) from Double Exponential V(φ)

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All models All models have have w<-0.98 for w<-0.98 for z<0.2z<0.2

Energy Density - DEPEnergy Density - DEP

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H(z) - DEPH(z) - DEP

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Forcing Forcing w(0) < -0.9 w(0) < -0.9 means means deviation < deviation < 2.5%2.5%

Δμ(z) - DEPΔμ(z) - DEP

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Solid line Solid line → → w(0) = -0.9 w(0) = -0.9 modelmodel

All All oscillating oscillating models models have |have |ΔμΔμ| | <0.032<0.032

Failure of standard parametrisations

Failure of standard parametrisations

• Chevalier-Polarski-Linder parametrisation

is most widely used • Forms the basis for the DETF Figure of Merit• If φ is to be a minimally coupled canonical scalar

field → w(z) ≥ -1 for all z• CPL cannot match both BBN and have

w(z) ≥ -1

• Logarithmic w(z) works, but requires zt > 12.4

• Chevalier-Polarski-Linder parametrisation

is most widely used • Forms the basis for the DETF Figure of Merit• If φ is to be a minimally coupled canonical scalar

field → w(z) ≥ -1 for all z• CPL cannot match both BBN and have

w(z) ≥ -1

• Logarithmic w(z) works, but requires zt > 12.4

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CPL Energy DensityCPL Energy Density

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PhantomPhantomw needed to w needed to match the match the BBN BBN constraintsconstraints

ConclusionsConclusions

• Detection of tracking dynamics will be limited until Stage IV experiments

• The standard CPL parametrisation cannot match BBN when describing fields with w(z) ≥ -1

• Detection of tracking dynamics will be limited until Stage IV experiments

• The standard CPL parametrisation cannot match BBN when describing fields with w(z) ≥ -1

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Conditions on modelsConditions on models• So if w large today it must stay flat:

• In all our models

• For the linear parametrisation we find

• So if w large today it must stay flat:

• In all our models

• For the linear parametrisation we find

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w(0) – w’(0) connectionw(0) – w’(0) connection• Empirical relation for other models?

• To be considered in more detail in future work

• Empirical relation for other models?

• To be considered in more detail in future work

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