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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
arXiv:0709.0526arXiv:0709.0526
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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
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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
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Dark Energy DensityDark Energy Density
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H(z) - quadraticH(z) - quadratic
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2.7%2.7%
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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 →∞
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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
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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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Early Early scalingscaling
Late-timeLate-timeAcceleration Acceleration with smooth with smooth w(z)w(z)
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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
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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%
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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
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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
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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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