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BBN Constraints on Scaling Quintessence Models and Dark Energy - - PowerPoint PPT Presentation
BBN Constraints on Scaling Quintessence Models and Dark Energy - - PowerPoint PPT Presentation
BBN Constraints on Scaling Quintessence Models and Dark Energy Surveys Antonio Cardoso University of Portsmouth Bruce Bassett, Mike Brownstone, Marina Cortes, Yabebal Fantaye, Renee Hlozek, Jacques Kotze, Patrice Okouma University of Cape
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Scaling models
Wetterich, 1988 ◮ Exponential potential
V (φ) = M4e−λκφ κ2 = 8πG
◮ λ2 > 3(1 + wb): scales with the background fluid
wφ = pφ/ρφ = wb Ωφ = 3(1 + wb)/λ2
◮ λ2 < 3(1 + wb): dominant component of the universe
wφ = −1 + λ2/3 Ωφ = 1 Ωφ = ρφ/ρc ρc = 3H2/8πG
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Constraints from BBN
◮ The presence of a scalar field changes the expansion rate of
the universe at a given temperature
◮ Affects the abundance of light elements at the time of
nucleosynthesis
◮ Constraint on Ωφ during the radiation dominated era Bean, Hansen and Melchiorri, 2001
Ωφ(T ∼ 1MeV ) < 0.045
◮ Constraint on the value of λ (in the scaling regime)
λ2 > 4 0.045 ⇒ λ 9.43
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Polynomial w(z) parametrization
◮ Scaling until zt and w(z) = w0 + w1z + w2z2 in the region
0 ≤ z < zt
◮ Assume w(zt) = wm = 0 and w(0) = −1
w(z) = −1 + w1z + 1 z2
t
− w1 zt
- z2
ΩDE(zt) = Ω(0)
DEf (zt)
Ω(0)
DEf (zt) + Ω(0) m (1 + zt)3 = 0.045
f (z) = exp
- 3
z 1 + w(z′) 1 + z′ dz′
- ◮ Solve w1 as a function of zt
◮ Use BBN bound to maximise deviations from Λ
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Polynomial w(z) parametrization
◮ Need the constraint w(z) > −1 for all z to describe a
canonical scalar field
0.1 1 10 −1 −0.8 −0.6 −0.4 −0.2
z
w(z)
0.01 0.1 1 10 1 1.005 1.01 1.015 1.02 1.025
z
HDE(z)/HΛCDM ◮ 2.7% deviations of H(z) from ΛCDM ◮ Largest deviation occurs at z ∼ 2
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Polynomial w(z) parametrization
◮ ∆µ(z) = 5 log10
dDE
L
(z) dΛCDM
L
(z)
- dL(z) = (1 + z)
z
dz′ H(z′)
0.5 1 1.5 2 −0.06 −0.04 −0.02 0.02 0.04
z
∆µ(z)
◮ Predicted errors in the DETF report for Stage III (blue) and
Stage IV (black) surveys
Albrecht et al, 2006
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Double exponential potential
◮ Potential with two exponential terms Barreiro, Copeland and Nunes, 2000
V (φ) = M4
1e−λκφ + M4 2e−µκφ ◮ Scales during the radiation and matter epochs and dominates
at late times
◮ Need µ2 < 2 to have acceleration and M2 such that
Ω(0)
φ
∼ 0.7 and Ω(0)
m ∼ 0.3 ◮ Evolution equations
¨ φ + 3H ˙ φ + V,φ = 0 ˙ ρm + 3Hρm = 0 ˙ ρr + 4Hρr = 0 H2 = κ2 3 1 2 ˙ φ2 + V (φ) + ρm + ρr
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Double exponential potential
◮ V (φ) = M4 1e−λκφ + M4 2e−µκφ
0.1 1 10 −1 −0.8 −0.6 −0.4 −0.2
z
w(z)
0.01 0.1 1 10 1 1.01 1.02 1.03 1.04 1.05
z
w(0) = −0.8
HDE(z)/HΛCDM
w(0) < −0.9
◮ wφ(0) −0.9 implies 2.7% deviations of H(z) from ΛCDM ◮ Largest deviation occurs at z ∼ 1
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Double exponential potential
0.5 1 1.5 2 −0.1 −0.05 0.05
z
∆µ(z)
◮ Predicted errors in the DETF report for Stage III (blue) and
Stage IV (black) surveys
Albrecht et al, 2006
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