Perspec'ves on Dark Energy beyond the spherical cow Robert Caldwell Cos moo 2008 Dartmouth College Madison, Wisconsin
Dark Energy Equa/on of State WMAP 5: Komatsu et al, arxiv:0803.0547 Ω m h 2 = 0 . 1369 ± 0 . 0037 Ω Λ = 0 . 721 ± 0 . 015 w = − 0 . 984 +0 . 065 Ω k = − 0 . 0046 +0 . 0066 − 0 . 0067 − 0 . 064
Dynamical Dark Energy: Quintessence aLempt a classifica'on of scalar field models thawing Field is cri'cally damped un'l Hubble fric'on drops; w starts at ‐1 and grows larger any field near minimum: V=V’=0 massive scalar, axion / pngb freezing Field decays un'l curvature of poten'al causes field to slow; w evolves towards ‐1 “tracker” / runaway or vacuumless field s'cking point & glaciers A simplisCc view may help to understand the range of possibiliCes CriLenden et al , PRL 98, 251301 (2007); Huterer & Peiris, PRD 75, 083503 (2007)
Dynamical Dark Energy: Quintessence phase space domains ALempt to iden'fy a scale for dw/d ln a In pracCce, these may be difficult to disCnguish Caldwell & Linder, PRL 95, 141301 (2005) also see: CriLenden et al , PRL 98, 251301 (2007); Huterer & Peiris, PRD 75, 083503 (2007)
Dynamical Dark Energy w ( a ) = w 0 + w a (1 − a ) chi‐by‐eye
w perspecCves on dark energy w=‐1? Simple parameteriza'ons of w(z) may be suscep'ble to bias towards w=‐1. w>‐1? Binned distance data may be suscep'ble to bias towards w>‐1 . w<‐1? Distance data may be suscep'ble to bias towards w<‐1 .
w w<‐1? Distance data may be suscep'ble to bias towards w<‐1 . 2 ( w − w 0 ) 2 ∂ 2 r r ( z, w ) = r | w 0 + ( w − w 0 ) ∂ r ∂ w | w 0 + 1 ∂ w 2 | w 0 + ... ∂ w , ∂ 2 r ∂ r ∂ w 2 < 0 An increase in w=w 0 + Δ produces more change in r than a decrease w=w 0 ‐ Δ . More change in r means poorer fit of model to data. Symmetric errors on distance or magnitude will cause the likelihood L(w)=exp(‐ χ 2 [ w ] /2) to be skewed towards nega've w : γ W <0. � w � − w peak ≈ 1 2 γ w σ w , � w � < w 0 , w peak > w 0
w w<‐1? Distance data may be suscep'ble to bias towards w<‐1 . marginalize! � w � < w 0 w 0 < w peak
w w<‐1? Distance data may be suscep'ble to bias towards w<‐1 . Sarkar, Cooray, Caldwell (in prepara'on, 2008)
Lost? Is Dark Energy Phenomena due to New GravitaCon?
Gravity? Is dark energy due to new gravita'onal phenomena? A problem of balance: 3 H 2 = 8 π G ρ Not enough curvature per unit mass? Consider a modulaCon in the strength of gravitaCon that produces dark energy phenomena consistent with LCDM. Local and Global descrip'ons of space'me curvature ds 2 = − (1 − 2 Gm r ) dt 2 + (1 + 2 γ Gm x 2 r ) d � ds 2 = − a 2 [(1 + 2 ψ ) dt 2 + (1 − 2 φ ) d � x 2 ] Consistent with a variety of gravitaConal theories!
Gravity? Is dark energy due to new gravita'onal phenomena? ds 2 = − a 2 [(1 + 2 ψ ) dt 2 + (1 − 2 φ ) d � x 2 ] x = − � ¨ ∇ 2 φ = 4 π G δρ φ � = ψ : � ∇ ψ ,
Gravity? Build a phenomenological model to test for consistency Consider a background expansion consistent with LCDM Impose inequality between gravita'onal poten'als ψ ≡ (1 + ̟ ) φ , ̟ = ̟ ( t, � x ) Toy model: dark energy domina'on causes gravita'onal “slip” ̟ ( t ) = ̟ 0 ρ DE / ρ m ( t ) expect ̟ 0 ∼ ± 1 Caldwell, Cooray, Melchiorri, PRD 76, 023507 (2007) Daniel et al, PRD 77, 103513 (2008) busy! Bertschinger, ApJ 648, 797 (2006) ̟ , γ , η , Φ ± , ... Bertschinger & Zukin, PRD 78, 024015 (2008) Hu & Sawicki, PRD 76, 104043 (2007) Zhang et al, PRL 99, 141302 (2007) …
Gravity? Build a phenomenological model to test for consistency cmb : WMAP5 + sne : Union + wl : CFHTLS + isw : SDSS x WMAP Daniel et al (in prepara'on, 2008)
Evidence for our Robertson‐Walker space'me A Mirage? Maartens et al, PRD 51, 1525 (1995) Is dark energy really there? Hogg et al, ApJ 624, 54 (2005) A Test of the Copernican Principle also: Goodman PRD 52, 1821 (1995) Stebbins & RC, PRL 100, 191302 (2008)
u ‐distor'on A blackbody spectrum at temperature T mixed with a blackbody at temperature T+ Δ T produces a u ‐distorted blackbody. Stebbins, astro‐ph/0703541 � ∞ 3 � dz ′ d τ n ′ ) 2 ) n ′ (1 + (ˆ u [ˆ n ] = d ˆ n · ˆ 16 π dz ′ 0 � 2 � ∆ T n, z ] − ∆ T n ′ , ˆ T [ˆ n, ˆ T [ˆ n, z ] × Degenerate with Compton y‐distor'on parameter: u = 2y FIRAS: y < 15 x 10 ‐6 (95%): Fixen et al, ApJ 473, 576 (1996)
Nonlinear Inhomogeneous Space'me ( ∂ r R ) 2 ds 2 = − dt 2 + 1 + k ( r ) r 2 dr 2 + R 2 ( t, r ) d Ω 2 Lemaitre (1933), Tolman (1934), Bondi (1947) (See Krasinski (1997) for more general inhomogeneous, perfect fluid models) k(r) : curvature func'on fixes the mass density profile R(t,r) : solve for the radially‐dependent scale factor k ( r ) 1 − Ω 0 = H 2 1 + ( r/r 0 ) n 0 InstrucCons : Garfinkle, CQG 23, 4811 (2006), Garcia‐Bellido & Haugbolle, JCAP 0804:003 (2008)
Nonlinear Inhomogeneous Space'me Single‐sca\ering recipe: √ 1 + kr 2 √ 1 − L 2 − ˙ R ′ dR R = ˙ (1 + z )(1 − L 2 Q ) dz R ′ R ( t, r ) = a ( t, r ) r a ′ √ 1 + kr 2 √ 1 − L 2 − ˙ aR ′ da ˙ = RR ′ ℓ L = (1+ z ) R , Q = 1 − ˙ dz R ˙ R ′ (1 + z )(1 − L 2 Q ) R ′
Nonlinear Inhomogeneous Space'me u ‐distor'on rules out a wide range of parameters describing an'‐Copernican, inhomogeneous cosmological models n=2 (smooth) future FIRAS Caldwell & Stebbins, in prepara'on (2008)
Nonlinear Inhomogeneous Space'me u ‐distor'on rules out a wide range of parameters describing an'‐Copernican alterna'ves to Dark Energy n=2 (smooth) future FIRAS BAO, CMB, H, SNe Caldwell & Stebbins, in prepara'on (2008)
Nonlinear Inhomogeneous Space'me u ‐distor'on rules out a wide range of parameters describing an'‐Copernican alterna'ves to Dark Energy n=4 (sharp) future FIRAS BAO, CMB, H, SNe Caldwell & Stebbins, in prepara'on (2008)
Λ ? Q ρ G
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