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Dark Energy's Dual Personality Dark Energy’s Dual Personality Rachel Bean Cornell University Dark Energy’s Dual Personality- Rachel Bean COSMO’08 Dark energy evidence I - Geometric distance measures Standard Candles Standard Rulers BAO SN1a GRBs? CMB SMBH? Parallax Water masers? Dark Energy’s Dual Personality- Rachel Bean COSMO’08 Dark Energy evidence II – Growth of structure So far lots focus on background evolution, little on perturbations… Yet the growth of structure provides lots of information ! Weak lensing Clusters Galaxies ISW Dark Energy’s Dual Personality- Rachel Bean COSMO’08 How do we interpret dark energy? No Is the universe Photons see extra dimension? Accelerating? Photon conversion? γ ? Yes No Is General Relativity correct? Modified gravity? Yes No Is Dark Energy matter Inhomogeneous universe: of some form? Beyond FLRW / Hubble Bubble? Yes No Is Dark Energy constant in our observable universe? New matter? Yes No Is Dark Energy constant Cosmological constant everywhere? Anthropic arguments? Yes Universal Cosmological Constant of unknown origin ? Dark Energy’s Dual Personality- Rachel Bean COSMO’08 How do we interpret dark energy? Modified gravity? New matter? Dark Energy’s Dual Personality- Rachel Bean COSMO’08 How do we interpret dark energy? Focus of this talk: Modified gravity? 1. Can modified gravity be a viable dark energy solution? 2. Can we distinguish modified gravity from L and matter? 3. Can we constrain dark sector New matter? interactions? Dark Energy’s Dual Personality- Rachel Bean COSMO’08 Why modify gravity? • Many theories predict deviations from GR • Conceivably, we don’t yet have the correct large (and small?) scale theory of gravity? • The starting point… the action describing motion in GR Action for gravity Action for matter (LHS of Einstein Eq) (LHS of Einstein Eq) Dark Energy’s Dual Personality- Rachel Bean COSMO’08 Why modify gravity? • Simplistically modifications -> scale/ time dependent G • Scalar tensor gravity - gravity mediated by scalar field φ? – e.g. Brans-Dicke theory R Φ R • Higher order terms? – e.g. f(R) theories R R + f(R) f(R) = A/R+… Low curvature (late time) modifications - dark energy f(R) = AR2+… High curvature (early time) modifications - inflation Dark Energy’s Dual Personality- Rachel Bean COSMO’08 Why modify gravity? • Gravity is a higher dimensional theory? – e.g. Dvali, Gabadaze, Porrati PLB 485:208(2000) – Induced intrinsic curvature on brane 2 – l >> lc 5D gravity (1/r ), l >> lc 4D gravity (1/r) gAB gAB lc Dark Energy’s Dual Personality- Rachel Bean COSMO’08 Constraining modifications to gravity Solar system Nucleosynthesis G/GN =1.21! G/GN =1.01! G/GN =0.85! Takeshi Chiba Copi, Davis, Krauss 2003 2 Tidal tails lite has a mass m and radius r which fill its tidal sat sat What about extra galactic constraints? radius rtid. When the satellite is much less massive than - galaxy distribution? the host galaxy, msat/MR 1, a distinct hierarchy, ! - peculiar velocities? Eorb Etid Ebin, (5) " " - weak lensing? …. exists in these three energy scales, implying that the dis- rupted stars and satellite will trace similar orbits in the Kesden & host galaxy’s potential regardless of the details of tidal Kamionkowski 2006 disruption or the satellite’s internal structure. The dis- rupted stars will act like purely baryonic test particles,Dark Energy’s Dual Personality- Rachel Bean COSMO’08 while the satellite itself behaves largely like a DM test particle, if it is DM dominated. Fortunately, the Sagittarius (Sgr) dwarf galaxy, the Milky Way’s closest satellite at a Galactocentric dis- tance of only 16 kpc, is nearly ideal for our purposes. The Sgr dwarf has extended leading and trailing tidal streams observed by the Two-Micron All Sky Survey (2MASS) [21] and the Sloan Digital Sky Survey (SDSS) [22]. Using a sample of over 1,000 M-giant stars with a known color-magnitude relation, the 2MASS collabora- FIG. 1: Simulations of the tidal disruption of a satellite galaxy tion have measured not just surface brightnesses along in the presence of a dark-matter force. The charge-to-mass the streams, but distances and spectroscopic velocities ratio β increases from 0.0 in increments of 0.1 going counter- as well [23]. Comparing these observations to simula- clockwise from the bottom left. The Galactic disk is in black. tions has led to estimates of the mass of the Sgr dwarf of Sgr stars are shown in red (dark grey) while the Sgr dark mat- 8 ter is blue (light grey). The tidal streams are projected onto MSgr = (2 5) 10 M!, mass-to-light ratio MSgr/LSgr = − × the orbital plane. Orbits are counterclockwise; the upper left 14 36 M!/L!, and Sgr orbit with pericenter 10–19 kpc, − figure shows that for β =0.3 (a dark-matter force 9% the apocenter 56–59 kpc, and period 0.85–0.87 Gyr [24]. The strength of gravity) stars are almost absent from the leading large mass-to-light ratio suggests that the Sgr dwarf is stream (at 12 o’clock with respect to the Galactic center). X’s indeed DM dominated and therefore a suitable place to denote the location of the bound Sgr core. search for DM forces. To study more carefully the effects of EP violation on tidal disruption, we performed our own simulations of the a modified version of the N-body code GADGET-2 [27]. 8 tidal disruption of a satellite with a mass (5 10 M!), A more detailed description of our simulations are pro- × mass-to-light ratio (40M!/L!), and orbit (pericenter 14 vided in Ref. [28]. kpc, apocenter 59 kpc) similar to that of the Sgr dwarf. Four simulations of tidal disruption are depicted in We could not compare our simulations directly with those Fig. 1, with DM forces given by Eq. (1) with different of Ref. [24], as we performed N-body simulations of a values of the charge-to-mass ratio β. The scalar field is Navarro-Frenk-White (NFW) profile for our Milky Way assumed massless (mφ = 0), so the DM force is a true halos, and they used a static logarithmic potential. An inverse square law. The ratio β increases from 0.0 at active halo allows for dynamical friction over the course of bottom left to 0.3 at top left as one proceeds counter- the simulation and possible backreaction on the halo due clockwise. The simulations begin with the satellite at to the DM force. While we did not attempt to reproduce apocenter 59 kpc from the Galactic center and last for the detailed features of the Sgr tidal streams, our simula- 2.4 Gyr (almost three full orbits). The tangential veloc- tions are sufficient to demonstrate that even a small DM ities are adjusted so that all orbits are projected to have force could have significant observational consequences. a pericenter of 14 kpc. The orbits are counterclockwise The initial conditions for our simulations were produced in the x-z plane, so that the edge of the leading stream using GALACTICS [25], which makes use of phase-space appears at 12 o’clock with respect to the Galactic center distribution functions (DFs) that are analytic in the or- in Fig. 1, while the edge of the trailing stream is at about bital energy and angular momentum. By Jeans’ theo- 10 o’clock. The Sgr dwarf is modelled with a truncated rem, these DFs are equilibrium solutions to the collision- NFW profile for both stars and DM, in keeping with the less Boltzmann equations [26], and they can be combined simulations of Ref. [24], where it was concluded that ob- to produce realistic and stable models of the composite servations could not yet determine distinct profiles for Milky Way bulge-disk-halo system [25]. We used the two the two components. Thus, the stars shown in red (dark Milky Way models of Ref. [25] that best fit observational grey) in the bottom left panel are simply a downsampling constraints, including the Galactic rotation curve and lo- of the DM distribution illustrated in blue (light grey). cal velocity ellipsoid. The simulations were evolved using As the DM force increases in strength, the leading Cosmological evolution in modified gravity Modified Friedmann and acceleration equations acceleration with normal matter (P>0) Example: f(R) gravity Standard GR modifications Dark Energy’s Dual Personality- Rachel Bean COSMO’08 a¨ κ2 = ρ +3P +2φ˙2 2V (φ) (1) An alternative aperspective− 6 − ! " “conformal transformation” 2 (J) √ 3 κCφ (E) Coordinate change (redefine the metric) gµν = e gµν (2) from Jordan frame to Einstein frame 2 Jordan frameφ¨ +3 Hφ˙ + V !(φ)= Cκ(ρ 3P ) (3) • Modified gravity F(Φ)R, or F(R) #3 − • Minimally coupled matter • Matter follows geodesics GccGbb 4 2 2 = 1 + C (4) Gbc 3 Einstein frame • Gravity is GR √ 2 κCφ 3(1+w) ρ e− 3 a− (5) • Matter coupled to scalar φ with strength∝ C • Matter doesn’t follow geodesics • Scalar potential V(φ) derived from F Dark Energy’s Dual Personality- Rachel Bean COSMO’08 1 a¨ κ2 = ρ +3P +2φ˙2 2V (φ) (1) a − 6 − ! " 2 (J) √ 3 κCφ (E) Evolution viewedgµν = e from thegµν Einstein frame (2) 2 a¨ κ ˙2 • GR + extra matter (scalar= field)ρ +3 P +2φ 2V (φ) (1) a − 6 − 2 φ¨ +3Hφ˙ !+ V !(φ)= Cκ(ρ" 3P ) (3) a¨ κ2 3 − = ρ +3P +2φ˙2# 2V (φ) (1) a − 6 2 − (J) √ 3 κCφ (E) gµν != e gµν " (2) • Matter and scalar coupledG togetherccGbb as fifth4 force2 with strength C (J) =2 1κ +Cφ (CE) (4) g 2 = e√ 3 g (2) Gµνbc 3µν2 φ¨ +3Hφ˙ + V !(φ)= Cκ(ρ 3P ) (3) #3 − 2 2 φ¨ +3Hφ˙ + V√!(φκ)=Cφ 3(1+wC)κ(ρ 3P ) (3) ρ e− 3 a− (5) ∝ #3 − GccGbb 4 2 2 = 1 + C (4) Gbc 3 GccGGRbb 4 2 C = 0 2 = 1 + C (4) Strength of coupling C Gbc 3 determined by theory F(R) C = 1/2 √ 2 κCφ 3(1+w) ρ e− 3 a− (5) ∝ F(√Φ2)RκC φ 3(1+w) C can take range of values ρ e− 3 a− (5) ∝ Dark Energy’s Dual Personality- Rachel Bean COSMO’08 1 1 1 a¨ κ2 = ρ +3P +2φ˙2 2V (φ) (1) a − 6 − Acceleration in! the Einstein frame" perspective 2 (J) √ 3 κCφ (E) gµν = e gµν (2) • Acceleration when scalar sits in minimum of effective potential 2 φ¨ +3Hφ˙ + V !(φ)= Cκ(ρ 3P ) (3) #3 − GccGbb 4 2 2 = 1 + C (4) Gbc 3 √ 2 κCφ 3(1+w) ρ e− 3 a− (5) ∝ φm Dark Energy’s Dual Personality- Rachel Bean COSMO’08 1 EF shows possible instabilities in structure growth • Jean’s instability in a general fluid undergoing gravitational collapse • If coupling too strong (minimum too steep) get catastrophic instabilities – Jean’s instability in matter growth with negative speed of sound N.
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