Modified Dark Matter: Does Dark Matter Know about the Cosmological Constant? Douglas Edmonds Emory & Henry College

Transcription

1 Modified Dark Matter: Does Dark Matter Know about the Cosmological Constant? Douglas Edmonds Emory & Henry College Collaborators Duncan Farrah Chiu Man Ho Djordje Minic Y. Jack Ng Tatsu Takeuchi

2 Outline Evidence for CDM Problems with CDM Observations of a universal acceleration scale Constructing MDM mass profiles: Heuristic argument based on gravitational thermodynamics Observations: MDM in galaxies MDM in galaxy clusters Conclusions and future work

3 Evidence of Dark Matter M33 Image: NOAO, AURA, NSF, T.A.Rector.

4 Evidence of Dark Matter X-ray: NASA/CXC/CfA/M.Markevitch et al.; Optical: NASA/STScI; Magellan/U.Arizona/ D.Clowe et al.; Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al.

5 Evidence of Dark Matter Copyright: ESA and the Planck Collaboration

6 Evidence of Dark Matter Dodelson 2011

7 Evidence it is Cold Kavli Institute for Cosmology, Cambridge

8 Evidence it is Cold

9 Evidence it is Cold

10 CDM Tensions at Small Scales Core-cusp problem Missing satellites Too big to fail F568-3

11 CDM Tensions at Small Scales D.H. Weinberg We will take the view that tensions between CDM predictions and observations are telling us something about the fundamental nature of dark matter

12 Modified Newtonian Dynamics (the theory that shall not be named) In MOND, Newton s equation of motion is modified to with an interpolating function that satisfies For a (baryonic) source mass, the above modification to the equation of motion implies On the outskirts of galaxies, this implies that leading to flat rotation curves, the baryonic Tully-Fisher relation But the really interesting thing is the discovery of a universal acceleration scale ac m/s2 ch 0 / 2π

13 Observational Constraint on Dark Matter 2693 data points for 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. The dark matter contribution is fully specified by that of the baryons. McGaugh

14 Modified dark matter (MDM) is a (non-local) form of dark matter that behaves like MOND at galactic scales and CDM at cluster and cosmic scales. Ho, Minic & Ng, 2010, Phys. Le<. B, 693, 567 Ho, Minic & Ng, 2011, Gen. Rel. and Grav., 43, 2567 Ho, Minic & Ng, 2012, Phys. Rev. D, 85,

15 Modified Dark Matter In the context of GR, the missing mass problem can be solved in two (disrnct) ways: We can change the Einstein tensor (modified gravity) or add an extra energy-momentum tensor (e.g., CDM). In CDM, the extra energy-momentum tensor is independent of the baryonic tensor. In MDM, we a<empt to recast Einstein s equaron such that the energy-momentum part contains the cosmological constant term in order to see if CDM mass profiles could know about the cosmological constant.

16 Modified Dark Matter from Gravitational Thermodynamics following Jacobson 1995 Local observer with acceleration a in a spatially flat de Sitter space In such a space, the thermodynamic relation has T as the Unruh temperature associated with the local accelerating (Rindler) observer The acceleration a can be interpreted as surface gravity on the associated (Rindler) horizon. The entropy is then associated with the area of this horizon. The energy is the integral of the energy-momentum tensor

17 Modified Dark Matter from Gravitational Thermodynamics following Jacobson 1995 The link between the thermodynamic relation and Einstein s equations is the Raychaudhuri equation (where λ is the appropriate affine parameter) Using the Raychaudhuri equation along with the Unruh temperature, the Bekenstein-Hawking entropy, and the thermodynamic relation between energy and entropy, it follows that Applying local conservation of energy and momentum then yields Einstein s equations

18 Modified Dark Matter from Gravitational Thermodynamics following Jacobson 1995 Our modification is to introduce a fundamental acceleration that is related to the cosmological constant a0 = c Λ /3 and Λ = 3H 0 / c We preserve entropy (in order to remain consistent with Einstein s theory) but change the temperature in such a way that the energy-momentum tensor knows about the inertial properties that temperature knows about. To change the temperature, we look to our observer with acceleration a in de Sitter space. The Unruh temperature experienced by this observer is

19 Modified Dark Matter from Gravitational Thermodynamics following Jacobson 1995 Since the de Sitter space has a cosmological horizon, it has a horizon temperature. We define an effective Temperature such that we get zero temperature for zero acceleration. Our model is thus and we define where ds remains unchanged in analogy with the normalized temperature. Therefore, energy is not changed in an arbitrary way, but instead in accordance with the change in temperature that should be fixed by the background.

20 MDM Mass Profiles Note that entropy is unchanged so that the Einstein tensor is unchanged. However, due to the change in temperature, energy is changed. If we rewrite the temperature as we can also write We now interpret the unprimed part as corresponding to baryonic matter. Then, Thus, the energy-momentum tensor of the extra sources must be related to that of the baryons.

21 MDM Mass Profiles Expanding the formula for the de Sitter temperature, we find a relation between the extra source (primed) and baryonic matter (unprimed). Expanding the formula for the de Sitter temperature, we find a relation between the extra source (primed) and baryonic matter (unprimed). This extra mass, we call dark matter. Our dark matter mass profile knows about the baryonic matter as well as the cosmological background (and the inertial properties of masses moving in that background). In essence, we have vacuum origin for the observed fundamental acceleration and a quantum origin for the dark matter mass profiles.

22 MDM Mass Profiles To get the full expression for the gravitational force, we must consider our temperature modification. From we get and Note that we recover Milgrom s scaling (usually associated with MOND).

23 MDM Mass Profiles Given the heuristic nature of our argument, the MDM mass profile can, in principle, be modified due to some physical effects associated with scale. For example, the temperature could be changed using the Tolman-Ehrenfest formula where and is determined by boundary conditions. We are therefore led to the MDM mass profile: M ' = f (r)(a0 / a)2 M For the following data fits, we adopt the following mass profile: where rmdm is a scale factor and is a dimensionless constant that depends, in principle, on the ratio of dimensionful values of at different scales.

24 Galactic Rotation Curves Data black squares Stars blue line Gas green line [Sanders & Verheijen, 1998] DE MDM red line CDM (NFW) black line

25 Galaxy Clusters kt (r)r! d ln ρ g d lnt (r) $ M (r) = + # & µ m pg " d ln r d ln r % Vikhlinin et al. (2006) spherical symmetry and hydrostarc equilibrium (Sarazin 1988) ρ g = 1.2m p ne n p modificaron of tradironal β- model T (r) = T0 tcool (r)t(r) Allen et al. (2001)

26 Galaxy Clusters Virial Mass: spherical symmetry and hydrostatic equilibrium (Sarazin 1988) kt (r)r! d ln ρ g d lnt (r) $ M (r) = + # & µ m pg " d ln r d ln r % Total mass with MDM: α a2 M! = M baryonic r / Rs a black solid: blue shaded: red solid: dashed: dot-dashed: dotted: virial mass 1-σ error MDM CDM gas MOND MOND effective mass: M MOND = M baryonic 1+ ( ac / a) 2

27 Galaxy Clusters DE

28 Conclusions We have constructed a dark matter mass profile that knows about the cosmological constant. The Modified Dark Matter mass profile depends on the baryonic mass profile, naturally accounting for the observed correlation between dark matter and baryonic matter. We have shown that the mass profile is consistent with galaxy and galaxy cluster data, and performs just as well as CDM and considerably better than MOND.