John Moffat Perimeter Institute Waterloo, Ontario, Canada

Transcription

1 New Results in Modified Gravity Without Dark Matter John Moffat Perimeter Institute Waterloo, Ontario, Canada The research was supported by the John Templeton Foundation Talk given at the topical conference on elementary particles, astrophysics, and cosmology, Fort Lauderdale, Florida, December 17, /12/2013 1

2 1. Introduction Observations of the dynamics of galaxies as well as the dynamics of the whole Universe reveal that a main part of the Universe s mass must be missing or, in modern terminology, this missing mass is made of dark matter (Bertone, Hooper & Silk 2005). Observations of galaxies reveal that there is a discrepancy between the observed dynamics and the mass inferred from luminous matter (Rubin et al. 1965, Rubin & Ford 1970). An alternative approach to the problem of missing mass is to replace dark matter by a modified gravity theory. The generally covariant Modified Gravity (MOG) theory is a scalar-tensor-vector theory (STVG, JM 2006). The new LUX experimental data from the Sanford Underground Research Facility (Lead, South Dakota) using a 370 kg liquid Xenon detector has ruled out low-mass WIMPs, and set new bounds on elastic scattering cross sections of WIMPs. No WIMP signals were detected. To-date no convincing detection of dark matter particles has been achieved. 15/12/2013 2

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4 2. MOG FIELD EQUATIONS The MOG action is given by (STVG JM 2006): where 15/12/2013 4

5 Varying the action with respect to the fields results in the MOG field equations. The variation of the actions S M, S φ and S S with respect to the metric yields the energy-momentum tensor: 15/12/2013 5

6 For the dynamics of a test particle, we adopt the action of a point article (JM. 2006; JM & V. Toth, 2009): As in GR, the equation of motion is independent of the test particle mass (weak equivalence principle). 15/12/2013 6

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8 We also have for the energy-momentum tensor: 15/12/2013 8

9 The effective MOG weak field potential is given by For a point mass particle: 15/12/2013 9

10 For an extended distribution of matter: Defining we get and the MOG acceleration law : ) : 15/12/

11 4. ROTATION CURVES OF GALAXIES (JM & S. Rahvar 2013) Recent applications of MOG to galaxy dynamics is based on continuous distributions of baryon matter and realistic models of galaxy bulges and disks. 15/12/

12 THINGS The HI nearby galaxy survey 15/12/

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14 The best fit for the subsample of THINGS galaxies with the corresponding likelihood functions of and M/L. 15/12/

15 We adopt the best-fitting values of and let and let the stellar-to-mass ratio M/L be the only free parameter and obtain fits to the Ursa Major catalogue of galaxies. The average value of for all the galaxies is 15/12/

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21 5. CLUSTER DYNAMICS (JM & S. Rahvar 2013) We have used the observations of the nearby cluster of galaxies obtained by the Chandra telescope to examine MOG. Using the Virial theorem or a relaxed spherically symmetric cluster, we can relate the temperature and gas profile to the internal acceleration of the cluster The left-hand side of this equation is given by data, which has to be consistent with the dynamical mass obtained from the above equation: 15/12/

22 We write the overall mass in Newtonian gravity in terms of the MOG dynamical mass: Here, is already fixed by the fits to the galaxy rotation curves =8.89. The majority of the baryonic cluster mass is gas. For MOG to be consistent with the data, the MOG dynamical mass has to be identically equal to the Newtonian baryonic mass. We find for the best fit value 15/12/

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24 Galaxy clusters baryon versus (MOG) dynamical mass profiles. 15/12/

25 6. MOG COSMOLOGY (JM & V. Toth 2013) Expanding the metric around an FRW spacetime, we can derive a cosmology for STVG that can be compared to WMAP and Planck Mission2013 CMB data. The Friedmann equation for MOG takes the form ( ): : For a -> 0 this reduces to the GR Friedmann equation, guaranteeing that the BBN experimental results are retained for z ~ Structure growth obtained from MOG can leads to growth as in the case of dark matter cosmology. for galaxy size 15/12/

26 MOG fit to angular power spectrum data. 15/12/

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30 7. C0NCLUSIONS If experiments continue not to discover dark matter particles in underground experiments, at the LHC and in astrophysical observations, then we should begin to worry that the existence of dark matter can only be inferred from gravity. We must then consider that the law of gravity should be modified. Scalar-Tensor-Vector Gravity (STVG) is a MOG theory that is fully covariant, local and classically stable. The only matter source is ordinary baryonic matter. Parameter-free fits to galaxy rotation curves and clusters of galaxies are in good agreement with observations. Explanations of the CMB data are also in agreement with the cosmological data. Work is in progress to investigate MOG strong and weak lensing and further applications to cosmology. 15/12/