Ming-Hua Li

Finslerian MOND versus observations of Bullet Cluster 1E 0657-558

It is known that theory of MOND (Modification of Newtonian Dynamics) with spherical symmetry cannot account for the convergence kappa-map of Bullet Cluster 1E 0657-558. In this paper, we try to set up a Finslerian MOND, a generalization of MOND in Finsler space-time. We use Ric = 0 to obtain the gravitational vacuum field equation in a 4D Finsler space-time. To leading order in the post-Newtonian approximation, we obtain the explicit form of the Finslerian line element. It is simply the Schwarzschilds metric except for the Finslerian rescaling coefficient f(v) of the radial coordinate r, i.e. R = f(v) r. By setting f (v) = root 1 - (GMa(0)/v(4)), we obtain the famous MOND in a Finslerian framework. Taking a dipole and a quadrupole term into consideration, we give the convergence kappa in gravitational lensing astrophysics in our model. Numerical analysis shows that our prediction is to a certain extent in agreement with the observations of Bullet Cluster 1E 0657-558. With the theoretical temperature T taking the observed value 14.8 keV, the mass density profile of the main cluster obtained in our model is of the same order as that given by the best-fitting King beta-model.

Galaxy Rotation Curves in the Grumiller's Modified Gravity

The effective potential in the Grumillers modified gravity includes the Newtonian potential and a Rindler term. The fitting to the rotation curve data of eight galaxies suggests a universal Rindler acceleration a approximate to 0.30 x 10(-10) ms(-2). We do a two-parameter fit first, with the mass-to-light ratio ((sic)(*)) and the Rindler acceleration (a) as free parameters. It is found that the data of six out of the eight galaxies fit well with the prediction of theory in the range 0 r less than or similar to 40 kpc, although the theoretical curves show a tendency of arising beyond this range. The Rindler accelerations of the six well-fitted galaxies have the same magnitude, with an average value (a) over bar approximate to 0.30 x 10(-10) ms(-2). Inspired by this fact, we then carry out a one-parameter ((sic)(*)) fit to the six galaxies, with a fixed at (a) over bar, and find that the theory can still reproduce the observation. The value of Rindler acceleration we get here is a quarter of that of Milgroms modified Newtonian dynamics. For the rest two galaxies, NGC 5055 and DDO 154, the fitting results are significantly improved if the photometric scale length (h) is included as another free parameter.

Effects of spacetime anisotropy on the galaxy rotation curves

The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom’s MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration GM/r2 is smaller than the critical acceleration a0. Interestingly, the critical acceleration a0, although varies between different galaxies, is in the order of magnitude

Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model

cH_{0}/2\pi\sim10^{-10}~\mathrm{m\,s}^{-2}

An inflationary scenario taking into account of possible dark energy effects in the early universe

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Finslerian MOND versus the strong gravitational lensing of the early-type galaxies

In Verlindes entropic force scenario of gravity, Newtons laws and Einstein equations can be obtained from the first principles and general assumptions. However, the equipartition law of energy is invalid at very low temperatures. We show clearly that the threshold of the equipartition law of energy is related with horizon of the universe. Thus, a one-dimensional Debye (ODD) model in the direction of radius of the modified entropic force (MEF) may be suitable in description of the accelerated expanding universe. We present a Friedmann cosmic dynamical model in the ODD-MEF framework. We examine carefully constraints on the ODD-MEF model from the Union2 compilation of the Supernova Cosmology Project (SCP) collaboration, the data from the observation of the large-scale structure (LSS) and the cosmic microwave background (CMB), i.e. SNe Ia+LSS+CMB. The combined numerical analysis gives the best-fit value of the model parameters zeta similar or equal to 10(-9) and Omega(m0) = 0.224, with chi(2)(min) = 591.156. The corresponding age of the universe agrees with the result of D. Spergel et al. [J.M. Bardeen, B. Carter, and S.W. Hawking, Commun. Math. Phys. 31 (1973) 161] at 95% confidence level. The numerical result also yields an accelerated expanding universe without invoking any kind of dark energy. Taking zeta( 2 pi omega(D)/H-0) as a running parameter associated with the structure scale r, we obtain a possible unified scenario of the asymptotic flatness of the radial velocity dispersion of spiral galaxies, the accelerated expanding universe and the Pioneer 10/11 anomaly in the entropic force framework of Verlinde.

GENERALIZATION OF RINDLER POTENTIAL AT CLUSTER SCALES IN RANDERS–FINSLERIAN SPACETIME: A POSSIBLE EXPLANATION OF THE BULLET CLUSTER 1E0657-558?

We investigate the possible effect of cosmological-constant type dark energy during the inflation period of the early universe. This is accommodated by a new dispersion relation in de Sitter space. The modified inflation model of a minimally coupled scalar field is still able to yield an observation-compatible scale-invariant primordial spectrum, simultaneously having the potential to generate a spectrum with lower power at large scales. A qualitative match to the WMAP 7-year data is presented. We obtain an ΩΛ of the same order of that in the Λ-CDM model. Possible relations between the de Sitter scenario and Doubly Special Relativity (DSR) are also discussed.

Cosmological model with local symmetry of very special relativity and constraints on it from supernovae

The gravitational lensing of Bullet Clusters and early-type galaxies pose serious challenges on the validity of MOND. Recently, Finslerian MOND, a generalization of MOND in the framework of Finsler gravity, has been proposed to explain the mass discrepancy problem of Bullet Cluster 1E0657-558. In this paper, we check the validity of the Finslerian MOND in describing the strong gravitational lensing of early-type galaxies. The investigation on ten strong lenses of the CASTLES samples shows that there is no strong evidence for the existence of dark matter.

Finsler geometric perspective on the bulk flow in the universe

The data of the Bullet Cluster 1E0657-558 released on November 15, 2006 reveal that the strong and weak gravitational lensing convergence

Finslerian MOND vs. observations of Bullet Cluster

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