On Einstein clusters as galactic dark matter halos

We consider global and gravitational lensing properties of the recently suggested Einstein clusters of WIMPs as galactic dark matter halos. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters, as compared to the singular isothermal density sphere model for dark matter. Therefore lensing observations may discriminate, at least in principle, between Einstein cluster and other dark matter models.Comment: MNRAS LaTeX, 7 pages, accepted by MNRAS; reference adde

Is dark matter an extra-dimensional effect?

We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the presence of dark matter, is the result of the dynamical evolution of particles in higher dimensional space-times. Hence, dark matter may be a direct consequence of the presence of an extra force, generated by the presence of extra-dimensions, which modifies the dynamic law of motion, but does not change the intrinsic properties of the particles, like, for example, the mass (inertia). We discuss in some detail several possible particular forms for the extra force, and the acceleration law of the particles is derived. Therefore, the constancy of the galactic rotation curves may be considered as an empirical evidence for the existence of the extra dimensions.Comment: 11 pages, no figures, accepted for publication in MPLA; references adde

Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach

Teleparallel gravity and its popular generalization $f(T)$ gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models. While inertial spin connections are commonplace in special relativity, and not something inherent to teleparallel gravity, the role of the inertial spin connection in removing the spurious inertial effects within a given frame of reference is emphasized here. The careful consideration of the inertial spin connection leads to the construction of a fully invariant theory of teleparallel gravity and its generalizations. Indeed, it is the nature of the spin connection that differentiates the relationship between what have been called good tetrads and bad tetrads and clearly shows that, in principle, any tetrad can be utilized. The field equations for the fully invariant formulation of teleparallel gravity and its generalizations are presented and a number of examples using different assumptions on the frame and spin connection are displayed to illustrate the covariant procedure. Various modified teleparallel gravity models are also briefly reviewed.Comment: v2: 72 pages, revised version, references added, matches published versio

Spherically Symmetric Solutions on a Non-Trivial Frame in f(T) Theories of Gravity

A new solution with constant torsion is derived using the field equations of f(T). Asymptotic forms of energy density, radial and transversal pressures are shown to meet the standard energy conditions, i.e., weak and null energy conditions according to some restrictions on T0, f(T0) and fT(T0). Other solutions are obtained for vanishing radial pressure and for specific choices of f(T). The physics relevant to the resulting models is discussed.Comment: 6 pages, 4 figures, published versio

Angular size test on the expansion of the Universe

Assuming the standard cosmological model as correct, the average linear size of galaxies with the same luminosity is six times smaller at z=3.2 than at z=0, and their average angular size for a given luminosity is approximately proportional to 1/z. Neither the hypothesis that galaxies which formed earlier have much higher densities nor their luminosity evolution, mergers ratio, or massive outflows due to a quasar feedback mechanism are enough to justify such a strong size evolution. Also, at high redshift, the intrinsic ultraviolet surface brightness would be prohibitively high with this evolution, and the velocity dispersion much higher than observed. We explore here another possibility to overcome this problem by considering different cosmological scenarios that might make the observed angular sizes compatible with a weaker evolution. One of the models explored, a very simple phenomenological extrapolation of the linear Hubble law in a Euclidean static universe, fits the angular size vs. redshift dependence quite well, which is also approximately proportional to 1/z with this cosmological model. There are no free parameters derived ad hoc, although the error bars allow a slight size/luminosity evolution. The type Ia supernovae Hubble diagram can also be explained in terms of this model with no ad hoc fitted parameter. WARNING: I do not argue here that the true Universe is static. My intention is just to discuss which theoretical models provide a better fit to the data of observational cosmology.Comment: 44 pages, accepted to be published in Int. J. Mod. Phys.

Palatini formulation of modified gravity with a nonminimal curvature-matter coupling

We derive the field equations and the equations of motion for massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We derive the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force is obtained in terms of the matter-geometry coupling functions and of their derivatives. Generally, the motion is non-geodesic, and the extra force is orthogonal to the four-velocity.Comment: 7 pages, no figures; v2, revised and corrected version; new Section adde

Conformal Invariance in Einstein-Cartan-Weyl space

We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein-Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb-Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight -1, which can be cast into some interesting form. We discuss some applications of the result.Comment: 10 pages, version to appear MPL

Dark Interactions and Cosmological Fine-Tuning

Cosmological models involving an interaction between dark matter and dark energy have been proposed in order to solve the so-called coincidence problem. Different forms of coupling have been studied, but there have been claims that observational data seem to narrow (some of) them down to something annoyingly close to the $\Lambda$CDM model, thus greatly reducing their ability to deal with the problem in the first place. The smallness problem of the initial energy density of dark energy has also been a target of cosmological models in recent years. Making use of a moderately general coupling scheme, this paper aims to unite these different approaches and shed some light as to whether this class of models has any true perspective in suppressing the aforementioned issues that plague our current understanding of the universe, in a quantitative and unambiguous way.Comment: 13 pages, 9 figures, accepted for publication in JCAP. Minor corrections, one figure replaced, references adde