Christian G. Böhmer

Extra force in f(R) modified theories of gravity

The equation of motion for massive particles in f(R) modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, R, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak-field limit. Connections with MOND and with the Pioneer anomaly are further discussed.

Can dark matter be a Bose–Einstein condensate?

We consider the possibility that the dark matter which is required to explain the dynamics of the neutral hydrogen clouds at large distances from the galactic centre could be in the form of a Bose–Einstein condensate. To study the condensate we use the non-relativistic Gross–Pitaevskii equation. By introducing the Madelung representation of the wavefunction, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. Hence dark matter can be described as a non-relativistic, Newtonian Bose–Einstein gravitational condensate gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index n = 1. In the framework of the Thomas–Fermi approximation the structure of the Newtonian gravitational condensate is described by the Lane–Emden equation, which can be exactly solved. General relativistic configurations with quartic non-linearity are studied, by numerically integrating the structure equations. The basic parameters (mass and radius) of the Bose–Einstein condensate dark matter halos sensitively depend on the mass of the condensed particle and of the scattering length. To test the validity of the model we fit the Newtonian tangential velocity equation of the model with a sample of rotation curves of low surface brightness and dwarf galaxies, respectively. We find a very good agreement between the theoretical rotation curves and the observational data for the low surface brightness galaxies. The deflection of photons passing through the dark matter halos is also analysed, and the bending angle of light is computed. The bending angle obtained for the Bose–Einstein condensate is larger than that predicted by standard general relativistic and dark matter models. The angular radii of the Einstein rings are obtained in the small angle approximation. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the Bose–Einstein condensate dark matter model and other dark matter models.

Dynamics of dark energy with a coupling to dark matter

Dark energy and dark matter are the dominant sources in the evolution of the late universe. They are currently only indirectly detected via their gravitational effects, and there could be a coupling between them without violating observational constraints. We investigate the background dynamics when dark energy is modeled as exponential quintessence and is coupled to dark matter via simple models of energy exchange. We introduce a new form of dark sector coupling, which leads to a more complicated dynamical phase space and has a better physical motivation than previous mathematically similar couplings.

Existence of relativistic stars in f(T) gravity

We examine the existence of relativistic stars in f(T) modified gravity and explicitly construct several classes of static perfect fluid solutions. We derive the conservation equation from the complete f(T) gravity field equations and present the differences with its teleparallel counterpart. Firstly, we choose the tetrad field in the diagonal gauge and study the resulting field equations. Some exact solutions are explicitly constructed and it is noted that these solutions have to give a constant torsion scalar. Next, we choose a non diagonal tetrad field which results in field equations similar to those of general relativity. For specific models we are able to construct exact solutions of these field equations. Among those new classes of solutions, we find negative pressure solutions, and an interesting class of polynomial solutions.

CMB anisotropies and inflation from non-standard spinors

The apparent alignment of the cosmic microwave background multipoles on large scales challenges the standard cosmological model. Scalar field inflation is isotropic and cannot account for the observed alignment. We explore the imprints, a non-standard spinor driven inflation would leave on the cosmic microwave background anisotropies. We show it is natural to expect an anisotropic inflationary expansion of the Universe which has the effect of suppressing the low multipole amplitude of the primordial power spectrum, while at the same time to provide the usual inflationary features.

Wormhole geometries in modified teleparallel gravity and the energy conditions

In this work, we explore the possibility that static and spherically symmetric traversable wormhole geometries are supported by modified teleparallel gravity or fðTÞ gravity, where T is the torsion scalar. Considering the field equations with an off-diagonal tetrad, a plethora of asymptotically flat exact solutions are found, which satisfy the weak and the null energy conditions at the throat and its vicinity. More specifically, considering T � 0, we find the general conditions for a wormhole satisfying the energy conditions at the throat and present specific examples that satisfy the energy conditions throughout the spacetime. As a consistency check, we also verify that in the teleparallel equivalent of general relativity, i.e., fðT Þ¼ T, one regains the standard general relativistic field equations for wormhole physics. Furthermore, considering specific choices for the fðTÞ form and for the redshift and shape functions, several solutions of wormhole geometries are found that satisfy the energy conditions at the throat and its neighborhood. As in their general relativistic counterparts, these fðTÞ wormhole geometries present farreaching physical and cosmological implications, such as being theoretically useful as shortcuts in spacetime and for inducing closed timelike curves, possibly violating causality.

Dark matter as a geometric effect in f(R) gravity

Abstract We consider the behavior of the tangential velocity of test particles moving in stable circular orbits in f ( R ) modified theories of gravity. A large number of observations at the galactic scale have shown that the rotational velocities of massive test particles (hydrogen clouds) tend towards constant values at large distances from the galactic center. We analyze the vacuum gravitational field equations in f ( R ) models in the constant velocity region, and the general form of the metric tensor is derived in a closed form. The resulting modification of the Einstein–Hilbert Lagrangian is of the form R 1 + n , with the parameter n expressed in terms of the tangential velocity. Therefore we find that to explain the motion of test particles around galaxies requires only very mild deviations from classical general relativity, and that modified gravity can explain the galactic dynamics without the need of introducing dark matter.

Dark spinor models in gravitation and cosmology

We introduce and carefully define an entire class of field theories based on non-standard spinors. Their dominant interaction is via the gravitational field which makes them naturally dark; we refer to them as Dark Spinors. We provide a critical analysis of previous proposals for dark spinors noting that they violate Lorentz invariance. As a working assumption we restrict our analysis to non-standard spinors which preserve Lorentz invariance, whilst being non-local and explicitly construct such a theory. We construct the complete energy-momentum tensor and derive its components explicitly by assuming a specific projection operator. It is natural to next consider dark spinors in a cosmological setting. We find various interesting solutions where the spinor field leads to slow roll and fast roll de Sitter solutions. We also analyse models where the spinor is coupled conformally to gravity, and consider the perturbations and stability of the spinor.

The generalized virial theorem in f(R) gravity

We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy. The total virial mass is proportional to the effective mass associated with the new geometrical term, which may account for the well-known virial theorem mass discrepancy in clusters of galaxies. The model predicts that the geometric mass and its effects extend beyond the virial radius of the clusters. We also consider the behavior of the galaxy cluster velocity dispersion in f(R) models. Thus, the f(R) virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.

Stability of the Einstein static universe in IR modified Hořava gravity

Recently, Hořava proposed a power counting renormalizable theory for (3+1)-dimensional quantum gravity, which reduces to Einstein gravity with a non-vanishing cosmological constant in IR, but possesses improved UV behaviors. In this work, we analyze the stability of the Einstein static universe by considering linear homogeneous perturbations in the context of an IR modification of Hořava gravity, which implies a ‘soft’ breaking of the ‘detailed balance’ condition. The stability regions of the Einstein static universe is parameterized by the linear equation of state parameter w=p/ρ and the parameters appearing in the Hořava theory, and it is shown that a large class of stable solutions exists in the respective parameter space.