Tekin Dereli

Cosmological Models with Linearly Varying Deceleration Parameter

We propose a new law for the deceleration parameter that varies linearly with time and covers Berman’s law where it is constant. Our law not only allows one to generalize many exact solutions that were obtained assuming constant deceleration parameter, but also gives a better fit with data (from SNIa, BAO and CMB), particularly concerning the late time behavior of the universe. According to our law only the spatially closed and flat universes are allowed; in both cases the cosmological fluid we obtain exhibits quintom like behavior and the universe ends with a big-rip. This is a result consistent with recent cosmological observations.

Signature dynamics in general relativity

The authors describe classical models of gravitation interacting with scalar fields whose solutions involve degenerate metrics. Some of these solutions exhibit transitions from a Euclidean domain to a Lorentzian spacetime corresponding to a spatially flat Robertson-Walker cosmology.

Non-Riemannian gravity and the Einstein - Proca system

We argue that all Einstein - Maxwell or Einstein - Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.

Gauge field interactions in spaces with arbitrary torsion

We argue that by treating gravity asa local SL(2,C) gauge theory, the gauge covariant tensor formulation of field theory is entirely adequate to discuss the coupling of all gauge fields to gravity in a manner that preserves gauge covariance. In particular we make precise the notion of minimal coupling in the presence of torsion.

Neutrino oscillations induced by spacetime torsion

The gravitational neutrino oscillation problem is studied by considering the Dirac Hamiltonian in a Riemann-Cartan spacetime and calculating the dynamical phase. Torsion contributions which depend on the spin direction of the mass eigenstates are found. These effects are of the order of Planck scales.The gravitational neutrino oscillation problem is studied by considering the Dirac Hamiltonian in a Riemann-Cartan space-time and calculating the dynamical phase. Torsion contributions which depend on the spin direction of the mass eigenstates are found. These effects are of the order of Planck scales.

Dynamical reduction of internal dimensions in the early universe

An (n+4) dimensional de Sitter model is constructed in which the metric scale factor for space-time expands exponentially in cosmic time while the internal space scale factor contracts exponentially.

Weyl scalings and spinor matter interactions in scalar-tensor theories of gravitation

An SL(2,C) gauge formulation of a scalar-tensor theory of gravitation is related to the Brans-Dicke theory in the absence of spinorial matter couplings although the natural connection of space-time has a torsion determined by the scalar field. Simplified scaling properties of gravitational variables are elucidated in this geometry. In the presence of matter with intrinsic spin a natural scalar-spinor coupling is exposed. A locally scale invariant limit exists without a Weyl gauge field.

Probing kinematics and fate of the Universe with linearly time-varying deceleration parameter

The parametrizations q = q0+q1z and q = q0+q1(1 − a/a0) (Chevallier-Polarski-Linder parametrization) of the deceleration parameter, which are linear in cosmic redshift z and scale factor a , have been frequently utilized in the literature to study the kinematics of the Universe. In this paper, we follow a strategy that leads to these two well-known parametrizations of the deceleration parameter as well as an additional new parametrization, q = q0+q1(1 − t/t0), which is linear in cosmic time t. We study the features of this linearly time-varying deceleration parameter in contrast with the other two linear parametrizations. We investigate in detail the kinematics of the Universe by confronting the three models with the latest observational data. We further study the dynamics of the Universe by considering the linearly time-varying deceleration parameter model in comparison with the standard ΛCDM model. We also discuss the future of the Universe in the context of the models under consideration.

Double Dual Solutions of Generalized Theories of Gravitation

Solutions to the Stephenson-Yang theory of gravity and its generalizations are discussed. By considering the inclusion of a cosmological term in the action spherically symmetric static solutions are presented that do not fall into the vacuum Einstein class. A simple double-duality ansatz is responsible for all the solutions that are discussed.

Nonminimally coupled gravitational and electromagnetic fields: pp-wave solutions

We give the Lagrangian formulation of a generic nonminimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first-order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact pp-wave solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton.