Related papers: Superspace and global stability in General Relativ…
The general theory of N=1 supergravity with supermatter is applied to a Bianchi type IX diagonal model. The supermatter is constituted by a complex scalar field and its spin-$1\over 2$ fermionic partners. The K\"ahler geometry is chosen to…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
The recently introduced relativistic Lagrangian darkon fluid model (EPJ C (2015) 75:9) is generalized to a self-gravitating, irrotational, pressure-less and stress free geodesic fluid, whose energy-momentum tensor is dust-like with…
We present exact quantum solutions for a noncommutative, multidimensional cosmological model and show that stabilization of extra dimensions sets in with the introduction of noncommutativity between the scale factors. An interpretation is…
We study multidimensional gravitational models with scalar curvature nonlinearity of the type 1/R and with form-fields (fluxes) as a matter source. It is assumed that the higher dimensional space-time undergoes Freund-Rubin-like spontaneous…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
The general theory of N=1 supergravity with supermatter is applied to a Bianchi type IX diagonal model. The supermatter is constituted by a complex scalar field and its spin-$1\over 2$ fermionic partners. The Lorentz invariant Ansatz for…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical…
We study the dynamics of the field equations in a four-dimensional isotropic and homogeneous spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry in the context of Einstein-Gauss-Bonnet theory with a matter source and a…
We discuss implications of the cosmological frame principle which states that cosmological effects of modified gravity must be stable as solutions of each of the corresponding sets of dynamical equations holding in the two…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
A unified theory of four-dimensional gravity together with the standard model is presented, with supersymmetry breaking of M-theory at a TeV. Masses of the the known particles are derived. The cosmological constant is quantum generated to…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
In this paper, a general FRW cosmological model has been constructed in $f(R,T)$ gravity reconstruction with variable cosmological constant. A number of solutions to the field equations has been generated by utilizing a form for the Hubble…
We analyze dynamics of the FRW models with global rotation in terms of dynamical system methods. We reduce dynamics of these models to the FRW models with some fictitious fluid which scales like radiation matter. This fluid mimics…
We study the static cosmological solutions and their stability at background level in the framework of massive bigravity theory with Friedmann-Robertson-Walker (FRW) metrics. By the modification proposed in the cosmological equations…
The current accelerating phase of the evolution of the universe is considered by constructing most economical cosmic models that use just general relativity and some dominating quantum effects associated with the probabilistic description…