John Miritzis

Isotropic cosmologies in Weyl geometry

We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that for homogeneous and isotropic spacetimes, the field equations can be reduced to the Einstein equations with a two-fluid source. We write the equations as a two-dimensional dynamical system and analyse the qualitative, asymptotic behaviour of the models. We examine the possibility that in certain theories the Weyl 1-form may give rise to a late accelerated expansion of the universe and conclude that such behaviour is not met as a generic feature of the simplest cosmologies.

Energy exchange for homogeneous and isotropic universes with a scalar field coupled to matter

We study the late time evolution of flat and negatively curved Friedmann?Robertson?Walker (FRW) models with a perfect fluid matter source and a scalar field arising in the conformal frame of f(R) theories nonminimally coupled to matter. Under mild assumptions on the potential V we prove that equilibria corresponding to the non-negative local minima for V are asymptotically stable, as well as horizontal asymptotes approached from above by V. We classify all cases of the flat model where one of the matter components eventually dominates. In particular for a nondegenerate minimum of the potential with zero critical value we prove in detail that if ?, the parameter of the equation of state, is larger than 1, then there is a transfer of energy from the fluid to the scalar field and the latter eventually dominates in a generic way.

The recollapse problem of closed Friedmann–Robertson–Walker models in higher-order gravity theories

We study the closed universe recollapse conjecture for positively curved Friedmann–Robertson–Walker models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the R+αR2 theory. By including ordinary matter, we extend the analysis of a previous work. We analyze the structure of the resulted four-dimensional dynamical system with the methods of the center manifold theory and the normal form theory. It is shown that an initially expanding closed FRW universe, starting close to the Minkowski space-time, cannot avoid recollapse. We discuss the posibility that potentials with a positive minimum may prevent the recollapse of closed universes.

Dynamical system approach to FRW models in higher-order gravity theories

We study the late time evolution of positively curved FRW models with a scalar field which arises in the conformal frame of the R+αR2 theory. The resulted three-dimensional dynamical system has two equilibrium solutions corresponding to a de Sitter space and an ever expanding closed universe. We analyze the structure of the first equilibrium with the methods of the center manifold theory and, for the second equilibrium, we apply the normal form theory to obtain a simplified system, which we analyze with special phase plane methods. It is shown that an initially expanding closed FRW space–time avoids recollapse.

Variational and conformal structure of nonlinear metric-connection gravitational Lagrangians

We examine the variational and conformal structures of higher-order theories of gravity that are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first-order formalism when applied to these theories may lead consistently to a new method of reduction of order of the associated field equations. We show that the similarity of the field equations that are derived from appropriate actions via this formalism to those produced by Hilbert varying purely metric Lagrangians is not merely formal but is implied by the diffeomorphism covariant property of the associated Lagrangians. We prove that the conformal equivalence theorem of these theories with general relativity plus a scalar field, holds in the extended framework of Weyl geometry with the same forms of field and self-interacting potential but, in addition, there is a new “source term” that plays the role of a stress. We point out how these results may be further exploited and ...

Scalar-field cosmologies with an arbitrary potential

We study the late-time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function V(). We prove, using the approach of dynamical systems, four general results for a large class of non-negative potentials and show that almost always the universe ever expands. In particular, for potentials having a local zero minimum, flat and negatively curved FRW models are ever expanding and the energy density asymptotically approaches zero. We investigate the conditions under which the scalar field asymptotically approaches the minimum of the potential. We discuss the question of whether a closed FRW with ordinary matter can avoid recollapse due to the presence of a scalar field with a non-negative potential.

Can Weyl geometry explain acceleration

We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that for homogeneous and isotropic spacetimes, the field equations can be reduced to the Einstein equations with a two-fluid source. We write the equations as a two-dimensional dynamical system and analyze the qualitative, asymptotic behavior of the models. We examine the possibility that in certain theories the Weyl 1-form may give rise to a late accelerated expansion of the Universe and conclude that such behaviour is not met as a generic feature of the simplest cosmologies.

Proof of the cosmic no-hair conjecture for some quadratic homogeneous cosmologies

We prove the cosmic no-hair conjecture for orthogonal, initially expanding Bianchi cosmologies in the theory with matter satisfying the strong and dominant energy conditions using the conformally equivalent Einstein field equations, with the scalar field having the full self-interacting potential. We assume that the universe is initially on the flat plateau of the potential and its initial kinetic energy is negligible with respect to its potential energy. We show, in particular, that the Bianchi IX universe asymptotically approaches de Sitter space provided that initially the scalar 3-curvature does not exceed the potential of the scalar field associated with the conformal transformation. Our proof relies on rigorous estimates of the possible bounds of the so-called Moss-Sahni function which obeys certain differential inequalities, and a non-trivial argument which connects the behaviour of this function to the evolution of the spatial part of the scalar curvature.

Negative potentials and collapsing universes

We study Friedmann--Robertson--Walker models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. We prove that a general class of bounded from above potentials which fall to minus infinity as the field goes to minus infinity, forces the Hubble function to diverge to

Coupled quintessence with double exponential potentials

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