- Romania
Tiberiu Harko
University College London, Mathematics, Department Member
We consider dark energy models obtained from the general conformal transformation of the Kropina metric, representing an $$(\alpha , \beta )$$ ( α , β ) -type Finslerian geometry, constructed as the ratio of the square of a Riemannian... more
We consider dark energy models obtained from the general conformal transformation of the Kropina metric, representing an $$(\alpha , \beta )$$ ( α , β ) -type Finslerian geometry, constructed as the ratio of the square of a Riemannian metric $$\alpha $$ α and the one-form $$\beta $$ β . Conformal symmetries appear in many fields of physics, and they may play a fundamental role in our understanding of the Universe. We investigate the possibility of obtaining conformal theories of gravity in the osculating Barthel–Kropina geometric framework, where gravitation is described by an extended Finslerian-type model, with the metric tensor depending on both the base space coordinates and a vector field. We show that it is possible to formulate a family of conformal Barthel–Kropina theories in an osculating geometry with second-order field equations, depending on the properties of the conformal factor, whose presence leads to the appearance of an effective scalar field of geometric origin in ...
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The classical tests of general relativity (perihelion precession, deflection of light, and the radar echo delay) are considered for the Dadhich, Maartens, Papadopoulos and Rezania (DMPR) solution of the spherically symmetric static vacuum... more
The classical tests of general relativity (perihelion precession, deflection of light, and the radar echo delay) are considered for the Dadhich, Maartens, Papadopoulos and Rezania (DMPR) solution of the spherically symmetric static vacuum field equations in brane world models. For this solution the metric in the vacuum exterior to a brane world star is similar to the Reissner-Nordstrom form of classical general relativity, with the role of the charge played by the tidal effects arising from projections of the fifth dimension. The existing observational solar system data on the perihelion shift of Mercury, on the light bending around the Sun (obtained using long-baseline radio interferometry), and ranging to Mars using the Viking lander, constrain the numerical values of the bulk tidal parameter and of the brane tension. PACS numbers: 04.80.Cc, 04.50.+h, 04.80.-y † c.boehmer@ucl.ac.uk ‡ harko@hkucc.hku.hk § francisco.lobo@port.ac.uk Solar system tests of brane world models 2
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We further investigate the dark energy model based on the Finsler geometry inspired osculating Barthel–Kropina cosmology. The Barthel–Kropina cosmological approach is based on the introduction of a Barthel connection in an osculating... more
We further investigate the dark energy model based on the Finsler geometry inspired osculating Barthel–Kropina cosmology. The Barthel–Kropina cosmological approach is based on the introduction of a Barthel connection in an osculating Finsler geometry, with the connection having the property that it is the Levi-Civita connection of a Riemannian metric. From the generalized Friedmann equations of the Barthel–Kropina model, obtained by assuming that the background Riemannian metric is of the Friedmann–Lemaitre–Robertson–Walker type, an effective geometric dark energy component can be generated, with the effective, geometric type pressure, satisfying a linear barotropic type equation of state. The cosmological tests, and comparisons with observational data of this dark energy model are considered in detail. To constrain the Barthel–Kropina model parameters, and the parameter of the equation of state, we use 57 Hubble data points, and the Pantheon Supernovae Type Ia data sample. The st s...
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We consider numerical black hole solutions in the Weyl conformal geometry and its associated conformally invariant Weyl quadratic gravity. In this model, Einstein gravity (with a positive cosmological constant) is recovered in the... more
We consider numerical black hole solutions in the Weyl conformal geometry and its associated conformally invariant Weyl quadratic gravity. In this model, Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity after the Weyl gauge field ($$\omega _{\mu }$$ ω μ ) becomes massive through a Stueckelberg mechanism and it decouples. As a first step in our investigations, we write down the conformally invariant gravitational action, containing a scalar degree of freedom and the Weyl vector. The field equations are derived from the variational principle in the absence of matter. By adopting a static spherically symmetric geometry, the vacuum field equations for the gravitational, scalar, and Weyl fields are obtained. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, we obtain their solutions numerically. We detect the formation of a black hole from the...
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Finsler geometry is an important extension of Riemann geometry, in which each point of the spacetime manifold is associated with an arbitrary internal variable. Two interesting Finsler geometries with many physical applications are the... more
Finsler geometry is an important extension of Riemann geometry, in which each point of the spacetime manifold is associated with an arbitrary internal variable. Two interesting Finsler geometries with many physical applications are the Randers and Kropina type geometries. A subclass of Finsler geometries is represented by the osculating Finsler spaces, in which the internal variable is a function of the base manifold coordinates only. In an osculating Finsler geometry, we introduce the Barthel connection, with the remarkable property that it is the Levi–Civita connection of a Riemannian metric. In the present work we consider the gravitational and cosmological implications of a Barthel–Kropina type geometry. We assume that in this geometry the Ricci type curvatures are related to the matter energy–momentum tensor by the standard Einstein equations. The generalized Friedmann equations in the Barthel–Kropina geometry are obtained by considering that the background Riemannian metric is...
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We consider a warm inflationary scenario in which the two major fluid components of the early Universe, the scalar field and the radiation fluid, evolve with distinct four-velocities. This cosmological configuration is equivalent to a... more
We consider a warm inflationary scenario in which the two major fluid components of the early Universe, the scalar field and the radiation fluid, evolve with distinct four-velocities. This cosmological configuration is equivalent to a single anisotropic fluid, expanding with a four-velocity that is a combination of the two fluid four-velocities. Due to the presence of anisotropies the overall cosmological evolution is also anisotropic. We obtain the gravitational field equations of the non-comoving scalar field–radiation mixture for a Bianchi Type I geometry. By assuming the decay of the scalar field, accompanied by a corresponding radiation generation, we formulate the basic equations of the warm inflationary model in the presence of two non-comoving components. By adopting the slow-roll approximation the theoretical predictions of the warm inflationary scenario with non-comoving scalar field and radiation fluid are compared in detail with the observational data obtained by the Pla...
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We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields... more
We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in the action. Imposing a flat, homogeneous and isotropic geometry, we extract the Friedmann equations, obtaining an effective dark-energy sector containing higher-derivatives of the matter energy density and pressure. For the cases of dust, radiation and stiff matter, we analyze the cosmological behavior, finding accelerating, de Sitter and non-accelerating phases, dominated by matter or dark-energy. Additionally, the effective dark-energy equation-of-state parameter can be quintessence-like, cosmological-constant-like or even phantom-like. The detailed study of these scenarios may provide signatures, that could distinguish them from other candidates of modified gravity.
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We propose a gravitational theory in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, the trace of the matter energy–momentum tensor, and the contraction of the Ricci tensor... more
We propose a gravitational theory in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, the trace of the matter energy–momentum tensor, and the contraction of the Ricci tensor with the matter energy–momentum tensor. The matter energy–momentum tensor is generally not conserved, thus leading to the appearance of an extra-force, acting on massive particles in a gravitational field. The stability conditions of the theory with respect to local perturbations are also obtained. The cosmological implications of the theory are investigated, representing an exponential solution. Hence, a Ricci tensor–energy–momentum tensor coupling may explain the recent acceleration of the universe, without resorting to the mysterious dark energy.
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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... more
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 spacetimes. 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.
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The well-formulation and the well-posedness of the Cauchy problem are discussed for hybrid metric-Palatini gravity, a recently proposed modified gravitational theory consisting of adding to the Einstein–Hilbert Lagrangian an f(R)-term... more
The well-formulation and the well-posedness of the Cauchy problem are discussed for hybrid metric-Palatini gravity, a recently proposed modified gravitational theory consisting of adding to the Einstein–Hilbert Lagrangian an f(R)-term constructed à la Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be well-formulated and, furthermore, can be well-posed depending on the adopted matter sources.