Geometric Scalar Field Research Articles

Screening mechanism and late-time cosmology: Role of a Chameleon–Brans–Dicke scalar field

ABSTRACT We discuss a way in which the geometric scalar field in a Brans–Dicke (BD) theory can evade local astronomical tests and act as a driver of the late-time cosmic acceleration. This requires a self-interaction of the BD scalar as well as an interaction with ordinary matter. The scalar field in this construct acquires a density-dependent effective mass much like a Chameleon field. We discuss the viability of this setup in the context of Equivalence Principle, Fifth Force, and Solar System tests. The cosmological consistency is adjudged in comparison with observational data from recalibrated light curves of type Ia supernova (JLA), the Hubble parameter measurements (OHD) and the Baryon Acoustic Oscillation (BAO). We deduct that the astrophysical constraints indeed favour the existence of a mild scalar-matter interaction in the Jordan Frame.

Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory

A generalized Brans-Dicke (GBD) theory in the framework of Palatini formalism is proposed in this paper. We derive the field equations by using the variational approach and obtain the linearized equations by using the weak-field approximation method. We show various properties of the geometrical scalar field in the Palatini-formalism of GBD theory: it is massless and source-free, which are different from the results given in the metric-formalism of GBD theory. Also, we investigate the polarization modes of gravitational waves (GWs) by using the geodesic deviation method and the Newman-Penrose method in the Palatini-GBD theory. It is observed that there are three polarizations modes and four oscillations in the Palatini-GBD theory. Concretely, they are the two transverse tensor (+) and (×) standard polarization modes, and one breathing mode (with two oscillations). The results of GWs polarization in the Palatini-GBD theory are different from that in the metric-GBD theory, where there are four polarizations modes: the two standard tensorial modes (+ and ×), a scalar breathing mode, and a massive scalar mode that is a mix of the longitudinal and the breathing polarization. Comparing with the Palatini-f(R˜) theory and the General Relativity, we can see that the extra breathing mode of GWs polarization can be found in the Palatini-GBD theory. At last, the expression of the parameterized post Newton (PPN) parameter is derived, which could pass through the experimental test.

Charged and Electromagnetic Fields from Relativistic Quantum Geometry

In the recently introduced Relativistic Quantum Geometry (RQG) formalism, the possibility was explored that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the dynamics of an auxiliary geometrical scalar field θ, in order that the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold. In this framework we study jointly the dynamics of electromagnetic fields produced by quantum complex vector fields, which describes charges without charges. We demonstrate that complex fields act as a source of tetra-vector fields which describe an extended Maxwell dynamics.

Inflationary back-reaction effects from Relativistic Quantum Geometry

Abstract We study the dynamics of scalar metric fluctuations in a non-perturbative variational formalism recently introduced, by which the dynamics of a geometrical scalar field θ , describes the quantum geometrical effects on a Weylian-like manifold with respect to a background Riemannian space–time. In this letter we have examined an example in the framework of inflationary cosmology. The resulting spectral predictions are in very good agreement with observations and other models of inflation.

Towards relativistic quantum geometry

We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.

The cosmology of a fundamental scalar

We observe that the standard homogeneous cosmologies, those of Minkowski, de Sitter, and anti-de Sitter, which form the matrix for the Robertson–Walker scale factor, live naturally as isolated points inside a larger family of conformally flat metrics obtained by allowing a tensor containing the information of conformal symmetry breaking to be more general. So the standard cosmological metrics are parametrically unstable in this sense, and therefore unphysical. When we pass to the stable family of perturbed metrics, we immediately encounter a scalar field, which drives the conformal expansion of the universe and which automatically obeys the non-linear sine-Gordon equation. The Lagrangian for the sine-Gordon equation is a cosine potential agreeing to the fourth order with the potential used in the approach to the generation of mass in gauge theories. Accordingly we identify our geometric scalar field—actually of the type of an abelian gauge field—with the recently discovered scalar field. There are two constants in the theory: the first, named \(m\), is positive and defines a mass scale for the universe; the second, named \(\varLambda \), is the cosmological constant. For the space–time to be everywhere non-singular, equivalently for the (strict) dominant energy condition to hold, these constants must obey the inequality \(\varLambda > m^2/4\).

Scalar torsion and a new symmetry of general relativity

We reformulate the general theory of relativity in the language of Riemann-Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed with torsion. In this new framework, the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field. We show that in this formulation general relativity has a new kind of invariance, whose invariance group consists of a set of conformal and gauge transformations, called Cartan transformations. These involve both the metric tensor and the torsion vector field, and are similar to the well known Weyl gauge transformations. By making use of the concept of Cartan gauges, we show that, under Cartan transformations, the new formalism leads to different pictures of the same gravitational phenomena. We show that in an arbitrary Cartan gauge general relativity has the form of a scalar-tensor theory. In this approach, the Riemann-Cartan geometry appears as the natural geometrical setting of the general relativity theory when the latter is viewed in an arbitrary Cartan gauge. We illustrate this fact by looking at the one of the classical tests of general relativity theory, namely the gravitational spectral shift. Finally, we extend the concept of space-time symmetry to the more general case of Riemann-Cartan space-times endowed with scalar torsion. As an example, we obtain the conservation laws for auto-parallel motion in a static spherically symmetric vacuum space-time in a Cartan gauge, whose orbits are identical to Schwarzschild orbits in general relativity.

Gravitational interaction of a geometric scalar field with a vortex gravitational field in five-dimensional spacetime

Within the framework of the five-dimensional geometric theory, the problem of gravitational interaction of a vortex gravitational and scalar fields is investigated. A solution of the five-dimensional Einstein vacuum equations is derived. The results obtained are compared with those obtained previously within the framework of the four-dimensional theory.

General relativity and Weyl geometry

We show that the general theory of relativity can be formulated in the language of Weyl geometry. We develop the concept of Weyl frames and point out that the new mathematical formalism may lead to different pictures of the same gravitational phenomena. We show that in an arbitrary Weyl frame general relativity, which takes the form of a scalar–tensor gravitational theory, is invariant with respect to Weyl transformations. A key point in the development of the formalism is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in terms of Riemannian geometry we find that the theory has some similarities with Brans–Dicke gravitational theory. In this scenario, the gravitational field is not described by the metric tensor only, but by a combination of both the metric and a geometrical scalar field. We illustrate this point by examining how distinct geometrical and physical pictures of the same phenomena may arise in different frames. To give an example, we discuss the gravitational spectral shift as viewed in a general Weyl frame. We further explore the analogy of general relativity with scalar–tensor theories and show how a known Brans–Dicke vacuum solution may appear as a solution of general relativity theory when reinterpreted in a particular Weyl frame. Finally, we show that the so-called WIST gravity theories are mathematically equivalent to Brans–Dicke theory when viewed in a particular frame.

Five-dimensional geometric electrovacuum problem with a geometric scalar field

A generalized geometric Reissner–Nordstrom problem taking into account a geometric scalar field G 44 (x) is treated in the context of the five-dimensional geometric theory of gravitation and electromagnetism. A general solution is obtained for the corresponding five-dimensional Einstein vacuum equations. The essential contribution of the geometric scalar field, which can give rise to wormholes, is shown.

Quintessence interacting dark energy and a scalar dark fluid from 5D vacuum

Considering a five-dimensional (5D) spacetime empty of matter, we develop a procedure from which an interacting scalar field and its potential are induced on our 4D spacetime by the 5D geometry. We use the procedure to derive a new 4D interacting quintessence scenario, where the quintessence field, its potential and the interaction between the dark matter and dark energy components have a geometrical origin. The mass of the interacting quintessence field depends on the extra dimension, thus giving more freedom to avoid conflicts with nucleosynthesis. Then, inspired from some scalar dark matter models, we extend the geometrical formalism to derive a novel 4D late-time cosmological scenario, where the whole dark sector of the universe (scalar dark matter plus dark energy) admits a unified description by a single geometrical scalar field.

WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

LOCALIZATION OF MATTERS ON A NON-Z2-SYMMETRIC THICK BRANE

We study localization of various matter fields on a non-Z2-symmetric scalar thick brane in a pure geometric Weyl integrable manifold in which variations in the length of vectors during parallel transport are allowed and a geometric scalar field is involved in its formulation. It is shown that, for spin 0 scalar field, the massless zero mode can be normalized on the brane. Spin 1 vector field cannot be normalized on the brane. And there is no spinor field which can be trapped on the brane for the case of no Yukawa-type coupling. By introducing the appropriate Yukawa coupling, the left or right chiral fermionic zero mode can be localized on the brane.

Mass gap for gravity localized on Weyl thick branes

We consider thick brane configurations in a pure geometric Weyl integrable 5D space-time, a non-Riemannian generalization of Kaluza-Klein (KK) theory involving a geometric scalar field. Thus, the 5D theory describes gravity coupled to a self-interacting scalar field which gives rise to the structure of the thick branes. We continue the study of the properties of a previously found family of solutions which is smooth at the position of the brane but involves naked singularities in the fifth dimension. Analyzing their graviton spectrum, we find that a particularly interesting situation arises for a special case in which the 4D graviton is separated from the KK gravitons by a mass gap. The corresponding effective Schr\odinger equation has a modified P\oschl-Teller potential and can be solved exactly. Apart from the massless 4D graviton, it contains one massive KK bound state, and the continuum spectrum of delocalized KK modes. We also discuss the mass hierarchy problem, and explicitly compute the corrections to Newton's law in the thin brane limit.

Gravitational collapse in Weyl integrable spacetimes

Spherically symmetric gravitational collapse in Weyl integrable spacetime is studied by some simplified models. The matter content is represented by a perfect fluid coupled with the geometric scalar field. A family of analytical solutions is found for a non-radiative collapsing nebulae of dust and the condition for black hole formation is established. Junction conditions with an exterior spacetime and the radiative collapse of a spherical star are also studied. In this case we find two classes of solutions with an exterior Vaidya spacetime: one with no internal heat flux while the other is obtained from a static initial condition.