An extended theory of gravity in a modified Riemann’s geometry

2019 ◽  
Vol 16 (05) ◽  
pp. 1950067 ◽  
Author(s):  
Hoavo Hova ◽  
Huanxiong Yang ◽  
Samuel Owusu
Keyword(s):  
Displacement Vector ◽  
Isotropic Universe ◽  
Extended Theory ◽  
Displacement Vector Field ◽  
Vectorial Function ◽  
State Formula ◽  
Normal Gauge ◽  
Theory Of Gravity ◽  
The Universe ◽  
Critical Scale

In this work, we study the evolution of an isotropic universe in an extended theory of gravity obtained geometrically by transforming the normal-gauge Lyra displacement vector field [Formula: see text] as a complex vectorial function depending on a dynamical scalar field [Formula: see text]. By using the latest observational data, we observe that for [Formula: see text] the universe starts accelerating at the critical scale factor [Formula: see text] which corresponds to a redshift of [Formula: see text]. We also find that the dark energy fluid considered in this model is a generalized fluid with equation of state [Formula: see text].

scholarly journals COSMOLOGICAL MODELS WITH A VARYING Λ-TERM IN LYRA'S GEOMETRY

2012 ◽  
Vol 27 (29) ◽  
pp. 1250164 ◽  
Author(s):  
V. K. SHCHIGOLEV
Keyword(s):  
Vector Field ◽  
Exact Solutions ◽  
Equations Of State ◽  
Displacement Vector ◽  
Cosmological Models ◽  
Displacement Vector Field ◽  
Varying Λ ◽  
Lyra’S Geometry ◽  
Model Equations ◽  
The Universe

Cosmological models in Lyra's geometry are constructed and investigated with the assumption of a minimal interaction of matter with the displacement vector field and the dynamical Λ-term. Exact solutions of the model equations are obtained for the different equations of state of the matter, that fills the universe, and for the certain assumptions on the decaying law for Λ.

A DARKLESS SPACE–TIME

2008 ◽  
Vol 17 (02) ◽  
pp. 275-299 ◽  
Author(s):  
ANGELO TARTAGLIA ◽  
MONICA CAPONE
Keyword(s):  
Vector Field ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Empty Space ◽  
Space Time ◽  
Accelerated Expansion ◽  
Displacement Vector Field ◽  
The One ◽  
Internal Viscosity ◽  
The Universe

In cosmology it has become usual to introduce new entities as dark matter and dark energy in order to explain otherwise unexplained observational facts. Here, we propose a different approach treating space–time as a continuum endowed with properties similar to those of ordinary material continua, such as internal viscosity and strain distributions originated by defects in the texture. A Lagrangian modeled on the one valid for simple dissipative phenomena in fluids is built and used for empty space–time. The internal "viscosity" is shown to correspond to a four-vector field. The vector field is shown to be connected with the displacement vector field induced by a point defect in a four-dimensional continuum. Using the known symmetry of the universe, assuming the vector field to be divergenceless and solving the corresponding Euler–Lagrange equation, we directly obtain inflation and a phase of accelerated expansion of space–time. The only parameter in the theory is the "strength" of the defect. We show that it is possible to fix it in such a way as to also quantitatively reproduce the acceleration of the universe. We have finally verified that the addition of ordinary matter does not change the general behavior of the model and that the proper Newtonian limit exists.

An obstacle problem for elliptic membrane shells

2018 ◽  
Vol 24 (5) ◽  
pp. 1503-1529 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Cristinel Mardare ◽  
Paolo Piersanti
Keyword(s):  
Vector Field ◽  
Asymptotic Analysis ◽  
Obstacle Problem ◽  
Displacement Vector ◽  
Middle Surface ◽  
Two Dimensional ◽  
Displacement Vector Field ◽  
Membrane Shells ◽  
Signorini Condition ◽  
Confinement Condition

Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the points of the admissible deformed configurations remain in a given half-space. To this end, we embed the shell into a family of linearly elastic elliptic membrane shells, all sharing the same middle surface [Formula: see text], where [Formula: see text] is a domain in [Formula: see text] and [Formula: see text] is a smooth enough immersion, all subjected to this confinement condition, and whose thickness [Formula: see text] is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as [Formula: see text] approaches zero, the corresponding “limit” two-dimensional variational problem. This problem takes the form of a set of variational inequalities posed over a convex subset of the space [Formula: see text]. The confinement condition considered here considerably departs from the Signorini condition usually considered in the existing literature, where only the “lower face” of the shell is required to remain above the “horizontal” plane. Such a confinement condition renders the asymptotic analysis substantially more difficult, however, as the constraint now bears on a vector field, the displacement vector field of the reference configuration, instead of on only a single component of this field.

scholarly journals A distance to dose difference tool for estimating the required spatial accuracy of a displacement vector field

2011 ◽  
Vol 38 (5) ◽  
pp. 2318-2323 ◽  
Author(s):  
Nahla K. Saleh-Sayah ◽  
Elisabeth Weiss ◽  
Francisco J. Salguero ◽  
Jeffrey V. Siebers
Keyword(s):  
Vector Field ◽  
Displacement Vector ◽  
Spatial Accuracy ◽  
Displacement Vector Field ◽  
Dose Difference

scholarly journals Standard model and graviweak unification with (super)renormalizable gravity. Part I: Visible and invisible sectors of the universe

2015 ◽  
Vol 30 (09) ◽  
pp. 1550044 ◽  
Author(s):  
L. V. Laperashvili ◽  
H. B. Nielsen ◽  
A. Tureanu
Keyword(s):  
Standard Model ◽  
Quantum Gravity ◽  
Consistent Theory ◽  
Invariant Model ◽  
Higher Derivative ◽  
Self Consistent ◽  
Renormalizable Theory ◽  
Theory Of Gravity ◽  
Higgs Fields ◽  
The Universe

We develop a self-consistent Spin (4, 4)-invariant model of the unification of gravity with weak SU(2) gauge and Higgs fields in the visible and invisible sectors of our universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.

scholarly journals What are the wild waves saying? Yet another meditation on the predictions, searches for, and detections of gravitational waves

2018 ◽  
Vol 27 (14) ◽  
pp. 1830009
Author(s):  
Virginia Trimble
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Point Of View ◽  
Large Majority ◽  
Laboratory Apparatus ◽  
New Information ◽  
Theory Of Gravity ◽  
To Come ◽  
The Universe

A large majority of the physics and astronomy communities are now sure that gravitational waves exist, can be looked for, and can be studied via their effects on laboratory apparatus as well as on astronomical objects. So far, everything found out has agreed with the predictions of general relativity, but hopes are high for new information about the universe and its contents and perhaps for hints of a better theory of gravity than general relativity (which even Einstein expected to come eventually). This is one version of the story, from 1905 to the present, told from an unusual point of view, because the author was, for 28.5 years, married to Joseph Weber, who built the first detectors starting in the early 1960s and operated one or more until his death on 30 September 2000.

scholarly journals Foundations of a Theory of Gravity with a Constraint and Its Canonical Quantization

2021 ◽  
Vol 52 (1) ◽  
Author(s):  
Alexander P. Sobolev
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Early Universe ◽  
Canonical Quantization ◽  
Entropy Density ◽  
Maximum Temperature ◽  
Past Century ◽  
Physical Point ◽  
Theory Of Gravity ◽  
The Universe

AbstractThe gravitational equations were derived in general relativity (GR) using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such equality of all coordinate systems may not correspond to reality. Nevertheless, no actual verification of the necessity of this assumption has been made to date. The paper proposes a theory of gravity with a constraint, the degenerate variants of which are general relativity (GR) and the unimodular theory of gravity. This constraint is interpreted from a physical point of view as a sufficient condition for the adiabaticity of the process of the evolution of the space–time metric. The original equations of the theory of gravity with the constraint are formulated. On this basis, a unified model of the evolution of the modern, early, and very early Universe is constructed that is consistent with the observational astronomical data but does not require the hypotheses of the existence of dark energy, dark matter or inflatons. It is claimed that: physical time is anisotropic, the gravitational field is the main source of energy of the Universe, the maximum global energy density in the Universe was 64 orders of magnitude smaller the Planckian one, and the entropy density is 18 orders of magnitude higher the value predicted by GR. The value of the relative density of neutrinos at the present time and the maximum temperature of matter in the early Universe are calculated. The wave equation of the gravitational field is formulated, its solution is found, and the nonstationary wave function of the very early Universe is constructed. It is shown that the birth of the Universe was random.

Most of the Universe is Missing!

2019 ◽  
pp. 64-72
Author(s):  
Nicholas Mee
Keyword(s):  
Dark Matter ◽  
Galaxy Clusters ◽  
Early Universe ◽  
The World ◽  
Unknown Form ◽  
Theory Of Gravity ◽  
Stable Particles ◽  
The Universe

Most of the matter in the universe exists in an unknown form called dark matter. All estimates of the mass of galaxies and galaxy clusters suggest they contain far more matter than is visible to us in the form of stars. Conventional explanations, such as the existence of large quantities of burnt-out stars known as MACHOs or dark gas clouds, have been ruled out. The most popular explanation is that dark matter consists of vast quantities of hypothetical stable particles known as WIMPs that were produced in vast quantities in the very early universe. Many laboratories around the world are searching for signs of these particles. These include the Italian Gran Sasso laboratory running the XENON100 experiment. Some theorists have suggested the evidence for dark matter would disappear if we had a better theory of gravity. Analysis of the Bullet Cluster indicates such proposals will not work.

scholarly journals Asymptotically flat vacuum solution in modified theory of Einstein’s gravity

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Surajit Kalita ◽  
Banibrata Mukhopadhyay
Keyword(s):  
General Relativity ◽  
Vacuum Solution ◽  
Compact Objects ◽  
Schwarzschild Solution ◽  
Asymptotically Flat ◽  
Symmetric Vacuum ◽  
Theory Of Gravity ◽  
Bound Orbits ◽  
Vacuum Spacetime ◽  
The Universe

Abstract A number of recent observations have suggested that the Einstein’s theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to surpass the general relativity which explains a number of phenomena where Einstein’s theory of gravity fails. In the f(R) gravity, behaviour of the spacetime is modified as compared to that of given by the Einstein’s theory of general relativity. This theory has already been explored for understanding various compact objects such as neutron stars, white dwarfs etc. and also describing evolution of the universe. Although researchers have already found the vacuum spacetime solutions for the f(R) gravity, yet there is a caveat that the metric does have some diverging terms and hence these solutions are not asymptotically flat. We show that it is possible to have asymptotically flat spherically symmetric vacuum solution for the f(R) gravity, which is different from the Schwarzschild solution. We use this solution for explaining various bound orbits around the black hole and eventually, as an immediate application, in the spherical accretion flow around it.

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