Gravity, Robertson–Walker metric and the Wodzicki residue

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jian Wang ◽  
Yong Wang ◽  
Chunling Yang
Keyword(s):  
Wodzicki Residue ◽  
Walker Metric

scholarly journals Varying Physical Constants, Astrometric Anomalies, Redshift and Hubble Units

Galaxies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 55 ◽  
Author(s):  
Rajendra P. Gupta
Keyword(s):  
Hubble Constant ◽  
Astronomical Unit ◽  
Lunar Laser Ranging ◽  
Current Time ◽  
Physical Constants ◽  
Lunar Laser ◽  
Walker Metric ◽  
The One ◽  
Two Parameters ◽  
Secular Increase

We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and which has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck unit increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is of interest.

Evolution of the Robertson–Walker metric under 2-loop renormalization group flow

2017 ◽  
Vol 26 (03) ◽  
pp. 1750021
Author(s):  
F. Hesamifard ◽  
M. M. Rezaii
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ricci Flow ◽  
Necessary Condition ◽  
Renormalization Group Flow ◽  
Twisted Product ◽  
Walker Metric ◽  
Group Flow

Here, we study the evolution of a Robertson–Walker (RW) metric under the Ricci flow and 2-loop renormalization group flow (RG-2 flow). We show that a RW metric is a fixed point of the Ricci flow and it is not a solution of the RG-2 flow. RG-2 flow is considered on a doubly twisted product metric with further assumptions and also we introduce a necessary condition for existence of the solution of RG-2 flow.

scholarly journals The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological `Coupling Constants’ in the Theory of Induced Gravity

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 81 ◽  
Author(s):  
Farkhat Zaripov
Keyword(s):  
Gravitational Interaction ◽  
Scalar Fields ◽  
Coupling Constants ◽  
De Sitter ◽  
Induced Gravity ◽  
Mean Values ◽  
Gravitational And Cosmological Constants ◽  
Centrally Symmetric ◽  
Walker Metric ◽  
Cosmological Constants

This work is the extension of author`s research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and “restructuring” (RS). We consider equations with quadratic potential that are symmetric with respect to scale transformations. The solutions of the equations obtained for the case of spaces defined by the Friedman-Robertson-Walker metric, as well as for a centrally symmetric space are investigated. In our model arise effective gravitational and cosmological “constants”, which are defined by the “mean square” of the scalar fields. In obtained solutions the values of such parameters as “Hubble parameter”, gravitational and cosmological “constants” in the RS stage fluctuate near monotonically evolving mean values. These parameters are matched with observational data, described as phenomena of dark energy and dark matter. The MTIG equations for the case of a centrally symmetric gravitational field, in addition to the Schwarzschild-de Sitter solutions, contain solutions that lead to the new physical effects at large distances from the center. The Schwarzschild-Sitter solution becomes unstable and enters the oscillatory regime. For distances greater than a certain critical value, the following effects can appear: deviation from General relativity and Newton’s law of gravitational interaction, antigravity.

scholarly journals Bounds on higher derivative f(R,□R,T) models from energy conditions

2019 ◽  
Vol 34 (11) ◽  
pp. 1950082 ◽  
Author(s):  
M. Ilyas ◽  
Z. Yousaf ◽  
M. Z. Bhatti
Keyword(s):  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Ricci Scalar ◽  
Energy Conditions ◽  
Higher Derivative ◽  
Derivative Formula ◽  
Cosmological Solutions ◽  
Walker Metric ◽  
Cosmic Parameters

This paper studies the viable regions of some cosmic models in a higher derivative [Formula: see text] theory with the help of energy conditions (where [Formula: see text], [Formula: see text] and [Formula: see text] are the Ricci scalar, d’Alembert’s operator and trace of energy–momentum tensor, respectively). For this purpose, we assume a flat Friedmann–Lemaître–Robertson–Walker metric which is assumed to be filled with perfect fluid configurations. We take two distinct realistic models that might be helpful to explore stable regimes of cosmological solutions. After taking some numerical values of cosmic parameters, like crackle, snap, jerk (etc.) as well as viable constraints from energy conditions, the viable zones for the under observed [Formula: see text] models are examined.

scholarly journals FLRW-cosmology in generic gravity theories

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Metin Gürses ◽  
Yaghoub Heydarzade
Keyword(s):  
Perfect Fluid ◽  
Gravity Theory ◽  
Fluid Type ◽  
Field Equations ◽  
Walker Metric ◽  
Flrw Cosmology ◽  
Arbitrary Dimensions ◽  
Gravity Theories

AbstractWe prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and $${\mathcal {F}}(R, {\mathcal {G}})$$ F ( R , G ) theories are given as examples.

Bound states of a fermion and a Dirac dyon in Robertson-Walker metric

1993 ◽  
Vol 26 (17) ◽  
pp. 4451-4462 ◽  
Author(s):  
Xin-Zhou Li ◽  
Jian-Zu Zhang
Keyword(s):  
Bound States ◽  
Walker Metric

scholarly journals Notes on Cosmology

1972 ◽  
Vol 44 ◽  
pp. 404-406 ◽  
Author(s):  
J. Pachner
Keyword(s):  
Point Of View ◽  
World Model ◽  
Present Epoch ◽  
Cosmological Principle ◽  
Cosmic Evolution ◽  
Cosmic Space ◽  
Walker Metric ◽  
Theory Of Gravitation ◽  
Isotropic Expansion ◽  
The Universe

The present short notes on cosmology start with two conclusions based on observational data. The first of them is the well-known conclusion that the Universe from the global point of view is at the present epoch of its evolution in a uniform and isotropic expansion. If we accept the very convincing arguments of Bondi (1962) that the geometry of the cosmic space is Riemannian, its properties are described at the present epoch of the cosmic evolution by the well-known Robertson-Walker metric expressing the cosmological principle (Robertson, 1935, 1936; Walker, 1936). The form of the geodesical lines depends on the assumed theory of gravitation. For instance, in the closed Friedman world model they are cycloids with a singularity at the start of the expansion.

scholarly journals Anisotropic evolution of D-dimensional FRW spacetime

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Chad Middleton ◽  
Bret A. Brouse ◽  
Scott D. Jackson
Keyword(s):  
Early Time ◽  
Scale Factor ◽  
Accelerated Expansion ◽  
Late Time ◽  
Time Behavior ◽  
Einstein Field Equations ◽  
Fluid Regime ◽  
Field Equations ◽  
Higher Dimensional ◽  
Walker Metric

AbstractWe examine the time evolution of the $$D=d+4$$D=d+4 dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scale factor as a function of the time. The fluid regime solution closely mimics that described by 4D FRW cosmology, offering a late-time behavior for the 3D scale factor after becoming valid in the early universe, and can give rise to a late-time accelerated expansion driven by vacuum energy. This is shown to be preceded by an earlier volume regime solution, which offers a very early-time epoch of accelerated expansion for a radiation-dominated universe for $$d=1$$d=1. The time scales describing these phenomena, including the transition from volume to fluid regime, are shown to fall within a small fraction of the first second when the fundamental constants of the theory are aligned with the Planck time. This model potentially offers a higher-dimensional alternative to scalar-field inflationary theory and a consistent cosmological theory, yielding a unified description of early- and late-time accelerated expansions via a 5D spacetime scenario.

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