Abstract:
$G$ measurements are made with torsion balance in "vacuum" to the aim of eliminating the air convection disturbances. Nevertheless, the accuracy of the measured values appears unsatisfying. In 2000 J.Luo and Z.K.Hu first denounced the presence of some unknown systematic error in high vacuum $G$ measurements. In this work a new systematic effect is analyzed which arises in calm air from the non-zero balance of the overall momentum discharged by the air molecules on the test mass. This effect is negligible at vacuum pressures higher than a millibar. However in the interval between the millibar and the nanobar the disturbing force is not negligible and becomes comparable to the gravitational force when the chamber pressure drops to about $10^{-5}$ bar. At the epoch of Heyl's benchmark measurement at 1-2 millibar (1927), the technology of high vacuum pumps was developed, but this chance was not utilized without declaring the reason. The recent $G$ measurements use high vacuum techniques up to $10^{-10}$ and $10^{-11}$ bar, but the effect of the air meatus is not always negligible. We wonder whether the measurements in the interval between the millibar and the nanobar have been made. As a matter of fact, we were not able to find the related papers in the literature. A physical explanation of the denounced unknown systematic error appears useful also in this respect.

Abstract:
The article reports on the results of an analysis of the torsind behavior long-term
observations. The torsind is a species of ultralight disc torsion balance. The
data analysis showed that the signal recorded contains the 24-hour periodic
component presumably associated with the Sun. Moreover, unpredictable strong
impacts, forcing torsind disk to rotate in one or another direction, were
revealed. Presumably the reason of these effects is the Sun. This indicates the
existence of an unknown radiation that bears a torque which
may impact on the mechanical systems dynamics. This fact leads to the need to
measure the gravitational constant G overnight and during periods of minimum of
the solar activity, provided that the G measurements are carried out using a
torsion balance.

Abstract:
The aim of this paper fundamentally lies in proposing an alternative explanation to the so-called gravitational redshift. The above-mentioned phenomenon, experimentally verified more than half a century ago, is commonly legitimised by means of Special Relativity. In our case, since time is considered as being absolute, we simply postulate a local variability of the Plank constant. Ultimately, we carry out an alternative deduction of the relation that expresses the gravitational redshift as a function of a parameter that, in our case, does not coincide with a Schwarzschild coordinate.

Abstract:
On August 29^{th}, 2018, a
scientific team reported a measure of the Universal Gravitational Constant G
with the highest precisionever. The team completed three experimental campaigns in the same cityover the course of a year. That work provided a complete data setuseful analyzing the values of Big G change with the distance to the Sun,
as is claimed by the author of this paper.

Abstract:
A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w = -0.98 , we predict a current variation of ？/G = -0.06H_{0}, a value within current observational bounds. H_{0} is Hubble’s parameter, G is Newton’s constant and ？ is the derivative of G with respect to time. Thus, G has a cosmic origin, is decreasing with respect to cosmological time, and is proportional to H_{0}, as originally proposed by the Dirac-Jordan hypothesis, albeit at a much slower rate. Within our model, we can explain the cosmological constant fine-tuning problem, the discrepancy between the present very weak value of the cosmological constant, and the much greater vacuum energy found in earlier epochs (we assume a connection exists). To formalize and solidify our model, we give two distinct parametrizations of G with respect to “a”, the cosmic scale parameter. We treat G^{-1} as an order parameter, which vanishes at high energies; at low temperatures, it reaches a saturation value, a value we are close to today. Our first parametrization for G^{-1} is motivated by a charging capacitor; the second treats G^{-1}(a) by analogy to a magnetic response, i.e., as a Langevin function. Both parametrizations, even though very distinct, give a remarkably similar tracking behavior for w(a) , but not of the conventional form, w(a) = w_{0} + w_{a}(1-a) , which can be thought of as only holding over a limited range in “a”. Interestingly, both parametrizations indicate the onset of G formation at a temperature of approximately 7×10^{21} degrees Kelvin, in contrast to the ΛCDM model where G is taken as a constant all the way back to the Planck temperature, 1.42×10^{32} degrees Kelvin. At the temperature of formation, we find that G has increased to roughly 4×10^{20} times its current value. For most of cosmic evolution, however, our variable G model gives results similar to the predictions of the ΛCDM model, except in the very early universe, as we shall demonstrate. In fact, in the limit where w approaches -1, the expression, ？/G , vanishes, and we are left with the concordance model. Within our framework, the emergence of dark energy over matter at a scale of a ≈ 0.5 is that point where

Abstract:
This paper deals with the Bianchi type I anisotropic models of the universe, filled with a bulk viscous cosmic fluid, in the presence of variable gravitational and cosmological constants. Some exact solutions of Einstein’s gravitational field equations with bulk viscosity, gravitational and cosmological constants have been obtained. Several well known forms of cosmological terms have been considered to discuss the effect of cosmological variables. The new cosmological models presented in this paper approaches to isotropic model with evolution of universe. The physical and dynamical properties of the models have also been discussed.

Abstract:
In this paper, we are going to rely on the first law
in physics through which we can obtain a precise ideal value of the universal
gravitational constant, a thing which has not happened so far. The significance
of this law lies in the fact that, besides determining a precise ideal value of
the gravitational constant, it connects three different physical disciplines together,
which are mechanics, electromagnetism and thermodynamics. It is what
distinguishes this from other law. Through this law, we have created the
theoretical value of the gravitational constant G_{i} and we found it equivalent to 6.674010551359 × 10^{-11} m^{3}·kg^{-1}·s^{-2}. In the discussion, the table of
measurements of the gravitational constant was divided into three groups, and
the average value of the first group G_{1} which is the best precision, equals the following sum 6.67401×10^{-11} m^{3}·kg^{-1}·s^{-2},
and it’s the same equal value to the ideal value G_{i} that results from the law, as shown through our
research that any other experimental values must not exceed the relative standard uncertainty
which has a certain amount that is equivalent to a value of 5.325×10^{-5} and that’s a square value of the fine-structure
constant.

We compared the small quantitative changes (range) in G over repeated
measures (days) with recently improved methods of determinations and those
recorded over 20 years ago. The range in the Newtonian constant of gravitation
G is usually in the order of 400 ppm as reflected in experimentally-determined
values. The moderate strength negative correlation between daily fluctuations
in G, in the range of 3 × 10^{-3} of the average value, and an index of
global geomagnetic activity reported by Vladimirsky and Bruns in 1998 was also
found for the daily fluctuations in the angular deflection θ (in arcseconds) and geomagnetic activity within 24 hr for the
Quinn et al. 2013 data. A temporal
coupling between increases of geomagnetic activity in the order of 10^{-9} T with decreases in G in the order of 10^{-14}^{ }m^{3}·kg^{-1}·s^{-2} could suggest a recondite shared source of variance. The energy equivalence for
this change in G and geomagnetic activity within 1 L of water is ~3 × 10^{-14} J.

Abstract:
The present work investigates the practical consequences of the recent experimental observations, achieved with the help of the tightly synchronized atomic clocks in orbit, on the current view about the nature of the gravitational fields. While clocks, stationary within gravitational fields, show exactly the gravitational slowing predicted by General Relativity (GR), the GPS clocks, in orbit round earth and moving with earth round the sun, do not show the gravitational slowing of the solar field, predicted by GR. This absence can only mean that the orbital motion of earth cancels this gravitational slowing, which obviously cancels too the spacetime curvature. On the other hand, the Higgs theory introduces the Higgs Quantum Space (HQS) giving mass to the elementary particles by the Higgs mechanism. The HQS thus necessarily governs the inertial motion of matter-energy and is locally their ultimate reference for rest and for motions. Motion with respect to the local HQS and not relative motion is what causes clock slowing, light anisotropy and all the, so-called relativistic effects. Non-uniform motion of the HQS itself necessarily creates inertial dynamics, which, after Einstein’s equivalence of gravitational and inertial effects, is gravitational dynamics. The absence of the gravitational slowing of the GPS clocks by the solar field, together with the null results of the light anisotropy experiments on earth, demonstrates that earth is stationary with respect to the local HQS. This can make sense only if the HQS is moving round the sun according to a Keplerian velocity field, consistent with the planetary motions. This Keplerian velocity field of the HQS is the quintessence of the gravitational fields and is shown to naturally and accurately create the gravitational dynamics, observed on earth, in the solar system, in the galaxy and throughout the universe, as well as all the observed effects of the gravitational fields on light and on clocks.

Abstract:
This paper is devoted to studying the generalized Chaplygin gas models in Bianchi type III space- time geometry with time varying bulk viscosity, cosmological and gravitational constants. We are considering the condition on metric potential _{}. Also to obtain deterministic models we have considered physically reasonable relations like _{} , and the equation of state for generalized Chaplygin gas given by_{} . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behaviour of the models has been discussed.