Abstract:
The gravitational Lagrangian based on special relativity and the assumption of a fourth rank tensor interaction, derived by Kennedy (1972), is used to check Mach's principle in a homogeneous isotropic expanding universe. The Lagrangian is found to be consistent with Mach's principle when the density is the critical density and inertial mass is suitably renormalized. The Kennedy approach only gives the Lagrangian to first order in the gravitational coupling constant. By invoking the equivalence principle higher order corrections are found which renormalize the gravitational masses to the same values as the inertial masses. It is not the same as the correction derived from general relativity by Einstein-Infeld-Hoffmann, but otherwise the Lagrangians agree.

Abstract:
Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach’s principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle. 1. Introduction and Outline We start by presenting the gravitational Lagrangians that form the basis of the present formalism in Section 2. After that we point out how the local equations of motion for a particle will be affected by the long range interactions with the other particles in the universe. Consistency demands that the only quantities that enter are velocities and accelerations relative to the rest of the universe. This is Mach’s principle. After that, in Section 4, the long range effects are calculated by integration over the universe as a whole out to the Hubble radius, where the expansion velocity reaches the speed of light. In Section 5 Mach’s principle is found to be obeyed provided the density is the critical density ( ). The original masses of the theory then, however, turn out to be renormalized. This problem is dealt with in Section 6 where it is shown that the addition of certain higher order terms in the gravitational coupling constant restores the usual interpretation of mass and the gravitational constant. In this way the formalism as a whole is consistent with both Mach’s principle and the equivalence principle. 2. Gravitational Lagrangians Fock [1] found the Lagrangian that yields the Einstein-Infeld-Hoffmann (EIH) equations of motion [2–4]. Modern derivations and discussions of this approach can be found in Landau and Lifshitz [5], Hirondel [6], Nordtvedt [7], Brumberg [8], and Louis-Martinez [9], among others. These are all based on general relativity and Hirondel’s is the shortest. Here we will, however, focus on the profound work by Kennedy [10] on approximately relativistic interactions and their Lagrangians. Kennedy first derives the (special) relativistic Lagrangian for one particle interacting with another particle with constant given velocity. In a second step one then wishes to combine such Lagrangians into a single two-body Lagrangian, symmetric in the particle indices. To do this it

Abstract:
In cosmology the number of scientists using the framework of an expanding universe is very high. This model, the big-bang, is now overwhelmingly present in almost all aspects of society. It is the main stream cosmology of today. A small number of scientists are researching on the possibility of a non-expanding universe. The existence of these two groups, one very large and the other very small, is a good proof of the use of the scientific method: it does not drive to an absolute certainty. All models have to be permanently validated, falsified. Ockham's razor, a powerful philosophical tool, will probably change the amount of scientists working in each of these groups. We present here a model where a big-bang is unnecessary. It ends, in a finite time, in a second INFLATION, or a disaggregation to infinity. We also discuss the possibilities of a non-expanding universe model. Only a few references will be cited, mainly concerned with our own work in the past, thus purposely avoiding citing the many thousands of professionals working in this field.

Abstract:
The kinematics and dynamic interpretation of the cosmological expansion is reviewed in a widely accessible manner with emphasis on the acceleration aspect. Virtually all the approaches that can in principle account for the accelerated expansion of the Universe are reviewed, including dark energy as an item in the energy budget of the Universe; modified Einstein equations; and, on a fundamentally new level, the use of the holographic principle.

Abstract:
The Schwarzchild solution insertion in an expanding universe, the so-called "Swiss cheese model," is shown to possess a very unphysical property. Specifically, in this model some trajectories are discontinuous functions of their initial conditions. An alternate metric is proposed as a remedy. It goes smoothly between the Schwarzchild exterior solution and the Friedmann-Lemaitre, expanding universe metric. It is further shown that the effects of the expansion on planetary motions in the solar system are too small to be currently observed for this alternate metric.

Abstract:
The Hubble law, determined from the distance modulii and redshifts of galaxies, for the past 80 years, has been used as strong evidence for an expanding universe. This claim is reviewed in light of the claimed lack of necessary evidence for time dilation in quasar and gamma-ray burst luminosity variations and other lines of evidence. It is concluded that the observations could be used to describe either a static universe (where the Hubble law results from some as-yet-unknown mechanism) or an expanding universe described by the standard Lambda cold dark matter model. In the latter case, size evolution of galaxies is necessary for agreement with observations. Yet the simple non-expanding Euclidean universe fits most data with the least number of assumptions. From this review it is apparent that there are still many unanswered questions in cosmology and the title question of this paper is still far from being answered.

Abstract:
An earlier elaborated model of the expanding universe with its contentsof dark energy, dark matter and normal matter is reconsideredand extended. The model is found to be reconcilable with the observedcosmical dimensions and with the magnitude of the present acceleratedexpansion. It has the form of a freely expanding cloud of zero-pointenergyphotons, with the inclusion of a small amount of normal matter.On a macroscopic scale, within the radius of the observable universe, themodel has the character of a flat Euclidian geometry, without the needof introducing curved space effects due to General Relativity. This flatgeometry is found to be stable with respect to expansive and compressiveperturbations, thus suggesting the universe to possess an intrinsicmechanism which aims at flat geometry.

Abstract:
In this paper, we prove the existence of two degrees of freedom that govern the movement of light in an expanding universe. The use of the fractal manifold model leads to reciprocal causality between variation of geometry and gravity, which both play a complementary role in the universe architecture. This study unravels new facts about the distribution of matter in the universe, and provides a new interpretation of Dark Matter and Dark Energy.

Abstract:
Who discovered the expanding universe? Was it Hubble, or Lema\^itre, or was it just the end result of a long series of investigations? In this article we summarise the main steps and contributions that led to one of the most exciting discoveries ever made, of which Lema\^itre was the principal architect. In 1927 he combined his dynamical solutions of the Einstein equations with astronomical observations to conclude that the universe is expanding. He derived the linear velocity-distance relationship and calculated the first numerical value of what later was called the "Hubble constant". His discovery paper of 1927 was written in French and in 1931 it was translated into English and published in Monthly Notices. However, the translation omits the section where Lema\^itre computed the "Hubble constant". Why was that done, and who was responsible? We do not speculate on this question, but present in a very condensed way the facts along the path of discovery. The documented details from primary sources can be found in our book "Discovering the Expanding Universe".