Scale invariant gravity and the quasi-static universe

The paper deals with the scale discrepancy between the observed vacuum energy in cosmology and the theoretical quantum vacuum energy (cosmological constant problem). Here, we demonstrate that Einstein's equation and an analogy to particle physics leads to the first physical justification of the so-called fine-tuning problem. This fine-tuning could be automatically satisfied with the variable cosmological term $\Lambda(a)=\Lambda_0+\Lambda_1 a^{-(4-\epsilon)}$, $0 < \epsilon \...

Although it's widely believed that gravity should have a quantum nature like every other force, the conceptual obstacles to constructing a quantum theory of gravity compel us to explore other perspectives. Gravity is not like any other force. It alone defines a universal space-time geometry, upon which quantum fields evolve. We feel gravity because matter causes space-time to bend. Time flows at unequal rates at different locations. The rate at which time flows, and the causa...

One of the major issues confronting theoretical physics is finding a quantum theory of gravity and a resolution to the cosmological constant problem. It is believed that a true quantum theory of gravity will lead to a solution to the this problem. Finding a quantum theory of gravity has been a difficult issue mainly because of the high energy scale required for testing quantum gravity which is far the reach of current accelerators. Also general relativity does not possess a n...

General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the high-energy regime of the very early universe. This review article introduces some of the results for the quantum nature of space-time which indicate that there is a discrete, atomic picture not just for matter but also for space and time....

We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schr\"odinger equation. As with the Wheeler--DeWitt equation, time disappears, and a frozen formalism that gives a static wavefunction on the space of possible shapes of the system is obtained. However, if one follows the Dirac procedure and quantizes by imposing constraints, th...

We propose a new phenomenological model for quantum gravity. This is based on a new interpretation in which quantum gravity is not an interaction, rather it is just responsible for generation of space-time-matter. Then we show this model is capable of solving the important problems of cosmology and particle physics.

The bare bones of a theory of quantum gravity are exposed. It may have the potential to solve the cosmological constant problem. Less certain is its behavior in the Newtonian limit.

A new and universal method for implementing scale invariance, called best matching, is presented. It extends to scaling the method introduced by Bertotti and the author to create a fully relational dynamics that satisfies Mach's principle. The method is illustrated here in the context of non-relativistic gravitational particle dynamics.. It leads to far stronger predictions than general Newtonian dynamics. The energy and angular momentum of an `island universe' must be exactl...

The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic and large scales where General Relativity may be applied, the empty space in the sense it is used in the Minkowski metric, is also scale invariant. It is shown that if this applies, the Einstein cosmological constant and the scale factor of...

Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories th...