Scale-invariance in gravity and implications for the cosmological constant

Recently a scale invariant theory of gravity was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms - to conformal superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. However, despite numerous attractive features, the theory suffers from at least one major problem: the volume of the universe is no longer a dynamical variable. In attempting to resolve this problem a new theory is found which has several surprising and atractive features from both quantisation and cosmological perspectives. Furthermore, it is an extremely restrictive theory and thus may provide testable predictions quickly and easily. One particularly interesting feature of the theory is the resolution of the cosmological constant problem.Comment: Replaced with final version: minor changes to text; references adde

The physical gravitational degrees of freedom

When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving 3-dimensional conformal Riemannian geometries obtained by imposing two general principles: 1) time is derived from change; 2) motion and size are relative. We write down an explicit action based on them. We obtain not only GR in the CMC gauge, in its Hamiltonian 3 + 1 reformulation but also all the equations used in York's conformal technique for solving the initial-value problem. This shows that the independent gravitational degrees of freedom obtained by York do not arise from a gauge fixing but from hitherto unrecognized fundamental symmetry principles. They can therefore be identified as the long-sought Hamiltonian physical gravitational degrees of freedom.Comment: Replaced with published version (minor changes and added references

Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme

I approach the Problem of Time and other foundations of Quantum Cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories entering regions of configuration space, which are computed within the semiclassical regime. Moreover, the objects that Halliwell uses in this approach commute with the Hamiltonian constraint, H. This approach has not hitherto been considered for models that also possess nontrivial linear constraints, Lin. This paper carries this out for some concrete relational particle models (RPM's). If there is also commutation with Lin - the Kuchar observables condition - the constructed objects are Dirac observables. Moreover, this paper shows that the problem of Kuchar observables is explicitly resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach for nontrivial linear constraints that is also a construction of Dirac observables, I consider theories for which Kuchar observables are formally known, giving the relational triangle as an example. As a second route, I apply an indirect method that generalizes both group-averaging and Barbour's best matching. For conceptual clarity, my study involves the simpler case of Halliwell 2003 sharp-edged window function. I leave the elsewise-improved softened case of Halliwell 2009 for a subsequent Paper II. Finally, I provide comments on Halliwell's approach and how well it fares as regards the various facets of the Problem of Time and as an implementation of QM propositions.Comment: An improved version of the text, and with various further references. 25 pages, 4 figure