Some Considerations on Discrete Quantum Gravity

Recent results in Local Regge Calculus are confronted with Spin Foam Formalism. Introducing Barrett-Crane Quantization in Local Regge Calculus makes it possible to associate a unique Spin $j_{h}$ with an hinge $h$, fulfilling one of the requirements of Spin Foam definition. It is shown that inter-twiner terms of Spin Foam can follow from the closure constraint in Local Regge Calculus. Dedicated to Beppe Marmo for his 65th BirthdayComment: 7 pages, FunInGeo Conference proceedings, Ischia-Italy, 08-12 June 2011; accepted for publication in the International Journal of Geometric Methods in Modern Physic

From Local Regge Calculus towards Spin Foam Formalism?

We introduce the basic elements of SO(n)-local theory of Regge Calculus. A first order formalism, in the sense of Palatini, is defined on the metric-dual Voronoi complex of a simplicial complex. The Quantum Measure exhibits an expansion, in four dimensions, in characters of irreducible representation of SO(4) which has close resemblance and differences as well with the Spin Foam Formalism. The coupling with fermionic matter is easily introduced which could have consequences for the Spin Foam Formalism and Loop Quantum Gravity.Comment: 14 pages, 1 figures, proceeding of the Albert Einstein's International Conference 18-22 July 200

String duality transformations in f(R)f(R) gravity from Noether symmetry approach

We select $f(R)$ gravity models that undergo scale factor duality transformations. As a starting point, we consider the tree-level effective gravitational action of bosonic String Theory coupled with the dilaton field. This theory inherits the Busher's duality of its parent String Theory. Using conformal transformations of the metric tensor, it is possible to map the tree-level dilaton-graviton string effective action into $f(R)$ gravity, relating the dilaton field to the Ricci scalar curvature. Furthermore, the duality can be framed under the standard of Noether symmetries and exact cosmological solutions are derived. Using suitable changes of variables, the string-based $f(R)$ Lagrangians are shown in cases where the duality transformation becomes a parity inversion.Comment: v1: 13 pages; v2: minor rephrasings, published versio

God and the Big-Bang: Past and Modern Debates Between Science and Theology

A short phenomenological account of the genesis and evolution of the universe is presented with emphasis on the primordial phases as well as its physical composition, i.e. dark matter and dark energy. We discuss Einstein's theory of General Relativity and its consequences for the birth of modern relativistic astrophysics. We introduce the Big-Bang theory of Mons. Lemaitre as well as the competing theory of the Steady State Universe of Fred Hoyle. Since Big-Bang theory appeared quite in agreement with Christian doctrine of creation, Pope Pius XII delivered a message to the pontifical Academy of Sciences in 1951 claiming a certain agreement between the creation account in the book of Genesis and the Big-Bang theory (a concordist view), a position which he did not repeat later. On the other hand, Lemaitre always kept separate the scientific and theological planes as two parallel "lines" never intersecting, i.e., as two complementary "magisteria". Similar kind of tensions, between science and theology, emerge also today with the Hartle-Hawking solution to the Wheeler-DeWitt equation in quantum cosmology and its related speculations. To avoid some sort of confusion between theological and physics concepts, we, briefly, summarise the concept of creation in Christian theology.Comment: 15 pages, accepted in the proceedings of the conference "Eternity between Space and Time", Padua, May 19-21 202