## Cosmology

The Vatican Observatory has been involved in cosmological research over the past 30 years through the theoretical work of Stoeger and his collaborators in South Africa and in Brazil. Most of that has centered on the standard isotropic and spatially homogeneous (Friedmann-Lemaître-Robertson-Walker (FLRW)) zeroth-order model. Stoeger and his collaborators (particularly Ellis, University of Cape Town) have also done related cosmological work clarifying certain conceptual issues related to inflationary models, multiverses, and in estimating the boundary between local and cosmological gravitational influences.

More recently, Gionti has been pursuing research in Quantum Gravity and quantum cosmology. In particular, he has published interesting results dealing with discrete formulations of general relativity. He has also investigated key issues in super-string theory, most recently concentrating on the phenomenon of T-duality. These results are oriented toward eventually developing an adequate description of the universe during the Planck era – before the Big Bang – when all the physics we know has broken down and where we must replace it with a complete quantum-gravitational description of realty.

More recently, Gionti has been pursuing research in Quantum Gravity and quantum cosmology. In particular, he has published interesting results dealing with discrete formulations of general relativity. He has also investigated key issues in super-string theory, most recently concentrating on the phenomenon of T-duality. These results are oriented toward eventually developing an adequate description of the universe during the Planck era – before the Big Bang – when all the physics we know has broken down and where we must replace it with a complete quantum-gravitational description of realty.

**Inhomogeneous Cosmologies: **Stoeger and his collaborators have been investigating inhomogeneous cosmologies including those which are spherically symmetric. Their emphasis has been on demonstrating how to constrain them with presently available cosmologically relevant astronomical data, as well as with types of data (e. g. redshift drifts of distant galaxies, or the maximum of the angular diameter distance and the redshift at which it is found) which are not yet available but which may be within the next decade and which provide information independent of other measurements.

This work has been motivated by the need to confirm the assumptions hidden in the standard FLRW models, as well as to see if there are viable alternatives to a flat universe with a significant amount of dark energy. It is very clear, for instance, that we can find an LTB model without dark energy which fits available cosmologically relevant data just as well as the concordance model. If, for instance, we as observers are within a large Gpc (gigaparsec) void – in other words, a region of the universe that is slightly underdense – then such a inhomogeneity can account for the fainter than usual SN1a’s without invoking dark energy or a flat universe.

**Early Universe: **If one goes back in time, the distances among galaxies will be smaller and smaller until we reach a minimal distance, the “Planck length”, which is 1.6 x 10^{-35} m. Below this distance, according to the laws of Quantum Physics, the entire universe should behave as a global system described by a wave function as for the Hydrogen Atom. The field of study regarding this early phase of the universe is called Quantum Gravity.

There are two main approaches to Quantum Gravity today: *Loop Quantum Gravity* and *String Theory*. Loop Quantum Gravity has a “conservative” approach and tends to quantize the gravitational field independently from all other fundamental interactions. String Theory aims, instead, to quantize gravity via a fundamental concept called a “string”. The string is a one-dimensional object that evolves in time. Strings can be open and closed. Quantum oscillations of strings reproduce fundamental particles. Gionti’s work is to examine if String Theory is a valuable route to Quantum Gravity.

Strings need to exist in extra dimensions, but since our world is four-dimensional we need to assume that the other dimensions are very small and undetectable; the trick is to “compactify” these other dimensions, which is in effect to wind up the extra dimensions around circles. Closed strings have a special symmetry when we compactify them, called “T-Duality”. This is an exact symmetry. A string compactified on a circle of radius R has the same energy spectrum of a String compactified on a circle of radius a’/R (a’ being the String tension). This symmetry is manifest at spectrum level but totally absent at the Lagrangian (starting) level. Physics suggests that at Planck level both types of strings plays an important role. Therefore it looks reasonable to push this symmetry even further in the sense that we make the Lagrangian function itself T-Duality invariant.

From this modified String Theory, it is possible to calculate the gravitational effective field, which emerges from the quantum theory given by a string theory that is manifestly T-Duality invariant. The effective theory emerging from the graviton scattering generally is an extended theory of gravity, which, as we have discussed in the cosmology section above, could explain Dark Matter and Dark Energy.