Constraining Extended Theories of Gravity by Large Scale Structure and Cosmography
Creators: name: Salzano, Vincenzo
Publisher: name: Università degli Studi di Napoli Federico II
Year: 2008

description: The main aim of this thesis is to show the viability of Extended Theories of Gravity in substituting General Relativity-based cosmological models in the explanation of Universe Dynamics and Origin.
After a brief review of all the questions posed by General Relativity and all the possible solutions to these ones, we start to describe deeper one of the alternative approaches to Gravity and Universe, namely the Extended Theories of Gravity. In this context we have chosen to work with a particular class of these theories, the f(R-
gravity models, so named because of starting from a general gravitational lagrangian, where the classical R term of the Hilbert-Einstein one is substituted by a general function f(R). We will start with a brief review of history, motivations, pros and cons of these approaches.
We also review some results from literature about the cosmological mimicking of dark components as a curvature (i.e. geometrical) e®ect of f(R) geometry and the possibility to explain rotational curves of spiral galaxies.
Then we pass to the original works presented in these pages. We think that we can extract three main characteristics of our work:
- We have never adopted a particular, well de¯ned f(R) model, in contrast with other works; we have always tried to work in the most general hypothesis it was possible.
When we will show results of our analysis on clusters of galaxies, it is important to underline that they only rely on the assumption of an analytical Taylor expandable f(R),
without any other speci¯cation. In the case of cosmological applications, namely in the Cosmography chapter, we could say that we have worked in an even more general
scenario: we chose Cosmography because it is a model independent approach to observational data, so we have no basic hypothesis not only on the mathematical form of
the f(R)- model, but even on the nature of the universe dynamics (General Relativity or f(R) one);
- Starting from previous point we have tried to give constraints to the hypothetical form of the f(R)-theories: we have derived values of some of the parameters that a viable f(R)-model should have to explain some of the question we have explored (mass profile of clusters of galaxies). We have also explored connections between General Relativity-based (dark energy ones) and f(R)-based models (in cosmography) studying their mutual mimicking ability and the possibility of discriminate between them;
² Last, but not least, our analysis has the important merit of having a strong predictive power, so that it can be con¯rmed or confuted by comparing with some tests. From the
Cosmography-based analysis, we are strongly dependent on the experimental possibilities of future surveys: if we will not have measurements within a certain sensibility range we were not be able (or we will have few possibilities) to discriminate what approach is
right and what one is wrong. On the contrary, in the case of clusters of galaxies, we are able to do predicitions on results which could come from the application of f(R)-models
to di®erent scales of gravitational systems (galaxies, solar system). If these predictions were exact, then we would have a solid and well founded theoretical model of gravity in alternative to General Relativity.
Even if many results we had make us con¯dent to be on the right way, it is important to underline also that our work is always built on a conservative hypothesis. We don't think that f(R) gravity is not the theory of gravity (like General Relativity is not), but it is an important
and interesting toy model which can take us nearer an effective and deeper comprehension of gravity.¯