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We explicate some epistemological implications of stationary principles and in particular of Noether Theorems. Noether's contribution to the problem of covariance, in fact, is epistemologically relevant, since it moves the attention from equations to conservation laws., 6 pages, misprints corrected, reference list updated, MSC added; presented at the XXXII Int. Congress of the Italian Society of Historians of Physics and Astronomy (SISFA), Rome 2012

Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers-Pirani-Schild framework. In this framework the structure of spacetime is described by a Weyl geometry which is enforced by dynamics. Standard General Relativity is just one possible theory within the class of extended theories of gravitation. Also all Palatini f(R) theories are shown to be extended theories of gravitation. This more general setting allows a more general interpretation scheme and more general possible couplings between gravity and matter. The definitions and constructions of extended theories will be reviewed. A general interpretation scheme will be considered for extended theories and some examples will be considered.

We discuss here possible tests for Palatini f(R)-theories together with their implications for different formulations of the Equivalence Principle. We shall show that Palatini f(R)-theories obey the Weak Equivalence Principle and violate the Strong Equivalence Principle. The violations of the Strong Equivalence Principle vanish in vacuum (and purely electromagnetic) solutions as well as on short time scales with respect to the age of the universe. However, we suggest that a framework based on Palatini f(R)-theories is more general than standard General Relativity (GR) and it sheds light on the interpretation of data and results in a way which is more model independent than standard GR itself.

This special issue contains the papers presented at THERMOCON '05, an international conference held in 2005 in Messina (Italy) in memory of Professor Gerrit Alfred Kluitenberg.

We calculate the relative conserved currents, superpotentials and conserved quantities between two homogeneous and isotropic universes. In particular we prove that their relative "energy" (defined as the conserved quantity associated to cosmic time coordinate translations for a comoving observer) is vanishing and so are the other conserved quantities related to a Lie subalgebra of vector fields isomorphic to the Poincar\'e algebra. These quantities are also conserved in time. We also find a relative conserved quantity for such a kind of solutions which is conserved in time though non-vanishing. This example provides at least two insights in the theory of conserved quantities in General Relativity. First, the contribution of the cosmological matter fluid to the conserved quantities is carefully studied and proved to be vanishing. Second, we explicitly show that our superpotential (that happens to coincide with the so-called KBL potential although it is generated differently) provides strong conservation laws under much weaker hypotheses than the ones usually required. In particular, the symmetry generator is not needed to be Killing (nor Killing of the background, nor asymptotically Killing), the prescription is quasi-local and it works fine in a finite region too and no matching condition on the boundary is required., Comment: Corrected typos and improved format