9 research outputs found
First Order Extended Gravity and the Dark Side of the Universe: the General Theory
General Relativity is not the definitive theory of Gravitation due to several
shortcomings which are coming out both from theoretical and experimental
viewpoints. At large scales (astrophysical and cosmological scales) the
attempts to match it with the today observational data lead to invoke Dark
Energy and Dark Matter as the bulk components of the cosmic fluid. Since no
final evidence, at fundamental level, exists for such ingredients, it is clear
that General Relativity presents shortcomings at infrared scales. On the other
hand, the attempts to formulate theories more general than the Einstein one
give rise to mathematical difficulties that need workarounds which, in turn,
generate problems from the interpretative viewpoint. We present here a
completely new approach to the mathematical objects in terms of which a theory
of Gravitation may be written in a first-order `a la Palatini formalism, and
introduce the concept of Dark Metric which could completely bypass the
introduction of disturbing concepts as Dark Energy and Dark Matter.Comment: Proceedings of the Conference "The Invisible Universe" Paris, June
29-July 3, 2009 10 page
From Dark Energy and Dark Matter to Dark Metric
It is nowadays clear that General Relativity cannot be the definitive theory
of Gravitation due to several shortcomings that come out both from theoretical
and experimental viewpoints. At large scales (astrophysical and cosmological)
the attempts to match it with the latest observational data lead to invoke Dark
Energy and Dark Matter as the bulk components of the cosmic fluid. Since no
final evidence, at fundamental level, exists for such ingredients, it is clear
that General Relativity presents shortcomings at infrared scales. On the other
hand, the attempts to formulate more general theories than Einstein's one give
rise to mathematical difficulties that need workarounds that, in turn, generate
problems from the interpretative viewpoint. We present here a completely new
approach to the mathematical objects in terms of which a theory of Gravitation
may be written in a first-order (a' la Palatini) formalism, and introduce the
concept of Dark Metric which could completely bypass the introduction of
disturbing concepts as Dark Energy and Dark Matter
New Cases of Universality Theorem for Gravitational Theories
The "Universality Theorem" for gravity shows that f(R) theories (in their
metric-affine formulation) in vacuum are dynamically equivalent to vacuum
Einstein equations with suitable cosmological constants. This holds true for a
generic (i.e. except sporadic degenerate cases) analytic function f(R) and
standard gravity without cosmological constant is reproduced if f is the
identity function (i.e. f(R)=R). The theorem is here extended introducing in
dimension 4 a 1-parameter family of invariants R' inspired by the
Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also
selfdual formulation). It will be proven that f(R') theories so defined are
dynamically equivalent to the corresponding metric-affine f(R) theory. In
particular for the function f(R)=R the standard equivalence between GR and
Holst Lagrangian is obtained.Comment: 10 pages, few typos correcte