2,523 research outputs found
Importance of torsion and invariant volumes in Palatini theories of gravity
We study the field equations of extensions of General Relativity formulated
within a metric-affine formalism setting torsion to zero (Palatini approach).
We find that different (second-order) dynamical equations arise depending on
whether torsion is set to zero i) a priori or ii) a posteriori, i.e., before or
after considering variations of the action. Considering a generic family of
Ricci-squared theories, we show that in both cases the connection can be
decomposed as the sum of a Levi-Civita connection and terms depending on a
vector field. However, while in case i) this vector field is related to the
symmetric part of the connection, in ii) it comes from the torsion part and,
therefore, it vanishes once torsion is completely removed. Moreover, the
vanishing of this torsion-related vector field immediately implies the
vanishing of the antisymmetric part of the Ricci tensor, which therefore plays
no role in the dynamics. Related to this, we find that the Levi-Civita part of
the connection is due to the existence of an invariant volume associated to an
auxiliary metric , which is algebraically related with the physical
metric .Comment: 14 one-column pages, no figures; v2: some minor changes and typos
corrections, new references adde
Brane-world and loop cosmology from a gravity-matter coupling perspective
We show that the effective brane-world and the loop quantum cosmology
background expansion histories can be reproduced from a modified gravity
perspective in terms of an gravity action plus a term
non-minimally coupled with the matter Lagrangian. The reconstruction algorithm
that we provide depends on a free function of the matter density that must be
specified in each case and allows to obtain analytical solutions always. In the
simplest cases, the function is quadratic in the Ricci scalar, ,
whereas is linear. Our approach is compared with recent results in the
literature. We show that working in the Palatini formalism there is no need to
impose any constraint that keeps the equations second-order, which is a key
requirement for the successful implementation of the reconstruction algorithm.Comment: 8 pages, revtex4-1 styl
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