The dark matter problem from f(R) gravity viewpoint

Abstract

An alternative view to the dark matter puzzle is represented by Extended Theories of Gravity. The approach consists in addressing issues like dark components from the point of view of gravitational field instead of requiring new material ingredients that, up to now, have not been detected at fundamental level. In this review paper, by extending the Hilbert‐Einstein action of gravitational field to more general actions (e.g. f(R) gravity), it is shown that several gravitating structures like stars, spiral galaxies, elliptical galaxies and clusters of galaxies can be self‐consistently described without asking for dark matter. It is also shown that standard General Relativity tests and Equivalence Principle constraints can be evaded at Solar System scales.

Breaking the Vainshtein screening in clusters of galaxies

“…The screening can be accomplished in many ways [19,60]: with a weak coupling between the field and matter in regions of high density, thus inducing a weak fifth-force as in symmetron theories [52,53]; the field can acquire a large mass in high density environments, being short-ranged and undetectable, and be light and long-ranged in lower density regions, as for chameleon fields [20,61,62,75,76] and f (R) models [27,28,36,96]; or one may change the kinetic contribution of the field to the Lagrangian, with first or second order derivatives becoming important in a certain range, as it happens with the Vainshtein screening mechanism [101].…”

Relativistic Celestial Metrology: Dark Matter as an Inertial Gauge Effect

“…The inverse transformation σ A ↦x μ ¼ z μ ðτ; σ r Þ defines the embeddings of the 3-spaces Σ τ into the space-time and the induced 4-metric is g AB ½zðτ; In the chosen family of space-times, the foliation needed for the 3þ1 splitting is nice and admissible if the lapse function satisfies Nðτ; σ r Þ > 0 in every point of Σ τ , 9 if E 4 g ττ ðτ; σ r Þ > 0 10 and if the positive-definite 3-metric 3 g rs ðτ; σ u Þ¼ÀE 4 g rs ðτ; σ u Þ has three positive eigenvalues.…”

“…However, to reconcile all the existing data with this 4-dimensional description, one must postulate the existence of dark matter and dark energy as the dominant components of the classical universe [6][7][8] after the recombination 3-surface (before it quantum mechanics is entering in the description and there is no acceptable description for the transition from quantum to classical astrophysics) already within galaxies before making the transition to cosmology and the replacement of ordinary space-time with the standard cosmological FLWR one, whose points describe a mean over a volume of 100 Mega-parsecs of the ordinary space-time. The attempts to avoid the appearance of "darkness" have led to many proposals of modifications of GR like MOND [9], f ðRÞ gravity [10][11][12] and the ones analyzed in Refs. [6][7][8].…”

Spacetime Exterior to a Star: Against Asymptotic Flatness

“…Similarly asymptotically flat solutions are rare for theories with quadratic Lagrangians, Buchdahl (1973) [15]. The absence of asymptotically flat solutions might have application to the "missing mass" problem, see Roberts (1991Roberts ( ,2004Roberts ( ,2011 [16,18,19] and Capazziello and De Laurentis (2012) [17]. In Bradley et al (1999) [20] it is shown that the Wahlquist perfect fluid spacetime cannot be smoothly joined to an exterior asymptotically flat vacuum region.…”