Problems with Modified Theories of Gravity, as Alternatives to Dark Energy

Abstract

In this contribution to the conference "Beyond Einstein: Historical Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century", we give a critical status report of attempts to explain the late accelerated expansion of the universe by modifications of general relativity. Our brief review of such alternatives to the standard cosmological model addresses mainly readers who have not pursued the vast recent literature on this subject. * Invited talk at the conference "BEYOND EINSTEIN", Mainz, 22 -26 September, 2008. 1 See, e.g., [1], [2], and references therein.

Superintegrable relativistic systems in scalar background fields

“…The action of a relativistic particle of rest mass m 0 in a scalar background field V(x) is, see e.g. [6],…”

“…where the dynamical mass appears as a conformal factor. This represents an old-fashioned 'scalar' model of gravity [4][5][6], see also [7]. Varying the action (1) yields the Euler-Lagrange equations,…”

“…It is possible to retain manifest covariance by working with a secondorder energy functional, L ∼ g µν ẋµ ẋν [9][10][11], rather than the homogeneous length functional or action (1). Minimising the former reproduces the equation of motion (6), hence geodesic motion in the metric (3). Alternatively, in order to e.g.…”

Poincaré gauge gravity primer

“…The Poincaré gauge gravity occupies a prominent place in the colorful landscape of modified gravitational theories that generalize or extend the physical and mathematical structure of Einstein's GR. Among such theories it is worthwhile to highlight the large classes of f (R) and f (T ) models, and of theories with nonminimal coupling to matter, developed mainly in the context of relativistic cosmology, see [31][32][33][34][35][36][37]. The so-called Palatini approach represents another class of widely discussed theories in which metric and connection are treated as independent variables in the action principle [38][39][40].…”