Alternatives to dark matter and dark energy

Abstract

We review the underpinnings of the standard Newton-Einstein theory of gravity, and identify where it could possibly go wrong. In particular, we discuss the logical independence from each other of the general covariance principle, the equivalence principle and the Einstein equations, and discuss how to constrain the matter energy-momentum tensor which serves as the source of gravity. We identify the a priori assumption of the validity of standard gravity on all distance scales as the root cause of the dark matter and dark energy problems, and discuss how the freedom currently present in gravitational theory can enable us to construct candidate alternatives to the standard theory in which the dark matter and dark energy problems could then be resolved. We identify three generic aspects of these alternate approaches: that it is a universal acceleration scale which determines when a luminous Newtonian expectation is to fail to fit data, that there is a global cosmological effect on local galactic motions which can replace galactic dark matter, and that to solve the cosmological constant problem it is not necessary to quench the cosmological constant itself, but only the amount by which it gravitates.

Fourth order Weyl gravity

“…Second, * Electronic address: eef3@cornell.edu 1 Our sign conventions differ from those used by Mannheim in Ref. [9] it was argued that the term coupling the Ricci scalar to the scalar field S can drive a gravity-mediated spontaneous symmetry breaking: namely, in the presence of a background value of R, the minimum energy state of S will occur at a nonzero value of S and will thereby give mass to the fermion field. In Refs.…”

“…In the fourth order Weyl theory of gravity [1,2,3,4,5,6,7,8,9], the Einstein-Hilbert action is replaced by a term proportional to the square of the Weyl tensor, and the action of the standard model of particle physics is modified to make it be conformally invariant. For simplicity and following Ref.…”

A Class of Elementary Particle Models Without Any Adjustable Real Parameters

“…In principle, this allows us to write exactly one kind of kinetic term forĝ μν , which would be locally conformally invariant and hence renormalizable, but unfortunately not manifestly unitary. Possible procedures to restore unitarity for such models were suggested by Mannheim [12][13][14][15][16][17][18], but these are controversial; operators referring to the metric fail to be hermitean, a serious flaw according to many researchers.…”

“…The problem here is that, regardless whether we are in the Higgs mode or not, this kinetic term is not of the standard canonical type, being quartic in the space and time derivatives, so that unitarity of the evolution operator is far from guaranteed. Authors of [12][13][14][15][16][17][18] made some brave attempts, but we note that local conformal invariance does not admit a unique definition of energy (as this is not a conformal invariant), so we cannot even begin constructing a Fock space with only positive energy physical particle states. iv.…”

“…In short, we now have a theory with a 5 dimensional local gauge group. Theories of this sort have been studied in detail [12][13][14][15][16][17][18]. The Riemann tensorR α βμν transforms as a decent tensor under the coordinate transformations (A.1), but it is not invariant (or even covariant) under the local conformal transformation (A.2).…”