Philip D. Mannheim

Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

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.

No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model.

A new realization of the fourth-order derivative Pais-Uhlenbeck oscillator is constructed. This realization possesses no states of negative norm and has a real energy spectrum that is bounded below. The key to this construction is the recognition that in this realization the Hamiltonian is not Dirac Hermitian. However, the Hamiltonian is symmetric under combined space reflection P and time reversal T. The Hilbert space that is appropriate for this PT-symmetric Hamiltonian is identified and it is found to have a positive-definite inner product. Furthermore, the time-evolution operator is unitary.

Making the Case for Conformal Gravity

We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever. With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by ’t Hooft in which a connection between conformal gravity and Einstein gravity has been found.

ARE GALACTIC ROTATION CURVES REALLY FLAT

In this paper we identify an apparently previously unappreciated regularity in the systematics of galactic rotation curves; namely, we find that at the last detected points in galaxies of widely varying luminosity, the centripetal acceleration is found to have the completely universal form (v2/c2R)last = γ0/2 + γ*N*/2 + β*N*/R2, where γ0 and γ* are new universal constants, β* is the Schwarzschild radius of the Sun, and N* is the total amount of visible matter in each galaxy. This regularity points to a possible role for the linear potentials associated with conformal gravity, with the galaxy-independent γ0 term being found not to be generated from within individual galaxies at all but rather to be of cosmological origin, being due to the global Hubble flow of a necessarily spatially open universe of 3-space scalar curvature k = -(γ0/2)2 = -2.3 × 10-60 cm-2.

Conformal cosmology with no cosmological constant

We present a locally conformal invariant cosmology based on the Weyl tensor rather than the Einstein one. The cosmology admits of a de Sitter solution with no cosmological constant.

Measuring velocity of sound with nuclear resonant inelastic x-ray scattering

Nuclear resonant inelastic x-ray scattering is used to measure the projected partial phonon density of states of materials. A relationship is derived between the low-energy part of this frequency distribution function and the sound velocity of materials. Our derivation is valid for harmonic solids with Debye-like low-frequency dynamics. This method of sound velocity determination is applied to elemental, composite, and impurity samples which are representative of a wide variety of both crystalline and noncrystalline materials. Advantages and limitations of this method are elucidated.

Fitting galactic rotation curves with conformal gravity and a global quadratic potential

We apply the conformal gravity theory to a sample of 111 spiral galaxies whose rotation curve data points extend well beyond the optical disk. With no free parameters other than galactic mass-to-light ratios, the theory is able to account for the systematics that is observed in this entire set of rotation curves without the need for any dark matter at all. In previous applications of the theory, a central role was played by a universal linear potential term

Impact of a global quadratic potential on galactic rotation curves.

V(r)={\ensuremath{\gamma}}_{0}{c}^{2}r/2

Solution to the Ghost Problem in Fourth Order Derivative Theories

that is generated through the effect of cosmology on individual galaxies, with the coefficient