# Conformal Gravity

1. Dec 7, 2004

### ohwilleke

The paper "Attractive and Repulsive Gravity", http://arxiv.org/PS_cache/gr-qc/pdf/0001/0001011.pdf by Philip Mannheim (2000) sets out at some length his theory of conformal gravity.

He starts by breaking the evidence in support of GR into those that flow from its geometric nature, which he seeks to preserve, and those which flow from the form of the Einstein-Hilbert action. He notes that his amendment of the EH action can make possible a MOND like gravity at galactic scales, eliminates the big bang and black hole singularities by making gravity repulsive in the presence of very dense energy sources and in the cosmological limit, and resolves a number of issues associated with the cosmological constant problem. It also states that at galactic and cosmological scales that there is a Machian component to gravity (i.e. the force of gravity is in part a function of the aggregate mass of the universe). Since it flows closely from the GR equations it is theoretically "well behaved".

It proposes rather than a big bang, a big time zero bounce from a minimum finite radius in which the universe has a maximal temperature (possiblity eliminating the issue of inflation), because beneath that radius the repulsive aspect of gravity overcomes other forces. It suggests that under this theory, the low ratio of matter to a running cosmological constant in the Omega sum is inevitable regardless of initial condition, rather than a coincidence.

Of particular interest to those looking to derive a quantum gravity, he accepts a figure for vaccum energy from cosmology, and uses that conclusion to determine that the gravitational constant must be deeply wrong.

While this theory has little independent support (i.e. it does not differ from GR where it reduces to GR, does not differ greatly from MOND where it reduces to MOND, does not differ from Newtonian gravity where it reduces to Newtonian gravity, and fits cosmological data by design rather than prediction) it should stand as a significant alternative to either cosmological constant cold dark matter models (the prevailing paradigm), or Relativistic MOND models (the main alternative at the galactic scale), or alternative cosmologies such as those of Arp (Quasi-Steady State).

The conclusions reached are not dramatically different from those of LQG, and indeed resemble LQG also in that LQG theorists sometimes see gravity as a counterpoint to QCD which like Mannheim's conformal gravity changes from repulsive to attractive at different distance scales.

Last edited: Dec 7, 2004