I admit that dark matter is apple pie and motherhood. I love Dark Matter just like you. But this paper has been accepted for publication in Physical Review Series D(adsbygoogle = window.adsbygoogle || []).push({});

they did not post the preprint at arxiv until it had passed peer review and been accepted.

this is a 72 page paper. we cannot ignore the possibility that what we think is the consequence of dark matter results at least in part from something else, something not as yet known in the law of gravitation (which may be related to quantizing it)

M. Reuter, H. Weyer

Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves

http://arxiv.org/abs/hep-th/0410117

here is a followup paper by the same authors

M. Reuter, H. Weyer

Quantum Gravity at Astrophysical Distances?

http://arxiv.org/abs/hep-th/0410119

---abstract of /hep-th/0410117---

A renormalization group (RG) improvement of the Einstein-Hilbert action is performed which promotes Newton's constant and the cosmological constant to scalar functions on spacetime. They arise from solutions of an exact RG equation by means of a ``cutoff identification'' which associates RG scales to the points of spacetime. The resulting modified Einstein equations for spherically symmetric, static spacetimes are derived and analyzed in detail. The modifications of the Newtonian limit due to the RG evolution are obtained for the general case. As an application, the viability of a scenario is investigated where strong quantum effects in the infrared cause Newton's constant to grow at large (astrophysical) distances. For two specific RG trajectories exact vacuum spacetimes modifying the Schwarzschild metric are obtained by means of a solution-generating Weyl transformation. Their possible relevance to the problem of the observed approximately flat galaxy rotation curves is discussed. It is found that a power law running of Newton's constant with a small exponent of the order $10^{-6}$ would account for their non-Keplerian behavior without having to postulate the presence of any dark matter in the galactic halo.

---end quote---

The followup paper, Quantum Gravity at Astrophysical Distances?, is 43 pages. Here is the abstract.

---abstract of hep-th/0410119---

Assuming that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales we use analytical results from nonperturbative renormalization group (RG) equations as well as experimental input in order to characterize the special RG trajectory of QEG which is realized in Nature and to determine its parameters. On this trajectory, we identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require any dark matter. We show that an extremely weak power law running of Newton's constant leads to flat galaxy rotation curves similar to those observed in Nature. Furthermore, a possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically give rise to a small cosmological constant.

---end quote---

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# Running Newton Constant (no dark matter)

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