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

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.Comment: 72pp, to appear in Phys. Rev.

Do we Observe Quantum Gravity Effects at Galactic Scales?

The nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) is reviewed. It is argued that there could be strong renormalization effects at large distances, in particular a scale dependent Newton constant, which mimic the presence of dark matter at galactic and cosmological scales.Comment: LaTeX, 6 pages, 1 figure. Talk given by M.R. at the 21st IAP meeting "Mass Profiles and Shapes of Cosmological Structures", Paris, July 4-9, 2005; to appear in the proceeding

Vacancy complexes with oversized impurities in Si and Ge

In this paper we examine the electronic and geometrical structure of impurity-vacancy complexes in Si and Ge. Already Watkins suggested that in Si the pairing of Sn with the vacancy produces a complex with the Sn-atom at the bond center and the vacancy split into two half vacancies on the neighboring sites. Within the framework of density-functional theory we use two complementary ab initio methods, the pseudopotential plane wave (PPW) method and the all-electron Kohn-Korringa-Rostoker (KKR) method, to investigate the structure of vacancy complexes with 11 different sp-impurities. For the case of Sn in Si, we confirm the split configuration and obtain good agreement with EPR data of Watkins. In general we find that all impurities of the 5sp and 6sp series in Si and Ge prefer the split-vacancy configuration, with an energy gain of 0.5 to 1 eV compared to the substitutional complex. On the other hand, impurities of the 3sp and 4sp series form a (slightly distorted) substitutional complex. Al impurities show an exception from this rule, forming a split complex in Si and a strongly distorted substitutional complex in Ge. We find a strong correlation of these data with the size of the isolated impurities, being defined via the lattice relaxations of the nearest neighbors.Comment: 8 pages, 4 bw figure

Background Independence and Asymptotic Safety in Conformally Reduced Gravity

We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG flow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity in the ``conformally reduced'' Einstein--Hilbert approximation which discards all degrees of freedom contained in the metric except the conformal one. Without the extra field dependence the resulting RG flow is that of a simple $\phi^4$-theory. Including it one obtains a flow with exactly the same qualitative properties as in the full Einstein--Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety.Comment: 4 figures

The golden rule of longevity

How much should society invest in medical care that extends the lives of the older generations? We derive a golden rule for the level of health care expenditures and find that the optimal level of life-extending health care expenditures should increase with rising productivity, increase with the retirement age, and also increase with the population growth rate if a higher growth rate lowers the ratio of retirees to working-age people sufficiently, while the effects of an improvement in medical technology are ambiguous. Moreover, we find that a market economy may be inefficient in terms of the provision of life-extending health care because an individual ignores the effect of his own longevity on the income of others

Acceleration of Diffusional Jumps of Interstitial Fe with Increasing Ge Concentration in Si1 − x Ge x Alloys Observed by Mössbauer Spectroscopy

Radioactive 57Mn isotopes have been implanted into Si1 − x Ge x crystals (x ≤ 0.1) at elevated temperatures for Mössbauer studies of the diffusion of interstitial 57Fe daughter atoms. The atomic jump frequency is found to increase upon Ge alloying. This is attributed to a lowering of the activation energy, i.e. the saddle point energy at hexagonal interstitial sites with Ge neighbour atom

Two-body Pion Absorption on 3He^3He at Threshold

It is shown that a satisfactory explanation of the ratio of the rates of the reactions $^3He(\pi^-,nn)$ and $^3He(\pi^-,np)$ for stopped pions is obtained once the effect of the short range two-nucleon components of the axial charge operator for the nuclear system is taken into account. By employing realistic models for the nucleon-nucleon interaction in the construction of these components of the axial charge operator, the predicted ratios agree with the empirical value to within 10-20\%.Comment: 19, UHPHYDOR-94-