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.

Modeling Scientists as Agents. How Scientists Cope with the Challenges of the New Public Management of Science

The paper at hand applies agent-based modeling and simulations (ABMS) as a tool to reconstruct and to analyze how the science system works. A Luhmannian systems perspective is combined with a model of decision making of individual actors. Additionally, changes in the socio-political context of science, such as the introduction of „new public management\", are considered as factors affecting the functionality of the system as well as the decisions of individual scientists (e.g. where to publish their papers). Computer simulation helps to understand the complex interplay of developments at the macro (system) and the micro (actor) level.Systems Theory, Theory of Action and Decision Making, Academic Publication System, Science System, New Public Management, Agent-Based Modeling and Simulation

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

Guaranteed Non-Asymptotic Confidence Ellipsoids for FIR Systems

Recently, a new finite-sample system identification algorithm, called Sign-Perturbed Sums (SPS), was introduced in [2]. SPS constructs finite-sample confidence regions that are centered around the least squares estimate, and are guaranteed to contain the true system parameters with a user-chosen exact probability for any finite number of data points. The main assumption of SPS is that the noise terms are independent and symmetrically distributed about zero, but they do not have to be stationary, nor do their variances and distributions have to be known. Although it is easy to determine if a particular parameter belongs to the confidence region, it is not easy to describe the boundary of the region, and hence to compactly represent the exact confidence region. In this paper we show that an ellipsoidal outer-approximation of the SPS confidence region can be found by solving a convex optimization problem, and we illustrate the properties of the SPS region and the ellipsoidal outer-approximation in simulation examples

Asymptotic properties of SPS confidence regions

Sign-Perturbed Sums (SPS) is a system identification method that constructs non-asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions. One of its main features is that, for any finite number of data points and any user-specified probability, the constructed confidence region contains the true system parameter with exactly the user-chosen probability. In this paper we examine the size and the shape of the confidence regions, and we show that the regions are strongly consistent, i.e., they almost surely shrink around the true parameter as the number of data points increases. Furthermore, the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory. The results are also illustrated by a simulation example

On the Possibility of Quantum Gravity Effects at Astrophysical Scales

The nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) is reviewed. It is argued that at large distances there could be strong renormalization effects, including a scale dependence of Newton's constant, which mimic the presence of dark matter at galactic and cosmological scales.Comment: LaTeX, 18 pages, 4 figures. Invited contribution to the Int. J. Mod. Phys. D special issue on dark matter and dark energ

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