Bulk versus brane running couplings

A simplified higher dimensional Randall-Sundrum-like model in 6 dimensions is considered. It has been observed previously by Goldberger and Wise that in such a self-interacting scalar theory on the bulk with a conical singularity there is mixing of renormalization of 4d brane couplings with that of the bulk couplings. We study the influence of the running bulk couplings on the running of the 4d brane couplings. We find that bulk quantum effects may completely alter the running of brane couplings. In particular, the structure of the Landau pole may be drastically altered and non-asymptotically free running may turn into asymptotically safe (or free) behavior.Comment: 11 pages, no figures, REVTeX

A Four-Dimensional Theory for Quantum Gravity with Conformal and Nonconformal Explicit Solutions

The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power type is proven to consist of precisely three conformal and three nonconformal solutions, given by remarkably simple (albeit nontrivial) functions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. The stability of the finite solutions is investigated and the possibility of renormalization group flows is discussed as well as several physical applications.Comment: LaTeX, 18 pages, no figure

One-loop f(R) Gravitational Modified Models

The one-loop quantisation of a general class of modified gravity models around a classical de Sitter background is presented. Application to the stability of the models is addressed.Comment: Latex, 8 pages, no figures. To appear in Journal of Physics A. Two references adde

Dark Energy Dominance and Cosmic Acceleration in First Order Formalism

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation.Comment: 21 pages, LaTeX file, no figures. Replaced version to be published on Phys. Rev.

Exact Renormalization Group and Running Newtonian Coupling in Higher Derivative Gravity

We discuss exact renormalization group (RG) in $R^2$-gravity using effective average action formalism. The truncated evolution equation for such a theory on De Sitter background leads to the system of nonperturbative RG equations for cosmological and gravitational coupling constants. Approximate solution of these RG equations shows the appearence of antiscreening and screening behaviour of Newtonian coupling what depends on higher derivative coupling constants.Comment: Latex file, 9 page

Strong correlation effects in single-wall carbon nanotubes

We present an overview of strong correlations in single-wall carbon nanotubes, and an introduction to the techniques used to study them theoretically. We concentrate on zigzag nanotubes, although universality dictates that much ofthe theory can also be applied to armchair or chiral nanotubes. We show how interaction effects lead to exotic low energy properties and discuss future directions for studies on correlation effects in nanotubes

Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary

The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the theory to second order in the scalar self-coupling pursued herein involves explicit calculations of up to third loop-order and reveals that, in addition to the renormalisation of the scalar self-coupling and scalar field, the removal of all divergences necessitates the introduction of conformally non-invariant counterterms proportional to $R\Phi^2$ and $K\Phi^2$ in the bare scalar action as well as counterterms proportional to $RK^2$, $R^2$ and $RK$ in the gravitational action. The substantial backreaction effects and their relevance to the renormalisation procedure are analysed.Comment: 25 pages, 1 figure. Minor elucidations in the Appendix regarding the cut-off $N_0$ and in p.4 regarding the gravitational action. Certain reference-related ommission corrected. To appear in Classical and Quantum Gravit

Introduction to Modified Gravity and Gravitational Alternative for Dark Energy

We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of $f(R)$, $f(G)$ or $f(R,G)$ gravity, model with non-linear gravitational coupling or string-inspired model with Gauss-Bonnet-dilaton coupling in the late universe where they lead to cosmic speed-up. It is shown that some of such theories may pass the Solar System tests. On the same time, it is demonstrated that they have quite rich cosmological structure: they may naturally describe the effective (cosmological constant, quintessence or phantom) late-time era with a possible transition from decceleration to acceleration thanks to gravitational terms which increase with scalar curvature decrease. The possibility to explain the coincidence problem as the manifestation of the universe expansion in such models is mentioned. The late (phantom or quintessence) universe filled with dark fluid with inhomogeneous equation of state (where inhomogeneous terms are originated from the modified gravity) is also described.Comment: LaTeX file, 21 pages, references are added, lectures for 42 Karpacz Winter School on Theor Physic