Coupling running through the Looking-Glass of dimensional Reduction

The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s in a context of HE Regge scattering. Recently, it got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behavior. We consider a QFT model $g\,\varphi^4\,$ with running coupling defined in both the two domains of different dimensionality; the \gbar(Q^2)\, evolutions being duly conjugated at the reduction scale $\,Q\sim M.$ Beyond this scale, in the deep UV 2-dim region, the running coupling does not increase any more. Instead, it {\it slightly decreases} and tends to a finite value \gbar_2(\infty) \,< \, \gbar_2(M^2)\, from above. As a result, the global evolution picture looks quite peculiar and can propose a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.Comment: 8 pages, 4 figures,Version to match the one which (besides the Appendix) will appear in "Particles and Nuclei (PEPAN), Letters", v.7, No 6(162) 2010 pp 625-631. Slightly edited, one more reference and related numerical estimate adde

Cosmological tachyon from cubic string field theory

The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gravity models. The cases of cubic (bosonic) and quartic (supersymmetric) tachyon potential in general relativity are automatically included. We comment the validity of the slow-roll approximation, the stability of the cosmological perturbations, and the relation between this tachyon and the Dirac-Born-Infeld one.Comment: 20 pages JHEP style, 1 figure; v4: misprints corrected, matches the published versio

Horava-Lifshitz Cosmology: A Review

This article reviews basic construction and cosmological implications of a power-counting renormalizable theory of gravitation recently proposed by Horava. We explain that (i) at low energy this theory does not exactly recover general relativity but instead mimic general relativity plus dark matter; that (ii) higher spatial curvature terms allow bouncing and cyclic universes as regular solutions; and that (iii) the anisotropic scaling with the dynamical critical exponent z=3 solves the horizon problem and leads to scale-invariant cosmological perturbations even without inflation. We also comment on issues related to an extra scalar degree of freedom called scalar graviton. In particular, for spherically-symmetric, static, vacuum configurations we prove non-perturbative continuity of the lambda->1+0 limit, where lambda is a parameter in the kinetic action and general relativity has the value lambda=1. We also derive the condition under which linear instability of the scalar graviton does not show up.Comment: 28 pages, invited review for CQG; version to be published (v2

Localization of the SFT inspired Nonlocal Linear Models and Exact Solutions

A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function $F(\Box)$, which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented.Comment: 20 pages, 3 figures, published in the proceedings of the VIII International Workshop "Supersymmetries and Quantum Symmetries" (SQS'09), Dubna, Russia, July 29 - August 3, 2009, http://theor.jinr.ru/~sqs09

Classical and Quantum Bianchi Type III vacuum Horava - Lifshitz Cosmology

A diagonal Bianchi Type III space-time is treated, both at the classical and quantum level, in the context of Horava - Lifshitz gravity. The system of the classical equations of motion is reduced to one independent Abel's equation of the first kind. Closed form solution are presented for various values of the coupling constants appearing in the action. Due to the method used, solutions of Euclidean, Lorentzian and neutral signature are attained. The solutions corresponding to \lamda 1 are seen to develop curvature singularities as the other constants approach their Einsteinian values, in contrast to those with \lamda = 1 which tend to the known Einstein gravity solutions. At the quantum level, the resulting Wheeler-DeWitt equation is explicitly solved for \lamda = 1, \sigma = 0 and \lamda = 1/3 . The ensuing wave-functions diverge in the Einsteinian limit.Comment: LaTeX 2e source file, 17 pages, no figure

Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators and the implications of restricting the contour of integration. Typos correcte

Barbero-Immirzi field in canonical formalism of pure gravity

The Barbero-Immirzi (BI) parameter is promoted to a field and a canonical analysis is performed when it is coupled with a Nieh-Yan topological invariant. It is shown that, in the effective theory, the BI field is a canonical pseudoscalar minimally coupled with gravity. This framework is argued to be more natural than the one of the usual Holst action. Potential consequences in relation with inflation and the quantum theory are briefly discussed.Comment: 10 page

Test of patch cosmology with WMAP

We calculate the power spectrum, spectral index, and running spectral index for inflationary patch cosmology arisen from Gauss-Bonnet braneworld scenario using the Mukhanov equation. This patch cosmology consists of Gauss-Bonnet(GB), Randall-Sundrum (RS-II), and four dimensional (4D) cosmological models. There exist several modifications in higher order calculations. However, taking the power-law inflation by choosing different potentials depending on the model, there exist minor changes up to second order corrections. Since second order corrections are rather small in the slow-roll limit, we could not choose a desired power-law model which explains the WMAP data. Finally we discuss the reliability of high order calculations based on the Mukhanov equation by comparing the perturbed equation including 5D metric perturbations. It turns out that first order corrections are reliable, while second order corrections are not proved to be reliable.Comment: 20 pages, 3 figures, final version to appear in IJMP

Vanishing Cosmological Constant in Modified Gauss-Bonnet Gravity with Conformal Anomaly

We consider dark energy cosmology in a de Sitter universe filled with quantum conformal matter. Our model represents a Gauss-Bonnet model of gravity with contributions from quantum effects. To the General Relativity action an arbitrary function of the GB invariant, f(G), is added, and taking into account quantum effects from matter the cosmological constant is studied. For the considered model the conditions for a vanishing cosmological constant are considered. Creation of a de Sitter universe by quantum effects in a GB modified gravity is discussed.Comment: 8 pages latex, 1 figure. To appear in Int. J. Mod. Phys.