Multibrane worlds and modification of gravity at large scales

Our main objective is to study how braneworld models of higher codimension differ from the 5D case and traditional Kaluza-Klein compactifications. We first derive the classical dynamics describing the physical fluctuations in a wide class of models incorporating gravity, non-Abelian gauge fields, the dilaton and two-form potential, as well as 3-brane sources. Next, we use these results to study braneworld compactifications in 6D supergravity, focusing on the bosonic fields in the minimal model; composed of the supergravity-tensor multiplet and the U(1) gauge multiplet whose flux supports the compactification. For unwarped models sourced by positive tension branes, a harmonic analysis allows us to solve the large, coupled, differential system completely and obtain the full 4D spin-2,1 and 0 particle spectra, establishing (marginal) stability and a qualitative behaviour similar to the smooth sphere compactification. We also find interesting results for models with negative tension branes; extra massless Kaluza-Klein vector fields can appear in the spectra, beyond those expected from the isometries in the internal space. These fields imply an enhanced gauge symmetry in the low energy 4D effective theory obtained by truncating to the massless sector, which is explicitly broken as higher modes are excited, until the full 6D symmetries are restored far above the Kaluza-Klein scale. Remarkably, the low energy effective theory does not seem to distinguish between a compactification on a smooth sphere and these singular, deformed spheres.

It is shown that negative tension branes in higher dimensions may lead to an effective lower dimensional theory where the gauge-invariant vector fields associated with the fluctuations of the metric are always massless and localized on the brane. Explicit five-dimensional examples of this phenomenon are provided. Furthermore, it is shown that higher dimensional gauge fields can also be localized on these configurations with the zero mode separated from the massive tower by a gap.

A rigorous thermodynamic formulation of the geometric model for heterogeneous nucleation including line tension effect is missing till date due to the associated mathematical hurdles. In this work, we develop a novel thermodynamic formulation based on Classical Nucleation Theory (CNT), which is supposed to illustrate a systematic and a more plausible analysis for the heterogeneous nucleation on a planar surface including the line tension effect. The appreciable range of the critical microscopic contact angle (θc), obtained from the generalized Young's equation and the stability analysis, is θ∞ < θc < θ' for positive line tension and is θM < θc < θ∞ for negative line tension. θ∞ is the macroscopic contact angle, θ' is the contact angle for which the Helmholtz free energy has the minimum value for the positive line tension, and θM is the local minima of the nondimensional line tension effect for the negative line tension. The shape factor f, which is basically the dimensionless critical free energy barrier, becomes higher for lower values of θ∞ and higher values of θc for positive line tension. The combined effect due to the presence of the triple line and the interfacial areas (f(L) + f(S)) in shape factor is always within (0, 3.2), resulting f in the range of (0, 1.7) for positive line tension. A formerly presumed appreciable range for θc(0 < θc < θ∞) is found not to be true when the effect of negative line tension is considered for CNT. Estimation based on the property values of some real fluids confirms the relevance of the present analysis.

The balance of force in a cylindrical tube (Oka-Azuma equation) indicates existence of a negative circumferential tension in the wall of blood vessels in vivo. However, we conventionally consider only a positive wall tension due to a positive transmural pressure in blood vessels. In this paper, the nature of such a negative circumferential tension in the vascular wall was reconsidered. The same type of negative tension or compressive force was shown to exist in any hollow and solid biological tissues placed in the atmospheric pressure. In living tissues, which have abundant water and are incompressible to external pressure, the compressive force by atmospheric pressure is simply the internal fluid pressure. The fluid pressure is a scalar and does not produce any effective net force vector. For this reason, there is no need to consider the compressive force component produced by the environmental pressure in the balance of force in living tissues.

Modified Gravity (MG) scenarios have been advocated to account for the dark energy phenomenon in the universe. These models predict departures from General Relativity on large cosmic scales that can be tested through a variety of probes such as observations of galaxy clusters among others. Here, we investigate the imprint of MG models on the internal mass distribution of cluster-like halos as probed by the dark matter halo sparsity. To this purpose we perform a comparative analysis of the properties of the halo sparsity using N-body simulation halo catalogs of a standard flat $\Lambda$CDM model and MG scenarios from the DUSTGRAIN-pathfinder simulation suite. We find that the onset of the screening mechanism leaves a distinct signature in the redshift evolution of the ensemble average halos sparsity. Measurements of the sparsity of galaxy clusters from currently available mass estimates are unable to test MG models due to the large uncertainties on the cluster masses. We show that this should be possible in the future provided large cluster samples with cluster masses determined to better than $30\%$ accuracy level.

We describe the spontaneous creation of the brane world in AdS 5 with external field. The resulting brane world consists of a flat 4d spatially finite expanding universe and curved expanding "regulator" branes. No negative tension branes are involved.

Numerical experiments of rotating stratified turbulence are conducted in order to investigate the mesoscale energy cascade process in the free atmosphere. We examine the downscale energy cascade process originated by energy injection at large scales. The energy spectrum created by this injection follows a power law, and its slope depends on planetary rotation rate and static stability. While the spectral slope tends to be steeper with increased static stability in cases without planetary rotation, it becomes insensitive to the planetary rotation rate and static stability and converges to the range from −1.9 to −2.1 in cases with an increased rotation rate. The roles of geostrophic and gravity modes in the cascade processes are discussed. It is shown that nonlinear interactions between geostrophic and gravity modes play a crucial role in the downscale energy cascades. In particular, the effect of the planetary rotation mainly influences the triad interaction composed of one geostrophic and two gravity modes in the energy cascade process. Energy flux to smaller scales is intensified by this type of triad interaction with increased planetary rotation rate.

Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh–Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods. Response functions are used to predict the filament tension of the alternative scrolls and it is shown that the slow-period scroll has negative filament tension, while the filament tension of the fast-period scroll changes sign within a hysteresis loop. The predictions are confirmed by direct simulations. Further investigations show that the slow-period scrolls display features similar to delayed after-depolarization and tend to develop into turbulence similar to ventricular fibrillation (VF). Scrolls with positive filament tension collapse or stabilize, similar to monomorphic ventricular tachycardia (VT). Perturbations, such as boundary interaction or shock stimulus, can convert the vortex with negative filament tension into the vortex with positive filament tension. This may correspond to transition from VF to VT unrelated to pinning.

We live at a time of contradictory messages about how successfully we understand gravity. General Relativity seems to work very well in the Earth's immediate neighborhood, but arguments abound that it needs modification at very small and/or very large distances. This essay tries to put this discussion into the broader context of similar situations in other areas of physics, and summarizes some of the lessons which our good understanding of gravity in the solar system has for proponents for its modification over very long and very short distances. The main message is that effective theories, in the technical sense of `effective', provide the natural language for testing proposals, and so are also effective in the colloquial sense.

In simulations of galaxies and structures in the universe, the particle-particle-particle-mesh "PPPM" (P3M) or "TreePM" approximations are used. The forces from objects at large distances are replaced by forces localized at meshes, and solving the Poisson equation determines their effect on an object. The particle-mesh approximation (PM) breaks the symmetry of pair interactions between objects and destroys the exact conservation of momentum and angular momentum. Here, the effects of the PM approximations are examined by performing "brute-force" simulations with and without the PM approximation. However, the exact simulations can only be performed for a small "dwarf galaxy" of ≈500 objects. The simulations show that the stability of the galaxy is sensitive to the approximations, which sooner or later lead to the objects being released from their bound rotation. However, the stability of the dwarf galaxy can be ensured by modifying Newton's gravitational long-range attractions from an inverse square attraction to an inverse attraction, a gravity modification often proposed in the f(R) modified general relativity theory.

Braneworlds, understood here as double domain wall spacetimes, can be described in terms of a linear harmonic function, with kinks at the locations of the boundary branes. In a dynamical setting, there is therefore the risk that the boundary brane of negative tension, at whose location the value of the harmonic function is always lowest, can encounter a zero of this harmonic function, corresponding to the formation of a singularity. We show that for certain types of brane-bound matter this singularity can be avoided, and the negative-tension brane can shield the bulk spacetime from the singularity by bouncing back smoothly before reaching the singularity. In our analysis we compare the 5- and 4-dimensional descriptions of this phenomenon in order to determine the validity of the moduli space approximation.

We describe how the kinematic consistency relations satisfied by density\ncorrelations of the large-scale structures of the Universe can be derived\nwithin the usual Newtonian framework. These relations express a kinematic\neffect and show how the $(\\ell+n)$-density correlation factors in terms of the\n$n$-point correlation and $\\ell$ linear power spectrum factors, in the limit\nwhere the $\\ell$ soft wave numbers become linear and much smaller than the $n$\nother wave numbers. We describe how these relations extend to multifluid cases.\nIn the standard cosmology, these consistency relations derive from the\nequivalence principle. A detection of their violation would indicate\nnon-Gaussian initial conditions, non-negligible decaying modes, or a\nmodification of gravity that does not converge to General Relativity on large\nscales.\n

The acceleration of the Universe can be explained either through dark energy or through the modification of gravity on large scales. In this paper we investigate modified gravity models and compare their observable predictions with dark energy models. Modifications of general relativity are expected to be scale independent on superhorizon scales and scale dependent on subhorizon scales. For scale-independent modifications, utilizing the conservation of the curvature scalar and a parametrized post-Newtonian formulation of cosmological perturbations, we derive results for large-scale structure growth, weak gravitational lensing, and cosmic microwave background anisotropy. For scale-dependent modifications, inspired by recent f(R) theories we introduce a parametrization for the gravitational coupling G and the post-Newtonian parameter {gamma}. These parametrizations provide a convenient formalism for testing general relativity. However, we find that if dark energy is generalized to include both entropy and shear stress perturbations, and the dynamics of dark energy is unknown a priori, then modified gravity cannot in general be distinguished from dark energy using cosmological linear perturbations.

Two time scales are distinguished in the geomagnetotail dynamics. The small scale (T1) corre� sponds to disturbances propagating in the tail lobes, which have a relatively strong magnetic field and low plasma density. The larger scale (T 2 ) corresponds to plasma motions in the plasma sheet and has a relatively weak magnetic field and a relatively higher density. A disturbance, which is initiated by a localized burst of magnetic reconnection and appears in the geomagnetotail on the time scale T1, generates the upset of equi� librium in the plasma sheet zones with intermediate spatial dimensions (about RE). The theoretical consid� erations and numerical simulation indicate that the relaxation process, which subsequently proceeds on the larger time scale (T 2 ), results in the appearance of extremely thin embedded current sheets and in the gener� ation of fast plasma flows. This process gives an effective mechanism by which the magnetic energy stored in the geomagnetotail is transformed into the plasma flow kinetic energy. Such fast flows can also generate eddy plasma motions on smaller spatial scales. On the one hand, fast MHD components of this process carry a dis� turbance in other plasma sheet zones, where new magnetic reconnection bursts can originate at a large dis� tance from the zone of an initial nonlinear disturbance. As a result, new recurrent processes of relaxation orig� inate on the T2 time scale. Alternation originating in such a way is apparently the characteristic feature of eddy disturbances actually observed in the plasma sheet.

In this paper, we extend the previous work by the authors, and elaborate further on the structure of the general solution to the graviton and dilaton equations of motion in brane world scenaria, in the context of five-dimensional effective actions with [Formula: see text] higher-curvature corrections, compatible with bulk string-amplitude calculations. We consider (multi)brane scenaria, dividing the bulk space into regions, in which one matches two classes of general solutions, a linear Randall–Sundrum solution and a (logarithmic) dilatonic domain wall (bulk naked singularity). We pay particular attention to examining the possibility of resolving the mass hierarchy problem together with the vanishing of the vacuum energy on the observable world, which is taken to be a positive tension brane. The appearance of naked dilatonic domain walls provides a dynamical restriction of the bulk space–time. Of particular interest is a dilatonic-wall solution, which after appropriate coordinate transformation, results in a linear dilaton conformal field theory. The latter may provide a holographic resolution of the naked singularity problem. All the string-inspired models involved have the generic feature that the brane tensions are proportional to the string coupling gs; it remains a challenge for string theory, therefore, to show whether microscopic models respecting this feature can be constructed.