Induced gravity on intersecting brane-worlds Part I: Maximally symmetric solutions

We explore models of intersecting brane-worlds with induced gravity terms on codimension one branes and on their intersection. Maximally symmetric solutions for the branes and the intersection are found. We find new self-accelerating solutions. In a 6d spacetime, the solutions realize the see-saw modification of gravity where the UV scale of the modification to 4d gravity is determined by 6d Planck scale given by $M_6 \sim 10^{-3}$eV and the IR scale of the modification is determined by $M_6^2/M_4 \sim H_0 \sim 10^{-42}$ GeV where $H_0$ is present-day Hubble scale. We find that it is increasingly difficult to construct phenomenologically viable models in higher-dimensional spacetime due to the necessity to have the lower value for the fundamental Planck scale to realize the late time acceleration. It is found that the system also admits self-tuning solutions where the tension at the intersection does not change the geometry of the intersection. The induced gravity terms can avoid the necessity to compactify the extra dimensions. Finally, we discuss the possibility to have ordinary matter at the intersection, without introducing any regularisation, using the induced gravity terms.Comment: 16 pages, some mistakes in the identification of the higher codimensional singular structure corrected. Main results unchange

Slow-roll corrections to inflaton fluctuations on a brane

Quantum fluctuations of an inflaton field, slow-rolling during inflation are coupled to metric fluctuations. In conventional four dimensional cosmology one can calculate the effect of scalar metric perturbations as slow-roll corrections to the evolution of a massless free field in de Sitter spacetime. This gives the well-known first-order corrections to the field perturbations after horizon-exit. If inflaton fluctuations on a four dimensional brane embedded in a five dimensional bulk spacetime are studied to first-order in slow-roll then we recover the usual conserved curvature perturbation on super-horizon scales. But on small scales, at high energies, we find that the coupling to the bulk metric perturbations cannot be neglected, leading to a modified amplitude of vacuum oscillations on small scales. This is a large effect which casts doubt on the reliability of the usual calculation of inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure

Slow-roll corrections to inflaton fluctuations on a brane

Quantum fluctuations of an inflaton field, slow-rolling during inflation are coupled to metric fluctuations. In conventional four dimensional cosmology one can calculate the effect of scalar metric perturbations as slow-roll corrections to the evolution of a massless free field in de Sitter spacetime. This gives the well-known first-order corrections to the field perturbations after horizon-exit. If inflaton fluctuations on a four dimensional brane embedded in a five dimensional bulk spacetime are studied to first-order in slow-roll then we recover the usual conserved curvature perturbation on super-horizon scales. But on small scales, at high energies, we find that the coupling to the bulk metric perturbations cannot be neglected, leading to a modified amplitude of vacuum oscillations on small scales. This is a large effect which casts doubt on the reliability of the usual calculation of inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure

Inflaton perturbations in brane-world cosmology with induced gravity

We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass $m^2 = -2(2\ell-1) (\ell +1) H^2$ and $m^2 = -2\ell(2\ell+3) H^2$ where $\ell$ is an integer. There are two branches ($\pm$ branches) of solutions for the background spacetime. In the $+$ branch, which includes the self-accelerating universe, a resonance appears for a mode with $m^2 = 2 H^2$ due to a spin-0 perturbation with $m^2 = 2H^2$. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with $m^2 = 2H^2$. In the $-$ branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the lineariaed gravity on the brane is well described by the Brans-Dicke theory with $\omega=3Hr_c$ in $-$ branch and $\omega = -3H r_c$ in $+$ branch, respectively, which confirms the existence of the ghost in $+$ branch. We also study large scale perturbations. In $+$ branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of Weyl tensor in the bulk, but no instability is shown to exist on the brane.Comment: 20 pages, 4 figure

Approximate Methods for State-Space Models

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This {\em Laplace-Gaussian filter} (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time.Comment: 31 pages, 4 figures. Different pagination from journal version due to incompatible style files but same content; the supplemental file for the journal appears here as appendices B--E

Magnetic Reynolds number dependence of reconnection rate and flow structure of the self-similar evolution model of fast magnetic reconnection

This paper investigates Magnetic Reynolds number dependence of the ``self-similar evolution model'' (Nitta et al. 2001) of fast magnetic reconnection. I focused my attention on the flow structure inside and around the reconnection outflow, which is essential to determine the entire reconnection system (Nitta et al. 2002). The outflow is consist of several regions divided by discontinuities, e.g., shocks, and it can be treated by a shock-tube approximation (Nitta 2004). By solving the junction conditions (e.g., Rankine-Hugoniot condition), the structure of the reconnection outflow is obtained. Magnetic reconnection in most astrophysical problems is characterized by a huge dynamic range of its expansion ($sim 10^7$ for typical solar flares) in a free space which is free from any influence of external circumstances. Such evolution results in a spontaneous self-similar expansion which is controlled by two intrinsic parameters: the plasma-$beta$ and the magnetic Reynolds number. The plasma-$beta$ dependence had been investigated in our previous paper. This paper newly clarifies the relation between the reconnection rate and the inflow structure just outside the Petschek-like slow shock: As the magnetic Reynolds number increases, strongly converging inflow toward the Petschek-like slow shock forms, and it significantly reduces the reconnection rate.Comment: 16 pages. to appear in ApJ (2006 Jan. 20 issue

Scalar cosmological perturbations in the Gauss-Bonnet braneworld

We study scalar cosmological perturbations in a braneworld model with a bulk Gauss-Bonnet term. For an anti-de Sitter bulk, the five-dimensional perturbation equations share the same form as in the Randall-Sundrum model, which allows us to obtain metric perturbations in terms of a master variable. We derive the boundary conditions for the master variable from the generalized junction conditions on the brane. We then investigate several limiting cases in which the junction equations are reduced to a feasible level. In the low energy limit, we confirm that the standard result of four-dimensional Einstein gravity is reproduced on large scales, whereas on small scales we find that the perturbation dynamics is described by the four-dimensional Brans-Dicke theory. In the high energy limit, all the non-local contributions drop off from the junction equations, leaving a closed system of equations on the brane. We show that, for inflation models driven by a scalar field on the brane, the Sasaki-Mukhanov equation holds on the high energy brane in its original four-dimensional form.Comment: 18 pages, v2: minor changes, reference added, v3: comments and references added, accepted for publication in JCA

Contiguous redshift parameterizations of the growth index

The growth rate of matter perturbations can be used to distinguish between different gravity theories and to distinguish between dark energy and modified gravity at cosmological scales as an explanation to the observed cosmic acceleration. We suggest here parameterizations of the growth index as functions of the redshift. The first one is given by $\gamma(a)=\tilde\gamma(a) \frac{1}{1+(a_{_{ttc}}/a)}+\gamma_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that interpolates between a low/intermediate redshift parameterization $\tilde\gamma(a)=\gamma_{_{late}}(a)= \gamma_0 + (1-a) \gamma_a$ and a high redshift $\gamma_{_{early}}$ constant value. For example, our interpolated form $\gamma(a)$ can be used when including the CMB to the rest of the data while the form $\gamma_{_{late}}(a)$ can be used otherwise. It is found that the parameterizations proposed achieve a fit that is better than 0.004% for the growth rate in a $\Lambda$CDM model, better than 0.014% for Quintessence-Cold-Dark-Matter (QCDM) models, and better than 0.04% for the flat Dvali-Gabadadze-Porrati (DGP) model (with $\Omega_m^0=0.27$) for the entire redshift range up to $z_{_{CMB}}$. We find that the growth index parameters $(\gamma_0,\gamma_a)$ take distinctive values for dark energy models and modified gravity models, e.g. $(0.5655,-0.02718)$ for the $\Lambda$CDM model and $(0.6418,0.06261)$ for the flat DGP model. This provides a means for future observational data to distinguish between the models.Comment: 7 pages, 6 figures, matches PRD accepted versio

Synthetic Observations of Carbon Lines of Turbulent Flows in Diffuse Multiphase Interstellar Medium

We examine observational characteristics of multi-phase turbulent flows in the diffuse interstellar medium (ISM) using a synthetic radiation field of atomic and molecular lines. We consider the multi-phase ISM which is formed by thermal instability under the irradiation of UV photons with moderate visual extinction $A_V\sim 1$. Radiation field maps of C$^{+}$, C$^0$, and CO line emissions were generated by calculating the non-local thermodynamic equilibrium (nonLTE) level populations from the results of high resolution hydrodynamic simulations of diffuse ISM models. By analyzing synthetic radiation field of carbon lines of [\ion{C}{2}] 158 $\mu$m, [\ion{C}{1}] $^3P_2-^3P_1$ (809 GHz), $^3P_1-^3P_0$ (492 GHz), and CO rotational transitions, we found a high ratio between the lines of high- and low-excitation energies in the diffuse multi-phase interstellar medium. This shows that simultaneous observations of the lines of warm- and cold-gas tracers will be useful in examining the thermal structure, and hence the origin of diffuse interstellar clouds.Comment: 16 pages, 10 figures : accepted for publication in ApJ. PDF version with high resolution figures is available (http://yso.mtk.nao.ac.jp/~ymasako/paper/ms_hires.pdf

From the warm magnetized atomic medium to molecular clouds

{It has recently been proposed that giant molecular complexes form at the sites where streams of diffuse warm atomic gas collide at transonic velocities.} {We study the global statistics of molecular clouds formed by large scale colliding flows of warm neutral atomic interstellar gas under ideal MHD conditions. The flows deliver material as well as kinetic energy and trigger thermal instability leading eventually to gravitational collapse.} {We perform adaptive mesh refinement MHD simulations which, for the first time in this context, treat self-consistently cooling and self-gravity.} {The clouds formed in the simulations develop a highly inhomogeneous density and temperature structure, with cold dense filaments and clumps condensing from converging flows of warm atomic gas. In the clouds, the column density probability density distribution (PDF) peaks at \sim 2 \times 10^{21} \psc and decays rapidly at higher values; the magnetic intensity correlates weakly with density from $n \sim 0.1$ to 10^4 \pcc, and then varies roughly as $n^{1/2}$ for higher densities.} {The global statistical properties of such molecular clouds are reasonably consistent with observational determinations. Our numerical simulations suggest that molecular clouds formed by the moderately supersonic collision of warm atomic gas streams.}Comment: submitted to A&