Self-accelerating universe in Galileon cosmology

We present a cosmological model with a solution that self-accelerates at late times without signs of ghost instabilities on small scales. The model is a natural extension of the Brans-Dicke (BD) theory including a nonlinear derivative interaction, which appears in a theory with the Galilean shift symmetry. The existence of the self-accelerating universe requires a negative BD parameter but, thanks to the nonlinear term, small fluctuations around the solution are stable on small scales. General relativity is recovered at early times and on small scales by this nonlinear interaction via the Vainshtein mechanism. At late time, gravity is strongly modified and the background cosmology shows a phantomlike behavior and the growth rate of structure formation is enhanced. Thus this model leaves distinct signatures in cosmological observations and it can be distinguished from standard LCDM cosmology

An asymptotic relationship between coupling methods for stochastically modeled population processes

This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a computational framework by providing reductions in variance for different Monte Carlo estimators, thereby allowing for significantly more accurate results for a fixed amount of computational time. Common applications of the couplings include the estimation of parametric sensitivities via finite difference methods and the estimation of expectations via multi-level Monte Carlo algorithms. While a number of coupling strategies have been proposed for the models considered here, and a number of articles have experimentally compared the different strategies, to date there has been no mathematical analysis describing the connections between them. Such analyses are critical in order to determine the best use for each. In the current paper, we show a connection between the common reaction path (CRP) method and the split coupling (SC) method, which is termed coupled finite differences (CFD) in the parametric sensitivities literature. In particular, we show that the two couplings are both limits of a third coupling strategy we call the "local-CRP" coupling, with the split coupling method arising as a key parameter goes to infinity, and the common reaction path coupling arising as the same parameter goes to zero. The analysis helps explain why the split coupling method often provides a lower variance than does the common reaction path method, a fact previously shown experimentally.Comment: Edited Section 4.

Numerical study of curvature perturbations in a brane-world inflation at high-energies

We study the evolution of scalar curvature perturbations in a brane-world inflation model in a 5D Anti-de Sitter spacetime. The inflaton perturbations are confined to a 4D brane but they are coupled to the 5D bulk metric perturbations. We numerically solve full coupled equations for the inflaton perturbations and the 5D metric perturbations using Hawkins-Lidsey inflationary model. At an initial time, we assume that the bulk is unperturbed. We find that the inflaton perturbations at high energies are strongly coupled to the bulk metric perturbations even on subhorizon scales, leading to the suppression of the amplitude of the comoving curvature perturbations at a horizon crossing. This indicates that the linear perturbations of the inflaton field does not obey the usual 4D Klein-Gordon equation due to the coupling to 5D gravitational field on small scales and it is required to quantise the coupled brane-bulk system in a consistent way in order to calculate the spectrum of the scalar perturbations in a brane-world inflation.Comment: 16 pages, 5 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

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

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