Parameterization of Dark-Energy Properties: a Principal-Component Approach

Considerable work has been devoted to the question of how to best parameterize the properties of dark energy, in particular its equation of state w. We argue that, in the absence of a compelling model for dark energy, the parameterizations of functions about which we have no prior knowledge, such as w(z), should be determined by the data rather than by our ingrained beliefs or familiar series expansions. We find the complete basis of orthonormal eigenfunctions in which the principal components (weights of w(z)) that are determined most accurately are separated from those determined most poorly. Furthermore, we show that keeping a few of the best-measured modes can be an effective way of obtaining information about w(z).Comment: Unfeasibility of a truly model-independent reconstruction of w at z>1 illustrated. f(z) left out, and w(z) discussed in more detail. Matches the PRL versio

Effects of a Cut, Lorentz-Boosted sky on the Angular Power Spectrum

The largest fluctuation in the observed CMB temperature field is the dipole, its origin being usually attributed to the Doppler Effect - the Earth's velocity with respect to the CMB rest frame. The lowest order boost correction to temperature multipolar coefficients appears only as a second order correction in the temperature power spectrum, $C_{\ell}$. Since v/c - 10-3, this effect can be safely ignored when estimating cosmological parameters [4-7]. However, by cutting our galaxy from the CMB sky we induce large-angle anisotropies in the data. In this case, the corrections to the cut-sky $C_{\ell}$s show up already at first order in the boost parameter. In this paper we investigate this issue and argue that this effect might turn out to be important when reconstructing the power spectrum from the cut-sky data.Comment: 12 pages, 1 figur

Real Space Approach to CMB deboosting

The effect of our Galaxy's motion through the Cosmic Microwave Background rest frame, which aberrates and Doppler shifts incoming photons measured by current CMB experiments, has been shown to produce mode-mixing in the multipole space temperature coefficients. However, multipole space determinations are subject to many difficulties, and a real-space analysis can provide a straightforward alternative. In this work we describe a numerical method for removing Lorentz- boost effects from real-space temperature maps. We show that to deboost a map so that one can accurately extract the temperature power spectrum requires calculating the boost kernel at a finer pixelization than one might naively expect. In idealized cases that allow for easy comparison to analytic results, we have confirmed that there is indeed mode mixing among the spherical harmonic coefficients of the temperature. We find that using a boost kernel calculated at Nside=8192 leads to a 1% bias in the binned boosted power spectrum at l~2000, while individual Cls exhibit ~5% fluctuations around the binned average. However, this bias is dominated by pixelization effects and not the aberration and Doppler shift of CMB photons that causes the fluctuations. Performing analysis on maps with galactic cuts does not induce any additional error in the boosted, binned power spectra over the full sky analysis. For multipoles that are free of resolution effects, there is no detectable deviation between the binned boosted and unboosted spectra. This result arises because the power spectrum is a slowly varying function of and does not show that, in general, Lorentz boosts can be neglected for other cosmological quantities such as polarization maps or higher-point functions.Comment: 8 pages, submitted to MNRA

Brane Localization and Stabilization via Regional Physics

Extra-dimensional scenarios have become widespread among particle and gravitational theories of physics to address several outstanding problems, including cosmic acceleration, the weak hierarchy problem, and the quantization of gravity. In general, the topology and geometry of the full spacetime manifold will be non-trivial, even if our ordinary dimensions have the topology of their covering space. Most compact manifolds are inhomogeneous, even if they admit a homogeneous geometry, and it will be physically relevant where in the extra-dimensions one is located. In this letter, we explore the use of both local and global effects in a braneworld scenario to naturally provide position-dependent forces that determine and stabilize the location of a single brane. For illustrative purposes, we consider the 2-dimensional hyperbolic horn and the Euclidean cone as toy models of the extra-dimensional manifold, and add a brane wrapped around one of the two spatial dimensions. We calculate the total energy due to brane tension and bending (extrinsic curvature) as well as that due to the Casimir energy of a bulk scalar satisfying a Dirchlet boundary condition on the brane. From the competition of at least two of these effects there can exist a stable minimum of the effective potential for the brane location. However, on more generic spaces (on which more symmetries are broken) any one of these effects may be sufficient to stabilize the brane. We discuss this as an example of physics that is neither local nor global, but regional.Comment: 4 pages, 2 figures. PRL submitte

Fermionic Zero Modes on Domain Walls

We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass terms could also be the coupling to a scalar field $\Phi$ or a vacuum expectation value of some other field acquired in a phase transition well above the phase transition of the field $\Phi$. We derive the fermionic equations of motion and find the necessary and sufficient conditions for a zero mode to exist. We also find the solutions numerically. In the absence of the Majorana mass terms, the equations are solvable analytically. In the case of massless fermions a zero energy solution exists and we show that although this mode is not discretely normalizable it is Dirac delta function normalizable and should be viewed as part of a continuum spectrum rather than as an isolated zero mode.Comment: 6 pages, 3 figures, matches version published in PR

Dynamical study of the hyperextended scalar-tensor theory in the empty Bianchi type I model

The dynamics of the hyperextended scalar-tensor theory in the empty Bianchi type I model is investigated. We describe a method giving the sign of the first and second derivatives of the metric functions whatever the coupling function. Hence, we can predict if a theory gives birth to expanding, contracting, bouncing or inflationary cosmology. The dynamics of a string inspired theory without antisymetric field strength is analysed. Some exact solutions are found.Comment: 18 pages, 3 figure