Initial conditions of the universe: A sign of the sine mode

In the standard big bang model the universe starts in a radiation dominated era, where the gravitational perturbations are described by second order differential equations, which will generally have two orthogonal set of solutions. One is the so called {\it growing(cosine)} mode and the other is the {\it decaying(sine)} mode, where the nomenclature is derived from their behaviour on super-horizon(sub-horizon) scales. The decaying mode is qualitatively different to the growing mode of adiabatic perturbations as it evolves with time on \emph{super-horizon} scales. The time dependence of this mode on super-horizon scales is analysed in both the synchronous gauge and the Newtonian gauge to understand the true gauge invariant behaviour of these modes. We then explore constraints on the amplitude of this mode on scales between $k \sim 10^{-5}$ Mpc$^{-1}$ and $k \sim 10^{-1}$ Mpc$^{-1}$ using the temperature and polarization anisotropies from the cosmic microwave background, by computing the Fisher information. Binning the primordial power non-parametrically into 100 bins, we find that the decaying modes are constrained at comparable variance as the growing modes on scales smaller than the horizon today using temperature anisotropies. Adding polrisation data makes the decaying mode more constrained. The decaying mode amplitude is thus constrained by $\sim 1/l$ of the growing mode. On super-horizon scales, the growing mode is poorly constrained, while the decaying mode cannot substantially exceed the scale-invariant amplitude. This interpretation differs substantially from the past literature, where the constraints were quoted in gauge-dependent variables, and resulted in illusionary tight super-horizon decaying mode constraints. The results presented here can generally be used to non-parametrically constrain any model of the early universe.Comment: Fixed typo in figure 6. Previously the noise curves were labelled incorrectly. New figure fixes that issue - main results are unchange

Isobaric Reconstruction of the Baryonic Acoustic Oscillation

In this paper, we report a significant recovery of the linear baryonic acoustic oscillation (BAO) signature by applying the isobaric reconstruction algorithm to the non-linear matter density field. Assuming only the longitudinal component of the displacement being cosmologically relevant, this algorithm iteratively solves the coordinate transform between the Lagrangian and Eulerian frames without requiring any specific knowledge of the dynamics. For dark matter field, it produces the non-linear displacement potential with very high fidelity. The reconstruction error at the pixel level is within a few percent, and is caused only by the emergence of the transverse component after the shell-crossing. As it circumvents the strongest non-linearity of the density evolution, the reconstructed field is well-described by linear theory and immune from the bulk-flow smearing of the BAO signature. Therefore this algorithm could significantly improve the measurement accuracy of the sound horizon scale. For a perfect large-scale structure survey at redshift zero without Poisson or instrumental noise, the fractional error is reduced by a factor of 2.7, very close to the ideal limit with linear power spectrum and Gaussian covariance matrix.Comment: 5 pages, 3 figures, accepted versio

Improved Dark Energy Detection through the Polarization-assisted WMAP-NVSS ISW Correlation

Integrated Sachs-Wolfe (ISW) effect can be estimated by cross-correlating Cosmic Microwave Background (CMB) sky with tracers of the local matter distribution. At late cosmic time, the dark energy induced decay of gravitation potential generates a cross-correlation signal on large angular scales. The dominant noise are the intrinsic CMB anisotropies from the inflationary epoch. In this Letter we use CMB polarization to reduce this intrinsic noise. We cross-correlate the microwave sky observed by Wilkinson Microwave Anisotropy Probe (WMAP) with the radio source catalog compiled by NRAO VLA Sky Survey (NVSS) to study the efficiency of the noise suppression . We find that the error bars are reduced about 5-12 %, improving the statistical power.Comment: 10 pages, 2 figure

Stochastic urban pluvial flood hazard maps based upon a spatial-temporal rainfall generator

It is a common practice to assign the return period of a given storm event to the urban pluvial flood event that such storm generates. However, this approach may be inappropriate as rainfall events with the same return period can produce different urban pluvial flooding events, i.e., with different associated flood extent, water levels and return periods. This depends on the characteristics of the rainfall events, such as spatial variability, and on other characteristics of the sewer system and the catchment. To address this, the paper presents an innovative contribution to produce stochastic urban pluvial flood hazard maps. A stochastic rainfall generator for urban-scale applications was employed to generate an ensemble of spatially—and temporally—variable design storms with similar return period. These were used as input to the urban drainage model of a pilot urban catchment (~9 km2) located in London, UK. Stochastic flood hazard maps were generated through a frequency analysis of the flooding generated by the various storm events. The stochastic flood hazard maps obtained show that rainfall spatial-temporal variability is an important factor in the estimation of flood likelihood in urban areas. Moreover, as compared to the flood hazard maps obtained by using a single spatially-uniform storm event, the stochastic maps generated in this study provide a more comprehensive assessment of flood hazard which enables better informed flood risk management decisions

Initial conditions of the universe: Decaying tensor modes

Many models of the early universe predict that there should be primordial tensor perturbations. These leave an imprint into the temperature and polarisation anisotropies of the cosmic microwave background (CMB). The differential equation describing the primordial tensor perturbations is a second order differential equation and thus has two solutions. Canonically, the decaying solution of this equation in radiation domination is dropped as it diverges at early times and on superhorizon scales while it is then suppressed at late times. Furthermore, if there is an inflationary phase prior to the radiation domination phase, the amplitude of the decaying mode will also be highly suppressed as it enters the radiation phase, thus its effect will be negligible. In this study we remain agnostic to the early universe models describing pre-radiation domination physics and allow this mode to be present and see what effect it has on the CMB anisotropies. We find that the decaying mode, if normalised at the same time on subhorizon scales as the growing mode leaves an imprint on the CMB anisotropies that is identical to the growing mode. Contrary to expectation, on large scales both modes are poorly constrained for a scale invariant spectrum, and the apparent divergence of the decaying mode does not lead to a divergent physical observable. Quantitatively, the decaying mode can be more constrained both from temperature and polarisation anisotropies. We use a model independent, non-parametric, approach to constrain both of these primordial tensor perturbations using the temperature and polarisation anisotropies. We find that both modes are best constrained at the reionisation and recombination bumps and crucially, at the reionisation bump the decaying mode can be distinguished from the growing mode.Comment: 10 pages, comments welcome