Amplitude and Phase Fluctuations for Gravitational Waves Propagating through Inhomogeneous Mass Distribution in the Universe

When a gravitational wave (GW) from a distant source propagates through the universe, its amplitude and phase change due to gravitational lensing by the inhomogeneous mass distribution. We derive the amplitude and phase fluctuations, and calculate these variances in the limit of a weak gravitational field of density perturbation. If the scale of the perturbation is smaller than the Fresnel scale $\sim 100 {pc} (f/{mHz})^{-1/2}$ ($f$ is the GW frequency), the GW is not magnified due to the diffraction effect. The rms amplitude fluctuation is $1-10$ for $f > 10^{-10}$ Hz, but it is reduced less than 5% for a very low frequency of $f < 10^{-12}$ Hz. The rms phase fluctuation in the chirp signal is $\sim 10^{-3}$ radian at LISA frequency band ($10^{-5} - 10^{-1}$ Hz). Measurements of these fluctuations will provide information about the matter power spectrum on the Fresnel scale $\sim 100$ pc.Comment: 6 pages, 6 figures, refferences added, accepted for publication in Ap

The scale of homogeneity in the Las Campanas Redshift Survey

We analyse the Las Campanas Redshift Survey using the integrated conditional density (or density of neighbors) in volume-limited subsamples up to unprecedented scales (200 Mpc/$h$) in order to determine without ambiguity the behavior of the density field. We find that the survey is well described by a fractal up to 20-30 Mpc/$h$, but flattens toward homogeneity at larger scales. Although the data are still insufficient to establish with high significance the expected homogeneous behavior, and therefore to rule out a fractal trend to larger scales, a fit with a CDM-like spectrum with high normalization well represents the data.Comment: 8 pages, 3 figures, accepted on Ap.J. Letter

Correlation between the Mean Matter Density and the Width of the Saturated Lyman Alpha Absorption

We report a scaling of the mean matter density with the width of the saturated Lyman alpha absorptions. This property is established using the ``pseudo-hydro'' technique (Croft et al. 1998). It provides a constraint for the inversion of the Lyman alpha forest, which encounters difficulty in the saturated region. With a Gaussian density profile and the scaling relation, a simple inversion of the simulated Lyman alpha forests shows that the one-dimensional mass power spectrum is well recovered on scales above 2 Mpc/h, or roughly k < 0.03 s/km, at z=3. The recovery underestimates the power on small scales, but improvement is possible with a more sophisticated algorithm.Comment: 7 pages, 9 figures, accepted for publication in MNRAS, replaced by the version after proo

Power Spectrum Correlations Induced by Non-Linear Clustering

Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to non-trivial cross-correlations between different band-powers. We calculate the power-spectrum covariance matrix in non-linear perturbation theory (weakly non-linear regime), in the hierarchical model (strongly non-linear regime), and from numerical simulations in real and redshift space. We discuss the impact of these results on parameter estimation from power spectrum measurements and their dependence on the size of the survey and the choice of band-powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the non-linear scale, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z=1, the non-Gaussian contribution rises significantly around l=1000, and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the 3D field falls faster than 1/k^2.Comment: 34 pages, 15 figures. Revised version, includes a clearer explanation of why the hierarchical ansatz does not provide a good model of the covariance matrix in the non-linear regime, and new constraints on the amplitudes Ra and Rb for general 4-pt function configurations in the non-linear regim

Isolating Geometry in Weak Lensing Measurements

Given a foreground galaxy-density field or shear field, its cross-correlation with the shear field from a background population of source galaxies scales with the source redshift in a way that is specific to lensing. Such a source-scaling can be exploited to effectively measure geometrical distances as a function of redshift and thereby constrain dark energy properties, free of any assumptions about the galaxy-mass/mass power spectrum (its shape, amplitude or growth). Such a geometrical method can yield a ~ 0.03 - 0.07 f_{sky}^{-1/2} measurement on the dark energy abundance and equation of state, for a photometric redshift accuracy of dz ~ 0.01 - 0.05 and a survey with median redshift of ~ 1. While these constraints are weaker than conventional weak lensing methods, they provide an important consistency check because the geometrical method carries less theoretical baggage: there is no need to assume any structure formation model (e.g. CDM). The geometrical method is at the most conservative end of a whole spectrum of methods which obtain smaller errorbars by making more restrictive assumptions -- we discuss some examples. Our geometrical approach differs from previous investigations along similar lines in three respects. First, the source-scaling we propose to use is less demanding on the photometric redshift accuracy. Second, the scaling works for both galaxy-shear and shear-shear correlations. Third, we find that previous studies underestimate the statistical errors associated with similar geometrical methods, the origin of which is discussed.Comment: 13 pages, 4 figures, submitted to Ap

Self Calibration of Tomographic Weak Lensing for the Physics of Baryons to Constrain Dark Energy

Numerical studies indicate that uncertainties in the treatment of baryonic physics can affect predictions for shear power spectra at a level that is significant for forthcoming surveys such as DES, SNAP, and LSST. Correspondingly, we show that baryonic effects can significantly bias dark energy parameter measurements. Eliminating such biases by neglecting information in multipoles beyond several hundred leads to weaker parameter constraints by a factor of approximately 2 to 3 compared with using information out to multipoles of several thousand. Fortunately, the same numerical studies that explore the influence of baryons indicate that they primarily affect power spectra by altering halo structure through the relation between halo mass and mean effective halo concentration. We explore the ability of future weak lensing surveys to constrain both the internal structures of halos and the properties of the dark energy simultaneously as a first step toward self calibrating for the physics of baryons. This greatly reduces parameter biases and no parameter constraint is degraded by more than 40% in the case of LSST or 30% in the cases of SNAP or DES. Modest prior knowledge of the halo concentration relation greatly improves even these forecasts. Additionally, we find that these surveys can constrain effective halo concentrations near m~10^14 Msun/h and z~0.2 to better than 10% with shear power spectra alone. These results suggest that inferring dark energy parameters with measurements of shear power spectra can be made robust to baryonic effects and may simultaneously be competitive with other methods to inform models of galaxy formation. (Abridged)Comment: 18 pages, 11 figures. Minor changes reflecting referee's comments. Results and conclusions unchanged. Accepted for publication in Physical Review

A Constraint on the Distance Scale to Cosmological Gamma--Ray Bursts

If \g--ray bursts are cosmological in origin, the sources are expected to trace the large--scale structure of luminous matter in the universe. I use a new likelihood method that compares the counts--in--cells distribution of \g--ray bursts in the BATSE 3B catalog with that expected from the known large--scale structure of the universe, in order to place a constraint on the distance scale to cosmological bursts. I find, at the 95\% confidence level, that the comoving distance to the ``edge'' of the burst distribution is greater than $630~h^{-1}$~Mpc ($z > 0.25$), and that the nearest burst is farther than $40~h^{-1}$~Mpc. The median distance to the nearest burst is $170~h^{-1}$~Mpc, implying that the total energy released in \g--rays during a burst event is of order $3\times 10^{51}~h^{-2}$ ergs. None of the bursts that have been observed by BATSE are in nearby galaxies, nor is a signature from the Coma cluster or the ``Great Wall'' likely to be seen in the data at present.Comment: 15 LaTeX pages with 2 encapsulated Postscript figures included, uses AASTeX (v. 4.0) available at ftp://ftp.aas.org/pubs

Weighing the Cosmological Energy Contents with Weak Gravitational Lensing

Bernardeau et al. (1997), using perturbation theory, showed that the skewness of the large-scale lensing-convergence, or projected mass density, could be used to constrain $\Omega_m$, the matter content of the universe. On the other hand, deep weak-lensing field surveys in the near future will likely measure the convergence on small angular scales (< 10 arcmin.), where the signal will be dominated by highly nonlinear fluctuations. We develop a method to compute the small-scale convergence skewness, using a prescription for the highly nonlinear three-point function developed by Scoccimarro and Frieman (1998). This method gives predictions that agree well with existing results from ray-tracing N-body simulations, but is significantly faster, allowing the exploration of a large number of models. We demonstrate that the small-scale convergence skewness is insensitive to the shape and normalization of the primordial (CDM-type) power spectrum, making it dependent almost entirely on the cosmological energy contents, through their influence on the global geometrical distances and fluctuation growth rate. Moreover, nonlinear clustering appears to enhance the differences between predictions of the convergence skewness for a range of models. Hence, in addition to constraining $\Omega_m$, the small-scale convergence skewness from future deep several- degree-wide surveys can be used to differentiate between curvature dominated and cosmological constant ($\Lambda$) dominated models, as well as to constrain the equation of state of a quintessence component, thereby distinguishing $\Lambda$ from quintessence as well. Finally, our method can be easily generalized to other measures such as aperture mass statistics.Comment: 13 pages, 2 ps figures, submitted to ApJ

Second Order Corrections to Weak Lensing by Large-Scale Structure

We calculate corrections to the power spectrum predictions of weak lensing by large scale structure due to higher order effects in the gravitational potential. Using a perturbative approach to third order in transverse displacements, we calculate a second order correction to the angular power spectra of E and B mode shear and convergence resulting from dropping the so-called Born approximation, where one integrates along the unperturbed photon path. We also consider a correction to the power spectra from the coupling between lenses at different redshifts. Both effects generate B-mode shear and the latter also causes a net rotation of the background galaxy images. We show all these corrections are at least two orders of magnitude below the convergence or E-mode power and hence relevant only to future ultra high precision measurements. These analytical calculations are consistent with previous numerical estimates and validate the use of current large scale structure weak lensing predictions for cosmological studies and future use of B-modes as a monitor of systematic effects.Comment: 4 pages, 1 figure, submitted to ApJ

Simulated Extragalactic Observations with a Cryogenic Imaging Spectrophotometer

In this paper we explore the application of cryogenic imaging spectrophotometers. Prototypes of this new class of detector, such as superconducting tunnel junctions (STJs) and transition edge sensors (TESs), currently deliver low resolution imaging spectrophotometry with high quantum efficiency (70-100%) and no read noise over a wide bandpass in the visible to near-infrared. In order to demonstrate their utility and the differences in observing strategy needed to maximize their scientific return, we present simulated observations of a deep extragalactic field. Using a simple analytic technique, we can estimate both the galaxy redshift and spectral type more accurately than is possible with current broadband techniques. From our simulated observations and a subsequent discussion of the expected migration path for this new technology, we illustrate the power and promise of these devices.Comment: 30 pages, 10 figures, accepted for publication in the Astronomical Journa