Magnification-Temperature Correlation: the Dark Side of ISW Measurements

Integrated Sachs-Wolfe (ISW) measurements, which involve cross-correlating the CMB with the foreground large-scale structure (e.g. galaxies/quasars), have proven to be an interesting probe of dark energy. We show that magnification bias, which is the inevitable modulation of the foreground number counts by gravitational lensing, alters both the shape and amplitude of the observed ISW signal. This is true especially at high redshifts because (1) the intrinsic galaxy-temperature signal diminishes greatly back in the matter dominated era, (2) the lensing efficiency increases with redshift and (3) the number count slope generally steepens with redshift in a magnitude limited sample. At z >~ 2, the magnification-temperature correlation dominates over the intrinsic galaxy-temperature correlation and causes the observed ISW signal to increase with z, despite dark energy subdominance -- a result of the fact that magnification probes structures between the observer and the sources. Ignoring magnification bias can then lead to erroneous conclusions about dark energy. While the lensing modulation opens up an interesting high z window for ISW measurements, high z measurements are not expected to add much new information to low z ones if dark energy is the cosmological constant. This is because lensing introduces significant covariance across redshifts. The most compelling reason to pursue high z ISW measurements is to look for a potential surprise such as early dark energy domination or the signature of modified gravity. We conclude with a discussion of existing measurements, the highest z of which is at the margin of being sensitive to magnification bias. We also develop a formalism which might be of general interest: to predict biases in estimating parameters when certain physical effects are ignored in interpreting data.Comment: 14 pages, 12 figures, references added, minor typos corrected, accepted for publication by PR

A Horizon Ratio Bound for Inflationary Fluctuations

We demonstrate that the gravity wave background amplitude implies a robust upper bound on the ratio: \lambda / H^{-1} < e^60, where \lambda is the proper wavelength of fluctuations of interest and H^{-1} is the horizon at the end of inflation. The bound holds as long as the energy density of the universe does not drop faster than radiation subsequent to inflation. This limit implies that the amount of expansion between the time the scales of interest leave the horizon and the end of inflation, denoted by e^N, is also bounded from above, by about e^60 times a factor that involves an integral over the first slow-roll parameter. In other words, the bound on N is model dependent -- we show that for vast classes of slow-roll models, N < 67. The quantities, \lambda / H^{-1} or N, play an important role in determining the nature of inflationary scalar and tensor fluctuations. We suggest ways to incorporate the above bounds when confronting inflation models with observations. As an example, this bound solidifies the tension between observations of cosmic microwave background (CMB) anisotropies and chaotic inflation with a \phi^4 potential by closing the escape hatch of large N (< 62).Comment: 4 pages, 1 figure; revised to close a loophole in the earlier version and clarify our assumption

Anisotropic Inflation and the Origin of Four Large Dimensions

In the context of (4+d)-dimensional general relativity, we propose an inflationary scenario wherein 3 spatial dimensions grow large, while d extra dimensions remain small. Our model requires that a self-interacting d-form acquire a vacuum expectation value along the extra dimensions. This causes 3 spatial dimensions to inflate, whilst keeping the size of the extra dimensions nearly constant. We do not require an additional stabilization mechanism for the radion, as stable solutions exist for flat, and for negatively curved compact extra dimensions. From a four-dimensional perspective, the radion does not couple to the inflaton; and, the small amplitude of the CMB temperature anisotropies arises from an exponential suppression of fluctuations, due to the higher-dimensional origin of the inflaton. The mechanism triggering the end of inflation is responsible, both, for heating the universe, and for avoiding violations of the equivalence principle due to coupling between the radion and matter.Comment: 24 pages, 2 figures; uses RevTeX4. v2: Minor changes and added references. v3: Improved discussion of slow-rol

Probing the dark energy: methods and strategies

The presence of dark energy in the Universe is inferred directly from the accelerated expansion of the Universe, and indirectly, from measurements of cosmic microwave background (CMB) anisotropy. Dark energy contributes about 2/3 of the critical density, is very smoothly distributed, and has large negative pressure. Its nature is very much unknown. Most of its discernible consequences follow from its effect on evolution of the expansion rate of the Universe, which in turn affects the growth of density perturbations and the age of the Universe, and can be probed by the classical kinematic cosmological tests. Absent a compelling theoretical model (or even a class of models), we describe the dark energy by an effective equation-of-state w=p_X/\rho_X which is allowed to vary with time. We describe and compare different approaches for determining w(t), including magnitude-redshift (Hubble) diagram, number counts of galaxies and clusters, and CMB anisotropy, focusing particular attention on the use of a sample of several thousand type Ia supernova with redshifts z\lesssim 1.7, as might be gathered by the proposed SNAP satellite. Among other things, we derive optimal strategies for constraining cosmological parameters using type Ia supernovae. While in the near term CMB anisotropy will provide the first measurements of w, supernovae and number counts appear to have the most potential to probe dark energy.Comment: 20 pages and 23 figures, revtex, submitted to Phys. Rev.

The Angular Correlation Function of Galaxies from Early SDSS Data

The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local Universe. In this Letter we present some of the initial results on the angular 2-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18<r*<22, is shown to be consistent with results from existing wide-field, photographic-based surveys and narrower CCD galaxy surveys. On scales between 1 arcminute and 1 degree the correlation function is well described by a power-law with an exponent of ~ -0.7. The amplitude of the correlation function, within this angular interval, decreases with fainter magnitudes in good agreement with analyses from existing galaxy surveys. There is a characteristic break in the correlation function on scales of approximately 1-2 degrees. On small scales, < 1', the SDSS correlation function does not appear to be consistent with the power-law form fitted to the 1'< theta <0.5 deg data. With a data set that is less than 2% of the full SDSS survey area, we have obtained high precision measurements of the power-law angular correlation function on angular scales 1' < theta < 1 deg, which are robust to systematic uncertainties. Because of the limited area and the highly correlated nature of the error covariance matrix, these initial results do not yet provide a definitive characterization of departures from the power-law form at smaller and larger angles. In the near future, however, the area of the SDSS imaging survey will be sufficient to allow detailed analysis of the small and large scale regimes, measurements of higher-order correlations, and studies of angular clustering as a function of redshift and galaxy type

KL Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early SDSS Data

We present measurements of parameters of the 3-dimensional power spectrum of galaxy clustering from 222 square degrees of early imaging data in the Sloan Digital Sky Survey. The projected galaxy distribution on the sky is expanded over a set of Karhunen-Loeve eigenfunctions, which optimize the signal-to-noise ratio in our analysis. A maximum likelihood analysis is used to estimate parameters that set the shape and amplitude of the 3-dimensional power spectrum. Our best estimates are Gamma=0.188 +/- 0.04 and sigma_8L = 0.915 +/- 0.06 (statistical errors only), for a flat Universe with a cosmological constant. We demonstrate that our measurements contain signal from scales at or beyond the peak of the 3D power spectrum. We discuss how the results scale with systematic uncertainties, like the radial selection function. We find that the central values satisfy the analytically estimated scaling relation. We have also explored the effects of evolutionary corrections, various truncations of the KL basis, seeing, sample size and limiting magnitude. We find that the impact of most of these uncertainties stay within the 2-sigma uncertainties of our fiducial result.Comment: Fig 1 postscript problem correcte

Partially ionizing the universe by decaying particles

We show that UV photons produced by decaying particles can partially reionize the universe and explain the large optical depth observed by Wilkinson Microwave Anisotropy Probe. Together with UV fluxes from early formed stars and quasars, it is possible that the universe is fully ionized at z \lesssim 6 and partially ionized at z \gtrsim 6 as observed by Sloan Digital Sky Survey for large parameter space of the decaying particle. This scenario will be discriminated by future observations, especially by the EE polarization power spectrum of cosmic microwave background radiation.Comment: 5 pages, 6 postscript figures include

Weak lensing, dark matter and dark energy

Weak gravitational lensing is rapidly becoming one of the principal probes of dark matter and dark energy in the universe. In this brief review we outline how weak lensing helps determine the structure of dark matter halos, measure the expansion rate of the universe, and distinguish between modified gravity and dark energy explanations for the acceleration of the universe. We also discuss requirements on the control of systematic errors so that the systematics do not appreciably degrade the power of weak lensing as a cosmological probe.Comment: Invited review article for the GRG special issue on gravitational lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). V3: subsection on three-point function and some references added. Matches the published versio