Gravitational lensing as a contaminant of the gravity wave signal in CMB

Gravity waves (GW) in the early universe generate B-type polarization in the cosmic microwave background (CMB), which can be used as a direct way to measure the energy scale of inflation. Gravitational lensing contaminates the GW signal by converting the dominant E polarization into B polarization. By reconstructing the lensing potential from CMB itself one can decontaminate the B mode induced by lensing. We present results of numerical simulations of B mode delensing using quadratic and iterative maximum-likelihood lensing reconstruction methods as a function of detector noise and beam. In our simulations we find the quadratic method can reduce the lensing B noise power by up to a factor of 7, close to the no noise limit. In contrast, the iterative method shows significant improvements even at the lowest noise levels we tested. We demonstrate explicitly that with this method at least a factor of 40 noise power reduction in lensing induced B power is possible, suggesting that T/S=10^-6 may be achievable in the absence of sky cuts, foregrounds, and instrumental systematics. While we do not find any fundamental lower limit due to lensing, we find that for high-sensitivity detectors residual lensing noise dominates over the detector noise.Comment: 6 pages, 2 figures, submitted to PR

A scale-dependent power asymmetry from isocurvature perturbations

If the hemispherical power asymmetry observed in the cosmic microwave background (CMB) on large angular scales is attributable to a superhorizon curvaton fluctuation, then the simplest model predicts that the primordial density fluctuations should be similarly asymmetric on all smaller scales. The distribution of high-redshift quasars was recently used to constrain the power asymmetry on scales k□1.5hMpc-1, and the upper bound on the amplitude of the asymmetry was found to be a factor of 6 smaller than the amplitude of the asymmetry in the CMB. We show that it is not possible to generate an asymmetry with this scale dependence by changing the relative contributions of the inflaton and curvaton to the adiabatic power spectrum. Instead, we consider curvaton scenarios in which the curvaton decays after dark matter freezes out, thus generating isocurvature perturbations. If there is a superhorizon fluctuation in the curvaton field, then the rms amplitude of these perturbations will be asymmetric, and the asymmetry will be most apparent on large angular scales in the CMB. We find that it is only possible to generate the observed asymmetry in the CMB while satisfying the quasar constraint if the curvaton's contribution to the total dark matter density is small, but nonzero. The model also requires that the majority of the primordial power comes from fluctuations in the inflaton field. Future observations and analyses of the CMB will test this model because the power asymmetry generated by this model has a specific spectrum, and the model requires that the current upper bounds on isocurvature power are nearly saturated

Spatial averaging and apparent acceleration in inhomogeneous spaces

As an alternative to dark energy that explains the observed acceleration of the universe, it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. To test this possibility, it is necessary to solve the null geodesics. In this paper we first give a detailed derivation of a fully analytical set of differential equations for the radial null geodesics as functions of the redshift in LTB models. As an application we use these equaions to show that a positive averaged acceleration $a_D$ obtained in LTB models through spatial averaging can be incompatible with cosmological observations. We provide examples of LTB models with positive $a_D$ which fail to reproduce the observed luminosity distance $D_L(z)$. Since the apparent cosmic acceleration $a^{FLRW}$ is obtained from fitting the observed luminosity distance to a FLRW model we conclude that in general a positive $a_D$ in LTB models does not imply a positive $a^{FLRW}$.Comment: 16 pages, 12 figures. Explicit derivation of the fully analytical null geodesic equations has been added. Published in GR

How to measure redshift-space distortions without sample variance

We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter beta=f/b=(dlnD/dlna)/b (where D is the growth rate and a the expansion factor), to a much better precision than one could achieve with a single tracer, to an arbitrary precision in the low noise limit. In combination with the power spectrum of the tracers this allows a much more precise measurement of the bias-free velocity divergence power spectrum, f^2 P_m - in fact, in the low noise limit f^2 P_m can be measured as well as would be possible if velocity divergence was observed directly, with rms improvement factor ~[5.2(beta^2+2 beta+2)/beta^2]^0.5 (e.g., ~10 times better than a single tracer for beta=0.4). This would allow a high precision determination of f D as a function of redshift with an error as low as 0.1%. We find up to two orders of magnitude improvement in Figure of Merit for the Dark Energy equation of state relative to Stage II, a factor of several better than other proposed Stage IV Dark Energy surveys. The ratio b_2/b_1 will be determined with an even greater precision than beta, producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with signal to noise of unity on scales of interest, and are not optimized for this technique. Our results suggest that this strategy may need to be revisited as there are large gains to be achieved from surveys with higher number densities of galaxies.Comment: 22 pages, 13 figure

Non-detection of a statistically anisotropic power spectrum in large-scale structure

We search a sample of photometric luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS) for a quadrupolar anisotropy in the primordial power spectrum, in which P(\vec{k}) is an isotropic power spectrum P(k) multiplied by a quadrupolar modulation pattern. We first place limits on the 5 coefficients of a general quadrupole anisotropy. We also consider axisymmetric quadrupoles of the form P(\vec{k}) = P(k){1 + g_*[(\hat{k}\cdot\hat{n})^2-1/3]} where \hat{n} is the axis of the anisotropy. When we force the symmetry axis \hat{n} to be in the direction (l,b)=(94 degrees,26 degrees) identified in the recent Groeneboom et al. analysis of the cosmic microwave background, we find g_*=0.006+/-0.036 (1 sigma). With uniform priors on \hat{n} and g_* we find that -0.41<g_*<+0.38 with 95% probability, with the wide range due mainly to the large uncertainty of asymmetries aligned with the Galactic Plane. In none of these three analyses do we detect evidence for quadrupolar power anisotropy in large scale structure.Comment: 23 pages; 10 figures; 3 tables; replaced with version published in JCAP (added discussion of scale-varying quadrupolar anisotropy

CMB Lensing Reconstruction on the Full Sky

Gravitational lensing of the microwave background by the intervening dark matter mainly arises from large-angle fluctuations in the projected gravitational potential and hence offers a unique opportunity to study the physics of the dark sector at large scales. Studies with surveys that cover greater than a percent of the sky will require techniques that incorporate the curvature of the sky. We lay the groundwork for these studies by deriving the full sky minimum variance quadratic estimators of the lensing potential from the CMB temperature and polarization fields. We also present a general technique for constructing these estimators, with harmonic space convolutions replaced by real space products, that is appropriate for both the full sky limit and the flat sky approximation. This also extends previous treatments to include estimators involving the temperature-polarization cross-correlation and should be useful for next generation experiments in which most of the additional information from polarization comes from this channel due to sensitivity limitations.Comment: Accepted for publication in Phys. Rev. D; typos correcte

Cross-Correlation Studies with CMB Polarization Maps

The free-electron population during the reionized epoch rescatters CMB temperature quadrupole and generates a now well-known polarization signal at large angular scales. While this contribution has been detected in the temperature-polarization cross power spectrum measured with WMAP data, due to the large cosmic variance associated with anisotropy measurements at tens of degree angular scales only limited information related to reionization, such as the optical depth to electron scattering, can be extracted. The inhomogeneities in the free-electron population lead to an additional secondary polarization anisotropy contribution at arcminute scales. While the fluctuation amplitude, relative to dominant primordial fluctuations, is small, we suggest that a cross-correlation between arcminute scale CMB polarization data and a tracer field of the high redshift universe, such as through fluctuations captured by the 21 cm neutral Hydrogen background or those in the infrared background related to first proto-galaxies, may allow one to study additional details related to reionization. For this purpose, we discuss an optimized higher order correlation measurement, in the form of a three-point function, including information from large angular scale CMB temperature anisotropies in addition to arcminute scale polarization signal related to inhomogeneous reionization. We suggest that the proposed bispectrum can be measured with a substantial signal-to-noise ratio and does not require all-sky maps of CMB polarization or that of the tracer field. A measurement such as the one proposed may allow one to establish the epoch when CMB polarization related to reionization is generated and to address if the universe was reionized once or twice.Comment: 13 pages, 7 figures; Version in press with Phys. Rev.

Solar Neutrinos: What We Have Learned

The four operating solar neutrino experiments confirm the hypothesis that the energy source for solar luminosity is hydrogen fusion. However, the measured rate for each of the four solar neutrino experiments differs significantly (by factors of 2.0 to 3.5) from the corresponding theoretical prediction that is based upon the standard solar model and the simplest version of the standard electroweak theory. If standard electroweak theory is correct, the energy spectrum for \b8 neutrinos created in the solar interior must be the same (to one part in $10^5$) as the known laboratory \b8 neutrino energy spectrum. Direct comparison of the chlorine and the Kamiokande experiments, both sensitive to \b8 neutrinos, suggests that the discrepancy between theory and observations depends upon neutrino energy, in conflict with standard expectations. Monte Carlo studies with 1000 implementations of the standard solar model confirm that the chlorine and the Kamiokande experiments cannot be reconciled unless new weak interaction physics changes the shape of the \b8 neutrino energy spectrum. The results of the two gallium solar neutrino experiments strengthen the conclusion that new physics is required and help determine a relatively small allowed region for the MSW neutrino parameters.Comment: LaTeX file, 19 pages. For hardcopy with figures contact [email protected]. Institute for Advanced Study number AST 93/6

Extension of the sum rule for the transition rates between multiplets to the multiphoton case

The sum rule for the transition rates between the components of two multiplets, known for the one-photon transitions, is extended to the multiphoton transitions in hydrogen and hydrogen-like ions. As an example the transitions 3p-2p, 4p-3p and 4d-3d are considered. The numerical results are compared with previous calculations.Comment: 10 pages, 4 table

Neutrino Interferometry In Curved Spacetime

Gravitational lensing introduces the possibility of multiple (macroscopic) paths from an astrophysical neutrino source to a detector. Such a multiplicity of paths can allow for quantum mechanical interference to take place that is qualitatively different to neutrino oscillations in flat space. After an illustrative example clarifying some under-appreciated subtleties of the phase calculation, we derive the form of the quantum mechanical phase for a neutrino mass eigenstate propagating non-radially through a Schwarzschild metric. We subsequently determine the form of the interference pattern seen at a detector. We show that the neutrino signal from a supernova could exhibit the interference effects we discuss were it lensed by an object in a suitable mass range. We finally conclude, however, that -- given current neutrino detector technology -- the probability of such lensing occurring for a (neutrino-detectable) supernova is tiny in the immediate future.Comment: 25 pages, 1 .eps figure. Updated version -- with simplified notation -- accepted for publication in Phys.Rev.D. Extra author adde