Clustering Fossils from the Early Universe

Many inflationary theories introduce new scalar, vector, or tensor degrees of freedom that may then affect the generation of primordial density perturbations. Here we show how to search a galaxy (or 21-cm) survey for the imprint of primordial scalar, vector, and tensor fields. These new fields induce local departures to an otherwise statistically isotropic two-point correlation function, or equivalently, nontrivial four-point correlation functions (or trispectra, in Fourier space), that can be decomposed into scalar, vector, and tensor components. We write down the optimal estimators for these various components and show how the sensitivity to these modes depends on the galaxy-survey parameters. New probes of parity-violating early-Universe physics are also presented.Comment: 4 pages, 2 figures, submitted to PR

Large-Scale Structure Observables in General Relativity

We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider i) redshift perturbation of cosmic clock events; ii) distortion of cosmic rulers, including weak lensing shear and magnification; iii) observed number density of tracers of the large-scale structure. We provide covariant and gauge-invariant expressions of these observables. Our expressions are given for a linearly perturbed flat Friedmann-Robertson-Walker metric including scalar, vector, and tensor metric perturbations. While we restrict ourselves to linear order in perturbation theory, the approach can be straightforwardly generalized to higher order.Comment: 24 pages, 3 figures. A review article submitted to CQG focus issue "Relativistic Effects in Cosmology". arXiv admin note: substantial text overlap with arXiv:1204.3625, v2: correct one missing referenc

Large-Scale Structure with Gravitational Waves II: Shear

The B-(curl-)mode of the correlation of galaxy ellipticities (shear) can be used to detect a stochastic gravitational wave background, such as that predicted by inflation. In this paper, we derive the tensor mode contributions to shear from both gravitational lensing and intrinsic alignments, using the gauge-invariant, full-sky results of arXiv:1204.3625. We find that the intrinsic alignment contribution, calculated using the linear alignment model, is larger than the lensing contribution by an order of magnitude or more, if the alignment strength for tensor modes is of the same order as for scalar modes. This contribution also extends to higher multipoles. These results make the prospects for probing tensor modes using galaxy surveys less pessimistic than previously thought, though still very challenging.Comment: 21 pages, 7 figures; v2: reflects PRD version, added section on second-order scalar B modes; v3: fixed typo in Eq. (A44

Cosmic Rulers

We derive general covariant expressions for the six independent observable modes of distortion of ideal standard rulers in a perturbed Friedmann-Robertson-Walker spacetime. Our expressions are gauge-invariant and valid on the full sky. These six modes are most naturally classified in terms of their rotational properties on the sphere, yielding two scalars, two vector (spin-1), and two tensor (spin-2) components. One scalar corresponds to the magnification, while the spin-2 components correspond to the shear. The vector components allow for a polar/axial decomposition analogous to the E/B-decomposition for the shear. Scalar modes do not contribute to the axial (B-)vector, opening a new avenue to probing tensor modes. Our results apply, but are not limited to, the distortion of correlation functions (of the CMB, 21cm emission, or galaxies) as well as to weak lensing shear and magnification, all of which can be seen as methods relying on "standard rulers".Comment: 31 pages, 3 figures (v3); v2: minor changes reflecting PRD published version; v3: evolving ruler case relegated to arXiv:1305.1299, added proper time condition for observer, additional test cases for magnificatio

Anisotropic imprint of long-wavelength tensor perturbations on cosmic structure

Inflationary models predict a correlation between primordial density perturbations (scalar metric perturbations) and gravitational waves (tensor metric perturbations) in the form of a scalar-scalar-tensor three-point correlation, or bispectrum in Fourier space. The squeezed limit of this bispectrum implies a quadrupolar asymmetry in the observed local power spectrum for matter and galaxies. Here we show (like others before) that an infrared divergence in the amplitude of this power asymmetry predicted in single-field slow-roll models is canceled by projection effects when considering the observed power spectrum. We then further evaluate the nonzero, but finite, residual quadrupolar power asymmetry that remains after the divergences are canceled. While the quadrupolar power asymmetry is small, it is conceptually important. Our calculation moreover clarifies how the predictions for this power asymmetry may change in models with different scalar-scalar-tensor bispectra, and shows that convincing detection of the quadrupolar power asymmetry would rule out the single-field slow-roll models of inflation.Comment: 20 pages, 3 figures, revised to match the published versio

The Galaxy Power Spectrum and Bispectrum in Redshift Space

We present the complete expression for the next-to-leading (1-loop) order galaxy power spectrum and the leading-order galaxy bispectrum in redshift space in the general bias expansion, or equivalently the effective field theory of biased tracers. We consistently include all line-of-sight dependent selection effects. These are degenerate with many, but not all, of the redshift-space distortion contributions, and have not been consistently derived before. Moreover, we show that, in the framework of effective field theory, a consistent bias expansion in redshift space must include these selection contributions. Physical arguments about the tracer sample considered and its observational selection have to be used to justify neglecting the selection contributions. In summary, the next-to-leading order galaxy power spectrum and leading-order galaxy bispectrum in the general bias expansion are described by 22 parameters, which reduces to 11 parameters if selection effects can be neglected. All contributions to the power spectrum can be written in terms of 28 independent loop integrals.Comment: 61 pages, 2 figures. The version published in JCAP, except that the supplementary material pointing to GitHu