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Register a new userRelativistic wide-angle galaxy bispectrum on the light-cone
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Added by
Daniele Bertacca DR.
Publication date
2017
fields
Physics
and research's language is
English
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Given the important role that the galaxy bispectrum has recently acquired in cosmology and the scale and precision of forthcoming galaxy clustering observations, it is timely to derive the full expression of the large-scale bispectrum going beyond approximated treatments which neglect integrated terms or higher-order bias terms or use the Limber approximation. On cosmological scales, relativistic effects that arise from observing on the past light-cone alter the observed galaxy number counts, therefore leaving their imprints on N-point correlators at all orders. In this paper we compute for the first time the bispectrum including all general relativistic, local and integrated, effects at second order, the tracers bias at second order, geometric effects as well as the primordial non-Gaussianity contribution. This is timely considering that future surveys will probe scales comparable to the horizon where approximations widely used currently may not hold; neglecting these effects may introduce biases in estimation of cosmological parameters as well as primordial non-Gaussianity.
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High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective $f_{rm NL}$ that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, $f_{rm NL}$, for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of $f_{rm NL}$ for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of $f_{rm NL}^{rm loc} sim {mathcal O}(1)$.
The simplest interpretation of the Bicep2 result is that the scalar primordial power spectrum is slightly suppressed at large scales. These models result in a large tensor-to-scalar ratio $r$. In this work we show that the type of inflationary trajectory favoured by Bicep2 also leads to a larger non-Gaussian signal at large scales, roughly an order of magnitude larger than a standard slow-roll trajectory.
The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodetic-deviation equation, and thus to derive an exact expression for the Jacobi map J^A_B(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J^A_B factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J^A_B is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on light-like signals.
If time-dependent disruptions from slow-roll occur during inflation, the correlation functions of the primordial curvature perturbation should have scale-dependent features, a case which is marginally supported from the cosmic microwave background (CMB) data. We offer a new approach to analyze the appearance of such features in the primordial bispectrum that yields new consistency relations and justifies the search of oscillating patterns modulated by orthogonal and local templates. Under the assumption of sharp features, we find that the cubic couplings of the curvature perturbation can be expressed in terms of the bispectrum in two specific momentum configurations, for example local and equilateral. This allows us to derive consistency relations among different bispectrum shapes, which in principle could be tested in future CMB surveys. Furthermore, based on the form of the consistency relations, we construct new two-parameter templates for features that include all the known shapes.
We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, the angular dependences on the two line-of-sight (LOS) directions pointing to each pair of objects, which are degenerate with each other in the conventional analysis under the small-angle or plane-parallel (PP) approximation, are unambiguously decomposed. By means of this, we, for the first time, compute the wide-angle auto and cross correlations between intrinsic ellipticities, number densities and velocities of galaxies, and compare them with the PP-limit results. For the ellipticity-ellipticity and density-ellipticity correlations, we find more than $10%$ deviation from the PP-limit results if the opening angle between two LOS directions exceeds $30^circ - 50^circ$. It is also shown that even if the PP-limit result is strictly zero, the non-vanishing correlation is obtained over the various scales, arising purely from the curved-sky effects. Our results indicate the importance of the data analysis not relying on the PP approximation in order to determine the cosmological parameters more precisely and/or find new physics via ongoing and forthcoming wide-angle galaxy surveys.
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