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Covariant Decomposition of The Nonlinear Galaxy Number Counts and Their Monopole.

TL;DR: In this article, the authors present a fully nonlinear and relativistically covariant expression for the observed galaxy density contrast, based on a null tetrad tailored to the cosmological observer's past light cone.
Abstract: We present a fully nonlinear and relativistically covariant expression for the observed galaxy density contrast. Building on a null tetrad tailored to the cosmological observer's past light cone, we find a decomposition of the nonlinear galaxy over-density into manifestly gauge-invariant quantities, each of which has a clear physical interpretation as a cosmological observable. This ensures that the monopole of the galaxy over-density field is properly accounted for. We anticipate that this decomposition will be useful for future work on nonlinearities in galaxy number counts, for example, deriving the relativistic expression for the galaxy bispectrum. We then specialise our results to conformal Newtonian gauge, with a Hubble parameter either defined globally or measured locally, illustrating the significance of the different contributions to the observed monopole of the galaxy density.
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TL;DR: In this article , the weak lensing Jacobi map is computed at first order in perturbation theory and it is shown to be both, gauge invariant and symmetric.
Abstract: We compute the weak lensing Jacobi map at first order in perturbation theory and show that it is both, gauge invariant and symmetric. Linear perturbations therefore do not induce any rotation. However, vector and tensor perturbations do induce B-modes in the shear. We show that contrary to what is often claimed in the literature, the shear B-mode power spectrum is not fully determined by the rotation power spectrum. Also the E-mode shear power spectrum is not determined by the convergence power spectrum. While this difference is small for scalar perturbations, it becomes very significant for tensor perturbations, i.e. gravitational waves.

5 citations

Journal ArticleDOI
TL;DR: In this paper , a fully nonlinear gauge-invariant formalism for describing the cosmological observables was developed and the second-order perturbative expressions associated with light propagation and observations without choosing a gauge condition.
Abstract: Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light propagation and observations without choosing a gauge condition. For the first time, we have performed a complete verification of the validity of our second-order expressions by comparing their gauge-transformation properties from two independent methods: one directly obtained from their expressions in terms of metric perturbations and the other expected from their nonlinear relations. The expressions for the cosmological observables such as galaxy clustering and the luminosity distance are invariant under diffeomorphism and gauge-invariant at the observed position. We compare our results to the previous work and discuss the differences in the perturbative expressions. Our second-order gauge-invariant formalism constitutes a major step forward in the era of precision cosmology and its applications in the future will play a crucial role for going beyond the power spectrum and probing the early universe.

4 citations

Journal ArticleDOI
TL;DR: In this article , the authors derived the expressions on the observed light-cone for some relevant cosmological gauge invariant variables, such as the Mukhanov-Sasaki variable and E- and B- modes of the tensor perturbations.
Abstract: We derive the expressions on the observed light-cone for some relevant cosmological gauge invariant variables, such as the Mukhanov-Sasaki variable and E- and B- modes of the tensor perturbations. Since the structure of the light-cone does not reflect in a direct way the FLRW symmetries, we develop a formalism which is coordinate independent and classifies the perturbations according to their helicities. Even though we work with linear perturbations, our formalism can be readily extended to non-linear theory and put the basis to study the evolution of cosmological perturbations, since the early- until the late-time Universe, directly along the observed light-cone.

2 citations

References
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Book
01 Jan 1972
TL;DR: In this paper, the General Theory of Relativity and Feneral Relativity are discussed, as well as applications of feneral relativity in cosmology and cosmology.
Abstract: Preface. Notation. Copyright Acknowledgements. Part One Preliminaries. Part Two the General Theory of Relativity. Part Three Applications of Feneral Relativity. Part Four Formal Developments. Part Five Cosmology. Appendix. Some Useful Numbers. Index.

4,056 citations

Book
19 May 2003
TL;DR: A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.
Abstract: A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

3,502 citations

Journal ArticleDOI
TL;DR: In this paper, a spinor affine connection is proposed for general relativity by means of a tetrad or spinor formalism, which is applied to two problems in radiationtheory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.
Abstract: A new approach to general relativity by means of a tetrad or spinor formalism is presented. The essential feature of this approach is the consistent use of certain complex linear combinations of Ricci rotation coefficients which give, in effect, the spinor affine connection. It is applied to two problems in radiationtheory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.

2,320 citations

Book
01 Jan 1984
TL;DR: The calculus of 2-spinors was introduced and systematically developed in this article, which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations.
Abstract: This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.

2,260 citations