77 research outputs found

    Proper-Time Hypersurface of Non-Relativistic Matter Flows: Galaxy Bias in General Relativity

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    We compute the second-order density fluctuation in the proper-time hypersurface of non-relativistic matter flows and relate it to the galaxy number density fluctuation in general relativity. At the linear order, it is equivalent to the density fluctuation in the comoving synchronous gauge, in which two separate gauge conditions coincide. However, at the second order, the density fluctuations in these gauge conditions differ, while both gauge conditions represent the proper-time hypersurface. Compared to the density fluctuation in the temporal comoving and the spatial C-gauge conditions, the density fluctuation in the commonly used gauge condition (N=1N=1 and Nα=0N^\alpha=0) violates the mass conservation at the second order. We provide their physical interpretations in each gauge condition by solving the geodesic equation and the nonlinear evolution equations of non-relativistic matter. We apply this finding to the second-order galaxy biasing in general relativity, which complements the second-order relativistic description of galaxy clustering in Yoo & Zaldarriaga (2014).Comment: 16 pages, no figures, accepted for publication in PR

    Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average

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    Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their theoretical description is verified by checking its gauge-invariance. We argue that cosmological observables are invariant scalars under diffeomorphisms and as a consequence their theoretical description is gauge-invariant, only at linear order in perturbations. Beyond linear order, they are usually not gauge-invariant, and we provide the general law for the gauge-transformation that the perturbation part of an observable does obey. We apply this finding to derive the second-order expression for the observational light-cone average in cosmology and demonstrate that our expression is indeed invariant under diffeomorphisms.Comment: 16 pages, no figures, published in JCA

    Light-Cone Observables and Gauge-Invariance in the Geodesic Light-Cone Formalism

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    The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.Comment: 25 pages, no figures, published in JCA

    Jacobi Mapping Approach for a Precise Cosmological Weak Lensing Formalism

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    Cosmological weak lensing has been a highly successful and rapidly developing research field since the first detection of cosmic shear in 2000. However, it has recently been pointed out in Yoo et al. that the standard weak lensing formalism yields gauge-dependent results and, hence, does not meet the level of accuracy demanded by the next generation of weak lensing surveys. Here, we show that the Jacobi mapping formalism provides a solid alternative to the standard formalism, as it accurately describes all the relativistic effects contributing to the weak lensing observables. We calculate gauge-invariant expressions for the distortion in the luminosity distance, the cosmic shear components and the lensing rotation to linear order including scalar, vector and tensor perturbations. In particular, the Jacobi mapping formalism proves that the rotation is fully vanishing to linear order. Furthermore, the cosmic shear components contain an additional term in tensor modes which is absent in the results obtained with the standard formalism. Our work provides further support and confirmation of the gauge-invariant lensing formalism needed in the era of precision cosmology.Comment: 33 pages, no figures, published in JCA

    Relativistic effects in galaxy clustering in a parametrized post-Friedmann universe

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    We explore the signatures of quintessence and modified gravity theories in the relativistic description of galaxy clustering within a parametrized post-Friedmann framework. For this purpose, we develop a calibration method to consistently account for horizon-scale effects in the linear parametrized Post-Friedmann perturbations of minimally and nonminimally coupled scalar-tensor theories and test it against the full model-specific fluctuations. We further study the relativistic effects in galaxy clustering for the normal and self-accelerating branches of the Dvali-Gabadadze-Porrati braneworld model as well as for phenomenological modifications of gravity. We quantify the impact of modified gravity and dark energy models on galaxy clustering by computing the velocity-to-matter density ratio F, the velocity contribution R, and the potential contribution P and give an estimate of their detectability in future galaxy surveys. Our results show that, in general, the relativistic correction contains additional information on gravity and dark energy, which needs to be taken into account in consistent horizon-scale tests of departures from LCDM using the galaxy-density field.Comment: 24 pages, 7 figures, 1 table; v2 matches published versio

    Joint Analysis of Gravitational Lensing, Clustering and Abundance: Toward the Unification of Large-Scale Structure Analysis

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    We explore three different methods based on weak lensing to extract cosmological constraints from the large-scale structure. In the first approach (method I), small-scale galaxy lensing measurements of their halo mass provide a constraint on the halo bias, which can be combined with the large-scale galaxy clustering to measure the dark matter clustering. In the second approach (method II), large-scale galaxy clustering and large-scale galaxy-galaxy lensing can be combined into a direct measurement of the dark matter clustering. These two methods can be combined into one method I+II to make use of lensing measurements on all scales. In the third approach (method III), we add abundance information to the method I. We explore the statistical power of these three approaches as a function of galaxy luminosity to investigate the optimal mass range for each method and their cosmological constraining power. In the case of the SDSS, we find that the three methods give comparable constraints, but not in the same mass range: the method II works best for halos of M~10^13 Msun, and the methods I and III work best for halos of M~10^14 Msun. We discuss the robustness of each method against various systematics. Furthermore, we extend the analysis to the future large-scale galaxy surveys and find that the cluster abundance method is not superior to the combined method I+II, both in terms of statistical power and robustness against systematic errors. The cosmic shear-shear correlation analysis in the future surveys yields constraints as strong as the combined method, but suffer from additional systematic effects. We thus advocate the combined analysis of clustering and lensing (method I+II) as a powerful alternative to other large-scale probes. Our analysis provides a guidance to observers planning large-scale galaxy surveys such as the DES, Euclid, and the LSST.Comment: published in PRD, 19 pages, 9 figure