17 research outputs found

    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

    Cosmological Information Contents on the Light-Cone

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    We develop a theoretical framework to describe the cosmological observables on the past light cone such as the luminosity distance, weak lensing, galaxy clustering, and the cosmic microwave background anisotropies. We consider that all the cosmological observables include not only the background quantity, but also the perturbation quantity, and they are subject to cosmic variance, which sets the fundamental limits on the cosmological information that can be derived from such observables, even in an idealized survey with an infinite number of observations. To quantify the maximum cosmological information content, we apply the Fisher information matrix formalism and spherical harmonic analysis to cosmological observations, in which the angular and the radial positions of the observables on the light cone carry different information. We discuss the maximum cosmological information that can be derived from five different observables: (1) type Ia supernovae, (2) cosmic microwave background anisotropies, (3) weak gravitational lensing, (4) local baryon density, and (5) galaxy clustering. We compare our results with the cosmic variance obtained in the standard approaches, which treat the light cone volume as a cubic box of simultaneity. We discuss implications of our formalism and ways to overcome the fundamental limit.Comment: 39 pages, no figures, submitted to JCA

    Non-Gaussianity in the squeezed three-point correlation from the relativistic effects

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    Assuming a ΛCDM universe in a single-field inflationary scenario, we compute the three-point correlation function of the observed matter density fluctuation in the squeezed triangular configuration, accounting for all the relativistic effects at the second order in perturbations. This squeezed three-point correlation function characterizes the local-type primordial non-Gaussianity, and it has been extensively debated in literature whether there exists a prominent feature in galaxy clustering on large scales in a single-field inflationary scenario either from the primordial origin or the intrinsic nonlinearity in general relativity. First, we show that theoretical descriptions of galaxy bias are incomplete in general relativity due to ambiguities in spatial gauge choice, while those of cosmological observables are independent of spatial gauge choice. Hence a proper relativistic description of galaxy bias is needed to reach a definitive conclusion in galaxy clustering. Second, we demonstrate that the gauge-invariant calculations of the cosmological observables remain unaffected by extra coordinate transformations like CFC or large diffeomorphism like dilatation. Finally, we show that the relativistic effects associated with light propagation in observations cancel each other, and hence there exists no non-Gaussian contribution from the so-called projection effects in the squeezed three-point correlation function

    Galaxy Power Spectrum in General Relativity

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    We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to k−4Pm(k)k^{-4}P_m(k) or k−2Pm(k)k^{-2}P_m(k) on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at k≲keqk\lesssim k_{eq}, they need to be taken into account in the analysis of large-scale data.Comment: 29 pages, 10 figures, accepted for publication in JCA

    General relativistic effects in weak lensing angular power spectra

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    Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. The wide sky coverage of Euclid makes angular scales down to lmin=10 accessible. At such large angular scales, general relativistic effects manifest themselves, and the lensing magnification cannot be correctly described by the standard lensing convergence only. The impact of line-of-sight velocities on the magnification angular power spectrum, referred to as the Doppler magnification, is already well recognized in literature. In particular, it was suggested that the Doppler magnification could be extracted by measurements of both cosmic shear and magnification. In this work, we point out two previously neglected aspects with respect to this method. First, the impact of the Doppler magnification is reduced through nonvanishing cross terms with the standard lensing convergence. This is particularly relevant when the sources are averaged over a bin of width Δz≈0.1, such as in Euclid’s tomographic weak lensing survey. Second, general relativistic potential terms slightly enhance the signal. We present numerical calculations of all relativistic effects in the weak lensing angular power spectra on large scales

    General Relativistic Effects in Cosmological Weak Lensing

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    New measurements of EGE_G: Testing General Relativity with the Weyl potential and galaxy velocities

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    International audienceWe combine measurements of galaxy velocities from galaxy surveys with measurements of the Weyl potential from the Dark Energy Survey to test the consistency of General Relativity at cosmological scales. Taking the ratio of two model-independent observables - the growth rate of structure and the Weyl potential - we obtain new measurements of the EGE_G statistic with precision of 5.8−10.7%5.8-10.7\% at four different redshifts. These measurements provide a considerable improvement to past measurements of EGE_G. They confirm the validity of General Relativity at three redshifts, while displaying a tension of 2.5σ2.5\sigma at z=0.47z=0.47 as a consequence of the tension found in the measurements of the Weyl potential. Contrary to conventional methods that rely on a common galaxy sample with spectroscopic resolution to measure two types of correlations, we directly combine two observables that are independent of the galaxy bias. This provides a novel approach to testing the relation between the geometry of our Universe and the motion of galaxies with improved precision

    First measurement of the Weyl potential evolution from the Year 3 Dark Energy Survey data: Localising the σ8\sigma_8 tension

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    International audienceWe present the first measurement of the Weyl potential at four redshifts bins using data from the first three years of observations of the Dark Energy Survey (DES). The Weyl potential, which is the sum of the spatial and temporal distortions of the Universe's geometry, provides a direct way of testing the theory of gravity and the validity of the Λ\LambdaCDM model. We find that the measured Weyl potential is 2.3σ\sigma, respectively 3.1σ\sigma, below the Λ\LambdaCDM predictions in the two lowest redshift bins. We show that these low values of the Weyl potential are at the origin of the σ8\sigma_8 tension between Cosmic Microwave Background (CMB) measurements and weak lensing measurements. Interestingly, we find that the tension remains if no information from the CMB is used. DES data on their own prefer a high value of the primordial fluctuations, followed by a slow evolution of the Weyl potential. A remarkable feature of our method is that the measurements of the Weyl potential are model-independent and can therefore be confronted with any theory of gravity, allowing efficient tests of models beyond General Relativity
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