We present a novel approach to compute systematically the relativistic projection effects at any order in perturbation theory within the weak field approximation. In this derivation the galaxy number counts is written completely in terms of the redshift perturbation. The relativistic effects break the symmetry along the line-of-sight and they source, contrarily to the standard perturbation theory, the odd multipoles of the matter power spectrum or 2-point correlation function, providing a unique signature for their detection in Large Scale Structure surveys. We show that our approach agrees with previous derivations (up to third order) of relativistic effects and, for the first time, we derive a model for the transverse Doppler effect. Moreover, we show that in the Newtonian limit this approach is consistent with standard perturbation theory at any order.
The galaxy bispectrum is affected on equality scales and above by relativistic observational effects, at linear and nonlinear order. These lightcone effects include local contributions from Doppler and gravitational potential terms, as well as integrated contributions like lensing, together with all the couplings at nonlinear order. We recently presented the correction to the galaxy bispectrum from all local lightcone effects up to second order in perturbations, using a plane-parallel approximation. Here we update our previous result by including the effects from relativistic nonlinear dynamic…
We investigate the corrections which relativistic light-cone computations induce on the correlation of the tangential shear with galaxy number counts, also known as galaxy-galaxy lensing. The standard-approach to galaxy-galaxy lensing treats the number density of sources in a foreground bin as observable, whereas it is in reality unobservable due to the presence of relativistic corrections. We find that already in the redshift range covered by the DES first year data, these currently neglected relativistic terms lead to a systematic correction of up to 50% in the density-shear correlation func…
The main goal of galaxy surveys is to map the distribution of the galaxies, for the purpose of understanding the properties of this distribution and its implications for the content and the evolution of the universe. However, in order to realise the full potential of these surveys, we need to ensure that we are using the correct analysis: a relativistic analysis, which has been widely studied recently. In this work, the known relativistic overdensity of galaxy surveys is re-examined. Unlike in previous works, a consistent approach for incorporating both the relativistic number-count overdensit…
The local galaxy bias formalism relies on the energy constraint equation at the formation time to relate the metric perturbation to the matter density contrast. In the Newtonian approximation, this relationship is linear, which allows us to specify the initial galaxy density as a function of local physical operators. In general relativity however, the relationship is intrinsically nonlinear and a modulation of the short-wavelength mode by the long-wavelength mode might be expected. We describe in detail how to obtain local coordinates where the coupling of the long- to the short-wavelength mod…
The Fourier-space galaxy bispectrum is complex, with the imaginary part arising from leading-order relativistic corrections, due to Doppler, gravitational redshift and related line-of-sight effects in redshift space. The detection of the imaginary part of the bispectrum is potentially a smoking gun signal of relativistic contributions. We investigate whether next-generation spectroscopic surveys could make such a detection. For a Stage IV spectroscopic $Hα$ survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is $\mathcal{O}(10)$. Long-mode relat…
The bispectrum will play an important role in future galaxy surveys. On large scales it is a key probe for measuring primordial non-Gaussianity which can help differentiate between different inflationary models and other theories of the early universe. On these scales a variety of relativistic effects come into play once the galaxy number-count fluctuation is projected onto our past lightcone. We show for the first time that the leading relativistic correction from these distortions in the galaxy bispectrum generates a significant dipole, mainly from relativistic redshift space distortions. Th…
The weak equivalence principle is one of the cornerstone of general relativity. Its validity has been tested with impressive precision in the Solar System, with experiments involving baryonic matter and light. However, on cosmological scales and when dark matter is concerned, the validity of this principle is still unknown. In this paper we construct a null test that probes the validity of the equivalence principle for dark matter. Our test has the strong advantage that it can be applied on data without relying on any modelling of the theory of gravity. It involves a combination of redshift-sp…
We calculate the relativistic corrections to hydrostatic X-ray masses for galaxy clusters in Kottler spacetime, which is the spherically symmetric solution to Einstein's equations in General relativity endowed with a cosmological constant. The hydrostatic masses for clusters (calculated assuming Newtonian gravity) have been found to be underestimated compared to lensing masses, and this discrepancy is known as hydrostatic mass bias. Since the relativistic hydrostatic X-ray masses are automatically lower than lensing masses, under the edifice of Kottler metric, we check if the hydrostatic mass …
Assuming a LCDM 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 intrin…
We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational pote…
Above the equality scale the galaxy bispectrum will be a key probe for measuring primordial non-Gaussianity which can help differentiate between different inflationary models and other theories of the early universe. On these scales a variety of relativistic effects come into play once the galaxy number-count fluctuation is projected onto our past lightcone. By decomposing the Fourier-space bispectrum into invariant multipoles about the observer's line of sight we examine in detail how the relativistic effects contribute to these. We show how to perform this decomposition analytically, which i…
Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power spectrum and bispectrum for high-precision measurements of primordial non-Gaussianity. In turn, these measurements will allow us to distinguish between various models of inflation. However, precision observations require theoretical precision at least at the same level. We extend the theoretical understanding of the galaxy bispectrum by incorporating a consistent general relativistic model of galaxy bias at second order, in the presence of local primordial non-Gaussianity. The influence of primord…
High-resolution, low-noise observations of the cosmic microwave background (CMB) planned for the near-future will enable new cosmological probes based on re-scattered CMB photons -- the secondary CMB. At the same time, enormous galaxy surveys will map out huge volumes of the observable Universe. Using the technique of kinetic Sunyaev Zel'dovich (kSZ) tomography these new probes can be combined to reconstruct the remote dipole field, the CMB dipole as observed from different vantage points in our Universe. The volume accessible to future galaxy surveys is large enough that general relativistic …
The galaxy bispectrum on scales around and above the equality scale receives contributions from relativistic effects. Some of these arise from lightcone deformation effects, which come from local and line-of-sight integrated contributions. Here we calculate the local contributions from the generated vector and tensor background which is formed as scalar modes couple and enter the horizon. We show that these modes are sub-dominant when compared with other relativistic contributions.
Halving and Doubling: Boosting the Detection of Relativistic Effects in the Galaxy Bispectrum with Optimal Subsample Selection
Università degli Studi di Torino（都灵大学）；INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino（意大利国家核物理研究所都灵分部）；INAF – Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino（意大利国家天体物理学研究所都灵天文台）；University of the Western Cape（西开普敦大学）；Queen Mary University of London（伦敦玛丽女王大学）；Università degli Studi di Ferrara（费拉拉大学）
Next generation surveys will be capable of determining cosmological parameters beyond percent level. To match this precision, theoretical descriptions should look beyond the linear perturbations to approximate the observables in large scale structure. A quantity of interest is the Number density of galaxies detected by our instruments. This has been focus of interest recently, and several efforts have been made to explain relativistic effects theoretically, thereby testing the full theory. However, the results at nonlinear level from previous works are in disagreement. We present a new and ind…
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 th…
We present a fully non-linear 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 non-linear 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 (the mean galaxy density as a function of observed redshift) is properly accounted for. We anticipate that this decomposition will be useful for future w…
We compute the dipole of the galaxy correlation function at 1-loop in perturbation theory by including all the relevant relativistic contributions. This provides a description and understanding of what the dipole truly measures, in particular in relation to the gravitational redshift effect in Large Scale Structure. In order to develop this perturbative approach we have computed for the first time the relevant relativistic corrections to third order in perturbation theory, including the corresponding non-linear galaxy bias model. This perturbative approach agrees on a wide range of scales with…
The central regions of galaxy clusters are permeated by magnetic fields and filled with relativistic electrons. When clusters merge, the magnetic fields are amplified and relativistic electrons are re-accelerated by turbulence in the intra cluster medium. These electrons reach energies of 1 -- 10 GeV and, in the presence of magnetic fields, produce diffuse radio halos that typically cover an area of ~1 square Mpc. Here we report observations of four clusters whose radio halos are embedded in much more extended, diffuse radio emission, filling a volume 30 times larger than that of radio halos. …
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 $k^{-4}P_m(k)$ or $k^{-2}P_m(k)$ 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 c…
The observed galaxy distribution via galaxy redshift surveys appears distorted due to redshift-space distortions (RSD). While one dominant contribution to RSD comes from the Doppler effect induced by the peculiar velocity of galaxies, the relativistic effects, including the gravitational redshift effect, are recently recognized to give small but important contributions. Such contributions lead to an asymmetric galaxy clustering along the line of sight, and produce non-vanishing odd multipoles when cross-correlating between different biased objects. However, non-zero odd multipoles are also gen…
We derive an estimator for the lensing potential from galaxy number counts which contains a linear and a quadratic term. We show that this estimator has a much larger signal-to-noise ratio than the corresponding estimator from intensity mapping. We show that this is due to the additional lensing term in the number count angular power spectrum which is present already at linear order. We estimate the signal-to-noise ratio for future photometric surveys. We find that particularly at high redshifts, $z\gtrsim 1.5$, the signal to noise ratio can become of order 30. We therefore claim that number c…
Going beyond the Kaiser redshift-space distortion formula: a full general relativistic account of the effects and their detectability in galaxy clustering
