Search

Studies show that the model-independent, fully non-perturbative covariant cosmographic approach is suitable for analyzing the local Universe $(z\lesssim 0.1)$. However, accurately characterizing large and inhomogeneous mass distributions requires the fourth-order term in the redshift expansion of the covariant luminosity distance $d_L(z,\boldsymbol{n})$. We calculate the covariant snap parameter $\mathbb{S}$ and its spherical harmonic multipole moments using the matter expansion tensor and the evolution equations for lightray bundles. The fourth-order term adds 36 degrees of freedom, since the highest independent multipole of the snap is the 32-pole (dotriacontapole) $(\ell=5)$. Including this term helps to de-bias estimations of the covariant deceleration parameter. Given that observations suggest axially symmetric anisotropies in the Hubble diagram for $z \lesssim 0.1$ and theory shows that only a subset of multipoles contributes to the signal, we demonstrate that only 12 degrees of freedom are needed for a model-independent description of the local universe. We use an analytical axisymmetric model of the local Universe, with data that matches the Zwicky Transient Facility survey, in order to provide a numerical example of the amplitude of the snap multipoles and to forecast precision., Comment: 13 + 7 pages

Upcoming galaxy surveys aim to map the Universe with unprecedented precision, depth and sky coverage. The galaxy bispectrum is a prime source of information as it allows us to probe primordial non-Gaussianity (PNG), a key factor in differentiating various models of inflation. On the scales where local PNG is strongest, Doppler and other relativistic effects become important and need to be included. We investigate the detectability of relativistic and local PNG contributions in the galaxy bispectrum. We compute the signal-to-noise ratio for the detection of the bispectrum including such effects. Furthermore, we perform information matrix forecasts on the local PNG parameter $f_{\rm NL}$ and on the parametrised amplitudes of the relativistic corrections. Finally, we quantify the bias on the measurement of $f_{\rm NL}$ that arises from neglecting relativistic effects. Our results show that detections of both first- and second-order relativistic effects are promising with forthcoming spectroscopic survey specifications -- and are largely unaffected by the uncertainty in $f_{\rm NL}$. Conversely, we show for the first time that neglecting relativistic corrections in the galaxy bispectrum can lead to $>\!1.5\sigma(f_{\rm NL})$ shift on the detected value of $f_{\rm NL}$, highlighting the importance of including relativistic effects in our modelling., Comment: 28 pages, 8 figures, comments are welcome

The galaxy bispectrum provides access to correlations among different scales that cannot be captured by the power spectrum alone, and with the Stage-IV galaxy surveys it enables the possibility of detecting both primordial non-Gaussianity (PNG) and general relativistic effects. Accounting for wide-separation corrections, which arise from the loss of symmetry in the correlation of widely separated points on the past light cone, is essential for their accurate modelling and detection. These corrections can be included perturbatively to the standard bispectrum and we compute them analytically for a generalised line of sight. We include the radial contribution to the wide-separations corrections for the first time. We show that the first-order corrections entering the odd multipoles with respect to the line of sight are large, up to $10 \%$ of the bispectrum monopole, and need to be included when considering the leading-order relativistic effects that could be detectable with surveys like DESI and Euclid. The second-order wide-separation and relativistic contributions, including their mixing terms, have implications for analysis of PNG and we show, for the local type, they can mimic $f_{\rm NL}$ of order 10 in the squeezed limit. We present full analytic expressions for all these contributions to the local bispectrum and its multipoles with a publicly available code for their computation., Comment: 36 pages, 17 figures. Prepared for submission to JCAP

Upcoming large-scale structure surveys will be able to measure new features in the galaxy two point correlation function. Relativistic effects appear on large scales as subtle corrections to redshift-space distortions, showing up as a dipole and octupole when cross-correlating two different tracers of dark matter. The dipole and octupole are very sensitive to the evolution and magnification biases of the observed tracers which are hard to model accurately as they depend upon the derivative of the luminosity function at the flux limit of the survey. We show that splitting a galaxy population into bright and faint samples allows us to cross-correlate these and constrain both the evolution bias and magnification bias of the two samples -- using the relativistic odd multipoles of the correlation function, together with the even Newtonian multipoles. Although the octupole has much lower signal-to-noise than the dipole, it significantly improves the constraints by breaking parameter degeneracies. We illustrate this in the case of a futuristic survey with the Square Kilometre Array, and demonstrate how splitting the samples in different ways can help improve constraints. This method is quite general and can be used on different types of tracers to improve knowledge of their luminosity functions. Furthermore, the signal-to-noise of the dipole and octupole peaks on intermediate scales, which means that that they can deliver a clean measurement of the magnification bias and evolution bias without contamination from local primordial non-Gaussianities or from systematics on very large scales., Comment: 34 pages, 10 figures, 7 tables

Galaxy surveys contain information on the largest scales via wide-angle and relativistic contributions. By combining two different galaxy populations, we can suppress the strong cosmic variance on ultra-large scales and thus enhance the detectability of the signals. The relativistic Doppler and Sachs-Wolfe effects are of a similar magnitude to the leading wide-angle corrections, so that it is important to treat them together, especially since they can partially cancel. The power spectra depend on the choice of line of sight for each galaxy pair and we present results for a general line of sight. Then we estimate the detection significance of the auto- and cross-power spectra for a variety of cases. We use two futuristic galaxy samples based on a `beyond-DESI' survey and a SKA Phase 2 survey, covering 15,000\,deg$^2$ up to $z=1$. We find a detection significance for the total relativistic wide-angle effects that ranges from $\sim 5\sigma$ to $>15\sigma$, depending on the line-of-sight configuration., Comment: 23 pages, 9 figures, 'version accepted by JCAP'

A major goal of cosmology is to understand the nature of the field(s) which drove primordial Inflation. Through future observations, the statistics of large-scale structure will allow us to probe primordial non-Gaussianity of the curvature perturbation at the end of Inflation. We show how a new correlation statistic can significantly improve these constraints over conventional methods. Next-generation radio telescope arrays are under construction which will map the density field of neutral hydrogen to high redshifts. These telescopes can operate as an interferometer, able to probe small scales, or as a collection of single dishes, combining signals to map the large scales. We show how to fuse these these operating modes in order to measure the squeezed bispectrum with higher precision and greater economy. This leads to constraints on primordial non-Gaussianity that will improve on measurements by Planck, and out-perform other surveys such as Euclid. We forecast that $\sigma(f_{\mathrm{NL}}^{\mathrm{loc}})\sim 3$, achieved by using a small subset, $\mathcal{O}(10^2-10^3)$, of the total number of accessible triangles. The proposed method can be used for any signal that peaks in squeezed configurations., Comment: 13 pages, 6 figures

Recent measurements of the 4-point correlation function in large-scale galaxy surveys have found apparent evidence of parity violation in the distribution of galaxies. This cannot happen via dynamical gravitational effects in general relativity. If such a violation arose from physics in the early Universe it could indicate important new physics beyond the standard model, and would be at odds with most models of inflation. It is therefore now timely to consider the galaxy trispectrum in more detail. While the intrinsic 4-point correlation function, or equivalently the trispectrum, its Fourier counterpart, is parity invariant, the observed trispectrum must take redshift-space distortions into account. Although the standard Newtonian correction also respects parity invariance, we show that sub-leading relativistic corrections do not. We demonstrate that these can be significant at intermediate linear scales and are dominant over the Newtonian parity-invariant part around the equality scale and above. Therefore when observing the galaxy 4-point correlation function, we should expect to detect parity violation on large scales., Comment: 8 pages, 6 figures. v2 has minor errors corrected and additional material and figures. Version to appear in Physical Review Letters

Anisotropies in the distance-redshift relation of cosmological sources are expected due to large-scale inhomogeneities in the local Universe. When the observed sources are tracing a large-scale matter flow in a general spacetime geometry, the distance-redshift relation with its anisotropies can be described with a geometrical prediction that generalises the well-known Friedmann-Lema\^itre-Robertson-Walker result. Furthermore, it turns out that a finite set of multipole coefficients contain the full information about a finite-order truncation of the distance-redshift relation of a given observer. The multipoles of the distance-redshift relation are interesting new cosmological observables that have a direct physical interpretation in terms of kinematical quantities of the underlying matter flow. Using light cones extracted from $N$-body simulations we quantify the anisotropies expected in a $\Lambda$ cold dark matter cosmology by running a Markov chain Monte Carlo analysis on the observed data. In this observational approach the survey selection implements an implicit smoothing scale over which the effective rest frame of matter is fitted. The perceived anisotropy therefore depends significantly on the redshift range and distribution of sources. We find that the multipoles of the expansion rate, as well as the observer's velocity with respect to the large-scale matter flow, can be determined robustly with our approach., Comment: 17 pages, 11 figures; v2: minor revision, accepted version

The disagreement between low- and high-redshift measurements of the Hubble parameter is emerging as a serious challenge to the standard model of cosmology. We develop a covariant cosmographic analysis of the Hubble parameter in a general spacetime, which is fully model-independent and can thus be used as part of a robust assessment of the tension. Here our focus is not on the tension but on understanding the relation between the physical expansion rate and its measurement by observers -- which is critical for model-independent measurements and tests. We define the physical Hubble parameter and its multipoles in a general spacetime and derive for the first time the covariant boost transformation of the multipoles measured by a heliocentric observer. The analysis is extended to the covariant deceleration parameter. Current cosmographic measurements of the expansion anisotropy contain discrepancies and disagreements, some of which may arise because the correct transformations for a moving observer are not applied. A heliocentric observer will detect a dipole, generated not only by a Doppler effect, but also by an aberration effect due to shear. In principle, the observer can measure both the intrinsic shear anisotropy and the velocity of the observer relative to the matter -- without any knowledge of peculiar velocities, which are gauge dependent and do not arise in a covariant approach. The practical implementation of these results is investigated in a follow-up paper. We further show that the standard cosmographic relation between the Hubble parameter, the redshift and the luminosity distance (or magnitude) is not invariant under boosts and holds only in the matter frame. A moving observer who applies the standard cosmographic relation should correct the luminosity distance by a redshift factor -- otherwise an incorrect dipole and a spurious octupole are predicted., Comment: Version accepted by JCAP: additional results and clarifications

Third-generation gravitational wave (GW) observatories such as the Einstein Telescope and Cosmic Explorer, together with the LSST survey at the Vera Rubin Observatory, will yield an abundance of extra-galactic transient objects. This opens the exciting possibility of using GW sources and Supernovae Type Ia (SNIa) as luminosity distance tracers of large-scale structure for the first time. The large volumes accessible to these surveys imply that we may need to include relativistic corrections, such as lensing and Doppler magnification. However, the amplitude of these effects depends on the magnification and evolution biases of the transient sources, which are not yet understood. In this paper we develop comprehensive frameworks to address and model these biases for both populations of transient objects; in particular, we define how to compute these biases for GW sources. We then analyse the impact of magnification and evolution biases on the relativistic corrections and on the angular power spectrum of these sources. We show that correct modelling and implementation of these biases is crucial for measuring the cross-correlations of transient sources at higher redshifts., Comment: 28 pages, 14 figures, 4 tables, comments welcome

The power spectrum and bispectrum of dark matter tracers are key and complementary probes of the Universe. Next-generation surveys will deliver good measurements of the bispectrum, opening the door to improved cosmological constraints and the breaking of parameter degeneracies, from the combination of the power spectrum and bispectrum. Multi-tracer power spectra have been used to suppress cosmic variance and mitigate the effects of nuisance parameters and systematics. We present a bispectrum multi-tracer formalism that can be applied to next-generation survey data. Then we perform a simple Fisher analysis to illustrate qualitatively the improved precision on primordial non-Gaussianity that is expected to come from the bispectrum multi-tracer. In addition, we investigate the parametric dependence of conditional errors from multi-tracer power spectra and multi-tracer bispectra, on the differences between the biases and the number densities of two tracers. Our results suggest that optimal constraints arise from maximising the ratio of number densities, the difference between the linear biases, the difference between the quadratic biases, and the difference between the products $b_1\,b_\Phi$ for each tracer, where $b_\Phi$ is the bias for the primordial potential., Comment: 30 pages, 7 figures, JCAP version

Next generation surveys will provide us with an unprecedented number of detections of supernovae Type Ia and gravitational wave merger events. Cross-correlations of such objects offer novel and powerful insights into the large-scale distribution of matter in the universe. Both of these sources carry information on their luminosity distance, but remain uninformative about their redshifts; hence their clustering analyses and cross-correlations need to be carried out in luminosity distance space, as opposed to redshift space. In this paper, we calculate the full expression for the number count fluctuation in terms of a perturbation to the observed luminosity distance. We find the expression to differ significantly from the one commonly used in redshift space. Furthermore, we present a comparison of the number count angular power spectra between luminosity distance and redshift spaces. We see a wide divergence between the two at large scales, and we note that lensing is the main contribution to such differences. On such scales and at higher redshifts the difference between the angular power spectra in luminosity distance and redshift spaces can be roughly 50$\%$. We also investigate cross-correlating different redshift bins using different tracers, i.e. one in luminosity distance space and one in redshift, simulating the cross-correlation angular power spectrum between background gravitational waves/supernovae and foreground galaxies. Finally, we show that in a cosmic variance limited survey, the relativistic corrections to the density-only term ought to be included., Comment: 34 pages, 9 figures, 1 table. Agrees with published version

The Cosmological Principle is part of the foundation that underpins the standard model of the Universe. In the era of precision cosmology, when stress tests of the standard model are uncovering various tensions and possible anomalies, it is critical to check the viability of this principle. A key test is the consistency between the kinematic dipoles of the cosmic microwave background and of the large-scale matter distribution. Results using radio continuum and quasar samples indicate a rough agreement in the directions of the two dipoles, but a larger than expected amplitude of the matter dipole. The resulting tension with the radiation dipole has been estimated at $\sim 5\sigma$ for some cases, suggesting a potential new cosmological tension and a possible violation of the CP. However, the standard formalism for predicting the dipole in the two-dimensional projection of sources overlooks possible evolution effects in the luminosity function. In fact, radial information from the luminosity function is necessary for a correct projection of the three-dimensional source distribution. Using a variety of current models of the quasar luminosity function, we show that neglecting redshift evolution can significantly overestimate the relative velocity amplitude. While the models we investigate are consistent with each other and with current data, the dipole derived from these, which depends on derivatives of the luminosity function, can disagree by more than $3\sigma$. This theoretical systematic bias needs to be resolved before robust conclusions can be made about a new cosmic tension., Comment: 13 pages, 3 figures, 2 tables. Version published in The Astrophysical Journal

We examine the computation of wide-angle corrections to the galaxy power spectrum including redshift-space distortions and relativistic Doppler corrections, and also including multiple tracers with differing clustering, magnification and evolution biases. We show that the inclusion of the relativistic Doppler contribution, as well as radial derivative terms, are crucial for a consistent wide-angle expansion for large-scale surveys, both in the single and multi-tracer cases. We also give for the first time the wide-angle cross-power spectrum associated with the Doppler magnification-galaxy cross correlation, which has been shown to be a new way to test general relativity. In the full-sky power spectrum, the wide-angle expansion allows integrals over products of spherical Bessel functions to be computed analytically as distributional functions, which are then relatively simple to integrate over. We give for the first time a complete discussion and new derivation of the finite part of the divergent integrals of the form $\int_{0}^{\infty} \mathrm{d} r r^{n} j_{\ell}(k r) j_{\ell^{\prime}}(q r)$, which are necessary to compute the wide-angle corrections when a general window function is included. This facilitates a novel method for integrating a general analytic function against a pair of spherical Bessel functions., Comment: 41 pages and 2 figures. V3 has substantial improvements and new results. V4 is to appear in JCAP

We combine cosmic chronometer and growth of structure data to derive the redshift evolution of the dark energy equation of state $w$, using a novel agnostic approach. The background and perturbation equations lead to two expressions for $w$, one purely background-based and the other relying also on the growth rate of large-scale structure. We compare the features and performance of the growth-based $w$ to the background $w$, using Gaussian Processes for the reconstructions. We find that current data is not precise enough for robust reconstruction of the two forms of $w$. By using mock data expected from next-generation surveys, we show that the reconstructions will be robust enough and that the growth-based $w$ will out-perform the background $w$. Furthermore, any disagreement between the two forms of $w$ will provide a new test for deviations from the standard model of cosmology., Comment: 10 pages, 6 figures. Version accepted in Physics of the Dark Universe

The Universe may feature large-scale inhomogeneities beyond the standard paradigm, implying that statistical homogeneity and isotropy may be reached only on much larger scales than the usually assumed $\sim$100 Mpc. This means that we are not necessarily typical observers and that the Copernican principle could be recovered only on super-Hubble scales. Here, we do not assume the validity of the Copernican principle and let Cosmic Microwave Background, Baryon Acoustic Oscillations, type Ia supernovae, local $H_0$, cosmic chronometers, Compton y-distortion and kinetic Sunyaev-Zeldovich observations constrain the geometrical degrees of freedom of the local structure, which we parametrize via the $\Lambda$LTB model -- basically a non-linear radial perturbation of a FLRW metric. In order to quantify if a non-Copernican structure could explain away the Hubble tension, we pay careful attention to computing the Hubble constant in an inhomogeneous universe, and we adopt model selection via both the Bayes factor and the Akaike information criterion. Our results show that, while the $\Lambda$LTB model can successfully explain away the $H_0$ tension, it is favored with respect to the $\Lambda$CDM model only if one solely considers supernovae in the redshift range that is used to fit the Hubble constant, that is, $0.023

Measurements of galaxy clustering in upcoming surveys such as those planned for the Euclid and Roman satellites, and the SKA Observatory, will be sensitive to distortions from lensing magnification and Doppler effects, beyond the standard redshift-space distortions. The amplitude of these contributions depends sensitively on magnification bias and evolution bias in the galaxy number density. Magnification bias quantifies the change in the observed number of galaxies gained or lost by lensing magnification, while evolution bias quantifies the physical change in the galaxy number density relative to the conserved case. These biases are given by derivatives of the number density, and consequently are very sensitive to the form of the luminosity function. We give a careful derivation of the magnification and evolution biases, clarifying a number of results in the literature. We then examine the biases for a variety of surveys, encompassing galaxy surveys and line intensity mapping at radio and optical/near-infrared wavelengths., Comment: Typo corrected in equation (A.10)

In this paper, we study how to directly measure the effect of peculiar velocities in the observed angular power spectra. We do this by constructing a new anti-symmetric estimator of Large Scale Structure using different dark matter tracers. We show that the Doppler term is the major component of our estimator and we show that we can measure it with a signal-to-noise ratio up to $\sim 50$ using a futuristic SKAO HI galaxy survey. We demonstrate the utility of this estimator by using it to provide constraints on the Euler equation., Comment: 24 pages, 9 figures, 4 tables. Updated explanations. Agrees with published version

We pursue a program to confront observations with inhomogeneous extensions of the FLRW metric. The main idea is to test the Copernican principle rather than assuming it a priori. We consider the $\Lambda$CDM model endowed with a spherical $\Lambda$LTB inhomogeneity around us, that is, we assume isotropy and test the hypothesis of homogeneity. We confront the $\Lambda$LTB model with the latest available data from CMB, BAO, type Ia supernovae, local $H_0$, cosmic chronometers, Compton y-distortion and kinetic Sunyaev-Zeldovich effect. We find that these data can constrain tightly this extra inhomogeneity, almost to the cosmic variance level: on scales $\gtrsim 100$ Mpc structures can have a small non-Copernican effective contrast of just $\delta_L \sim 0.01$. Furthermore, the constraints on the standard $\Lambda$CDM parameters are not weakened after marginalizing over the parameters that model the local structure, to which we assign ignorance priors. In other words, dropping the Copernican principle assumption does not imply worse constraints on the cosmological parameters. This positive result confirms that the present and future data can be meaningfully analyzed within the framework of inhomogeneous cosmology., Comment: 13 pages, 6 figures, 2 tables, v2 reflects version accepted for publication in MNRAS

Next-generation large-scale structure surveys will deliver a significant increase in the precision of growth data, allowing us to use `agnostic' methods to study the evolution of perturbations without the assumption of a cosmological model. We focus on a particular machine learning tool, Gaussian processes, to reconstruct the growth rate $f$, the root mean square of matter fluctuations $\sigma_8$, and their product $f\sigma_8$. We apply this method to simulated data, representing the precision of upcoming Stage IV galaxy surveys. We extend the standard single-task approach to a multi-task approach that reconstructs the three functions simultaneously, thereby taking into account their inter-dependence. We find that this multi-task approach outperforms the single-task approach for future surveys and will allow us to detect departures from the standard model with higher significance. By contrast, the limited sensitivity of current data severely hinders the use of agnostic methods, since the Gaussian processes parameters need to be fine tuned in order to obtain robust reconstructions., Comment: 14 pages; 7 figures; Significant improvements. Version accepted by Phys. Dark Universe

Two-parameter perturbation theory (2PPT) is a framework designed to include the relativistic gravitational effects of small-scale nonlinear structures on the large-scale properties of the Universe. In this paper we use the 2PPT framework to calculate and study the bispectrum of matter in a spatially-flat $\Lambda$CDM cosmology. This is achieved by deploying Newtonian perturbation theory to model the gravitational fields of quasi-nonlinear structures, and then subsequently using them as source terms for the large-scale cosmological perturbations. We find that our approach reproduces some of the expected relativistic effects from second-order cosmological perturbation theory, but not all. This work therefore provides a first step in deploying a formalism that can simultaneously model the weak gravitational fields of both linear and nonlinear structures in a realistic model of the Universe., Comment: 21 pages, 10 figures

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 primordial non-Gaussianity on the bispectrum extends beyond the galaxy bias and the dark matter density, due to redshift-space effects. The standard redshift-space distortions at first and second order produce a well-known primordial non-Gaussian imprint on the bispectrum. Relativistic corrections to redshift-space distortions generate new contributions to this primordial non-Gaussian signal, arising from: (1)~a coupling of first-order scale-dependent bias with first-order relativistic observational effects, and (2)~linearly evolved non-Gaussianity in the second-order velocity and metric potentials which appear in relativistic observational effects. Our analysis allows for a consistent separation of the relativistic `contamination' from the primordial signal, in order to avoid biasing the measurements by using an incorrect theoretical model. We show that the bias from using a Newtonian analysis of the squeezed bispectrum could be $\Delta \fnl\sim 5$ for a Stage IV H$\alpha$ survey., Comment: Version accepted by JCAP (JCAP_030P_1220) + 18 pages + 4 figures + appendices + references

The standard cosmological model is inherently relativistic, and yet a wide range of cosmological observations can be predicted accurately from essentially Newtonian theory. This is not the case on `ultra-large' distance scales, around the cosmic horizon size, however, where relativistic effects can no longer be neglected. In this paper, we present a novel suite of 53 fully relativistic simulations generated using the gevolution code, each covering the full sky out to $z \approx$ 0.85, and approximately 1930 square degrees out to $z \approx$ 3.55. These include a relativistic treatment of massive neutrinos, as well as the gravitational potential that can be used to exactly calculate observables on the past light cone. The simulations are divided into two sets, the first being a set of 39 simulations of the same fiducial cosmology (based on the Euclid Flagship 2 cosmology) with different realisations of the initial conditions, and the second which fixes the initial conditions, but varies each of seven cosmological parameters in turn. Taken together, these simulations allow us to perform statistical studies and calculate derivatives of any relativistic observable with respect to cosmological parameters. As an example application, we compute the cross-correlation between the Doppler magnification term in the convergence, $\kappa_v$, and the CDM+baryon density contrast, $\delta_{\rm cb}$, which arises only in a (special) relativistic treatment. We are able to accurately recover this term as predicted by relativistic perturbation theory, and study its sample variance and derivatives with respect to cosmological parameters., Comment: 9 pages, 6 figures, corresponds to published version

We investigate the detectability of leading-order relativistic effects in the bispectrum of future 21cm intensity mapping surveys. The relativistic signal arises from Doppler and other line-of-sight effects in redshift space. In the power spectrum of a single tracer, these effects are suppressed by a factor $\cH^2/k^2$. By contrast, in the bispectrum the relativistic signal couples to short-scale modes, leading to an imaginary contribution that scales as $\cH/k$, thus increasing the possibility of detection. Previous work has shown that this relativistic signal is detectable in a Stage IV H$\alpha$ galaxy survey. {We show that the signal is also detectable by next-generation 21cm intensity maps, but typically with a lower signal-to-noise, due to foreground and telescope beam effects., Comment: 18 pages, 12 figures, Version accepted by JCAP

Planned efforts to probe the largest observable distance scales in future cosmological surveys are motivated by a desire to detect relic correlations left over from inflation, and the possibility of constraining novel gravitational phenomena beyond General Relativity (GR). On such large scales, the usual Newtonian approaches to modelling summary statistics like the power spectrum and bispectrum are insufficient, and we must consider a fully relativistic and gauge-independent treatment of observables such as galaxy number counts in order to avoid subtle biases, e.g. in the determination of the $f_{\rm NL}$ parameter. In this work, we present an initial application of an analysis pipeline capable of accurately modelling and recovering relativistic spectra and correlation functions. As a proof of concept, we focus on the non-zero dipole of the redshift-space power spectrum that arises in the cross-correlation of different mass bins of dark matter halos, using strictly gauge-independent observable quantities evaluated on the past light cone of a fully relativistic N-body simulation in a redshift bin $1.7 \le z \le 2.9$. We pay particular attention to the correct estimation of power spectrum multipoles, comparing different methods of accounting for complications such as the survey geometry (window function) and evolution/bias effects on the past light cone, and discuss how our results compare with previous attempts at extracting novel GR signatures from relativistic simulations., Comment: Minor corrections in the text of version 2

We perform null tests of the concordance model, using $H(z)$ measurements that mimic next-generation surveys such as Euclid and the SKA. To this end, we deploy a non-parametric method, so that we make minimal assumptions about the fiducial cosmology as well as the statistical analysis. We produce simulations assuming different cosmological models in order to verify how well we can distinguish between their signatures. We find that SKA- and Euclid-like surveys should be able to discriminate sharply between the concordance and alternative dark energy models that are compatible with the Planck CMB data. We conclude that SKA and Euclid will be able to falsify the concordance model in a statistically significant way, if one of the benchmarks models represents the true Universe, without making assumptions about the underlying cosmology., Comment: Revised manuscript, minor edition, conclusions unchanged. To appear in Phys. Dark Univ

We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first-order in the vector part, frame dragging. Integrating the photon geodesics backwards from the observer to the emitters, we solve the Sachs optical equations and study in detail the weak-lensing convergence, ellipticity and rotation. For the first time, we apply such an analysis to a high-resolution relativistic N-body simulation, which consistently includes the leading-order corrections due to general relativity on both large and small scales. These are related to the question of gauge choice and to post-Newtonian corrections, respectively. We present the angular power spectra and one-point probability distribution functions for the weak-lensing variables, which we find are broadly in agreement with comparable Newtonian simulations. Our geometric approach, however, is more robust and flexible, and can therefore be applied consistently to non-standard cosmologies and modified theories of gravity., Comment: 20 pages, 17 figures, corresponds to published version

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 is significantly faster for subsequent computations. While all multipoles receive a contribution from the relativistic part, odd multipoles arising from the imaginary part of the bispectrum have no Newtonian contribution, making the odd multipoles a smoking gun for a relativistic signature in the bispectrum for single tracers. The dipole and the octopole are significant on equality scales and above where the Newtonian approximation breaks down. This breakdown is further signified by the fact that the even multipoles receive a significant correction on very large scales., Comment: v3 has improved presentation. Version accepted by JCAP

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 $H\alpha$ survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is $\mathcal{O}(10)$. Long-mode relativistic effects couple to short-mode Newtonian effects in the galaxy bispectrum, but not in the galaxy power spectrum. This is the basis for detectability of relativistic effects in the bispectrum of a single galaxy survey, whereas the power spectrum requires multiple galaxy surveys to detect the corresponding signal., Comment: 13 pages, 10 figures, Typo in equation (3.8) corrected - results unchanged

Two-parameter perturbation theory is a scheme tailor-made to consistently include nonlinear density contrasts on small scales ($<100\; \mathrm{Mpc}$), whilst retaining a traditional approach to cosmological perturbations in the long-wavelength universe. In this paper we study the solutions that arise from this theory in a spatially-flat dust-filled cosmology, and what these imply for the bispectrum of matter. This is achieved by using Newtonian perturbation theory to model the gravitational fields of nonlinear structures in the quasi-linear regime, and then using the resulting solutions as source terms for the cosmological equations. We find that our approach results in the leading-order part of the cosmological gravitational potentials being identical to those that result from standard cosmological perturbation theory at second-order, while the dark matter bispectrum itself yields some differences on Hubble scales. This demonstrates that our approach is sufficient to capture most leading-order relativistic effects, but within a framework that is far easier to generalize. We expect this latter property to be particularly useful for calculating leading-order relativistic corrections to the matter power spectrum, as well as for deriving predictions for relativistic effects in alternative theories of gravity., Comment: 51 pages, 14 figures

The rate at which the universe is expanding today is a fundamental parameter in cosmology which governs our understanding of structure formation and dark energy. However, current measurements of the Hubble constant, $H_0$, show a significant tension ($\sim 4-6\sigma$) between early- and late-Universe observations. There are ongoing efforts to check the diverse observational results and also to investigate possible theoretical ways to resolve the tension~-- which could point to radical extensions of the standard model. Here we demonstrate the potential of next-generation spectroscopic galaxy surveys to shed light on the Hubble constant tension. Surveys such as those with Euclid and the Square Kilometre Array (SKA) are expected to reach sub-percent precision on Baryon Acoustic Oscillation (BAO) measurements of the Hubble parameter, with a combined redshift coverage of $0.1

The main science driver for the coming generation of cosmological surveys is understanding dark energy which relies on testing General Relativity on the largest scales. Once we move beyond the simplest explanation for dark energy of a cosmological constant, the space of possible theories becomes both vast and extremely hard to compute realistic observables. A key discriminator of a cosmological constant, however, is that the growth of structure is scale-invariant on large scales. By carefully weighting observables derived from distributions of galaxies and a dipole pattern in their apparent sizes, we construct a null test which vanishes for any model of gravity or dark energy where the growth of structure is scale-independent. It relies only on very few assumptions about cosmology, and does not require any modelling of the growth of structure. We show that with a survey like DESI a scale-dependence of the order of 10-20 percent can be detected at 3 sigma with the null test, which will drop by a factor of 2 for a survey like the Square Kilometre Array. We also show that the null test is very insensitive to typical uncertainties in other cosmological parameters including massive neutrinos and scale-dependent bias, making this a key null test for dark energy., Comment: v1: 6 pages, 3 figures. v2: 6 pages, 4 figures, new paragraph on non-linearities, matches version published in MNRAS Letters

The weak gravitational lensing formalism can be extended to the strong lensing regime by integrating a nonlinear version of the geodesic deviation equation. The resulting "roulette" expansion generalises the notion of convergence, shear and flexion to arbitrary order. The independent coefficients of this expansion are screen space gradients of the optical tidal tensor which approximates to the usual lensing potential in the weak field limit. From lensed images, knowledge of the roulette coefficients can in principle be inverted to reconstruct the mass distribution of a lens. In this paper, we simplify the roulette expansion and derive a family of recursion relations between the various coefficients, generalising the Kaiser-Squires relations beyond the weak-lensing regime., Comment: 18 pages, 1 figure

The beyond-Horndeski gravity has recently been reformulated in the dark energy paradigm - which has been dubbed, Unified Dark Energy (UDE). The evolution equations for the given UDE appear to correspond to a non-conservative dark energy scenario, in which the total energy-momentum tensor is not conserved. We investigate both the background cosmology and, the large-scale imprint of the UDE by probing the angular power spectrum of galaxy number counts, on ultra-large scales; taking care to include the full relativistic corrections in the observed overdensity. The background evolution shows that only an effective mass smaller than the Planck mass is needed in the early universe in order for predictions in the given theory to match current observational constraints. We found that the effective mass-evolution-rate parameter, which drives the evolution of the UDE, acts to enhance the observed power spectrum and, hence, relativistic effects (on ultra-large scales) by enlarging the UDE sound horizon. Conversely, both the (beyond) Horndeski parameter and the kineticity act to diminish the observed power spectrum, by decreasing the UDE sound horizon. Our results show that, in a universe with UDE, a multi-tracer analysis will be needed to detect the relativistic effects in the large-scale structure. In the light of a multi-tracer analysis, the various relativistic effects hold the potential to distinguish different gravity models. Moreover, while the Doppler effect will remain significant at all epochs and, thus can not be ignored, the integrated Sachs-Wolfe, the time-delay and the potential (difference) effects, respectively, will only become significant at epochs near z=3 and beyond, and may be neglected at late epochs. In the same vein, the Doppler effect alone can serve as an effective cosmological probe for the large-scale structure or gravity models, in the angular power spectrum - at all z., Comment: 28 pages, 13 figures. Version accepted by JCAP

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 modes is removed through a change of coordinates (in the absence of the primordial non-Gaussianity). We derive the general-relativistic correction to the galaxy bias expansion at second order. The correction does not come from the modulation of small-scale clustering by the long-wavelength mode; instead, it arises from distortions of the volume element by the long-wavelength mode and it does not lead to new bias parameters., Comment: Version accepted by JCAP. Key contributions clearly summarised. Few typos fixed

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. The amplitude of the dipole can be more than 10% of the monopole even on equality scales. Such a dipole is absent in the Newtonian approximation to the redshift space bispectrum, so it offers a clear signature of relativistic effects on cosmological scales in large scale structure., Comment: 5 pages, 2 figures. v2 has slight changes to the figures and is the version to appear in MNRAS Letters

An important part of cosmological model fitting relies on correlating distance indicators of objects (for example type Ia supernovae) with their redshift, often illustrated on a Hubble diagram. Comparing the observed correlation with a homogeneous model is one of the key pieces of evidence for dark energy. The presence of cosmic structures introduces a bias and scatter, mainly due to gravitational lensing and peculiar velocities, but also due to smaller non-linear relativistic contributions which are more difficult to account for. For the first time we perform ray tracing onto halos in a relativistic N-body simulation. Our simulation is the largest that takes into account all leading-order corrections from general relativity in the evolution of structure, and we present a novel methodology for working out the non-linear projection of that structure onto the observer's past light cone. We show that the mean of the bias in the Hubble diagram is indeed as small as expected from perturbation theory. However, the distribution of sources is significantly skewed with a very long tail of highly magnified objects and we illustrate that the bias of cosmological parameters strongly depends on the function of distance which we consider., Comment: 6 pages, 3 figures; v2: some additional analysis, matches accepted version

Weak lensing will play an important role in future cosmological surveys, including e.g. Euclid and SKA. Sufficiently accurate theoretical predictions are important for correctly interpreting these surveys and hence for extracting correct cosmological parameter estimations. We quantify for the first time in a relativistic setting how many post-Born and lens-lens coupling corrections are required for sub-percent accuracy of the theoretical weak lensing convergence for $z\le 2$ (the primary weak lensing range for Euclid and SKA). We do this by ray-tracing through a fully relativistic exact solution of the Einstein Field Equations which consists of randomly packed mass-compensated underdensities of realistic amplitudes. We find that including lens-lens coupling terms and post-Born corrections up to second and third order respectively is sufficient for sub-percent accuracy of the convergence along $94\%$ of the studied light rays. We also find that a significant percentage of the studied rays have post-Born corrections of size over $10\%$ of the usual gravitational convergence, $\kappa^{(1)}$, and several rays even have post-Born corrections several times the size of $\kappa^{(1)}$ at $z = 2$., Comment: 5 pages, 4 figures. v2: More data added with figures and text changed appropriately. Overall results unchanged. v3: Significant changes to presentation to match published version. Overall results unchanged

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., Comment: 14 pages, 4 figures. v2 has minor changes, to appear in JCAP

The apparent sizes and brightnesses of galaxies are correlated in a dipolar pattern around matter overdensities in redshift space, appearing larger on their near side and smaller on their far side. The opposite effect occurs for galaxies around an underdense region. These patterns of apparent magnification induce dipole and higher multipole terms in the cross-correlation of galaxy number density fluctuations with galaxy size/brightness (which is sensitive to the convergence field). This provides a means of directly measuring peculiar velocity statistics at low and intermediate redshift, with several advantages for performing cosmological tests of GR. In particular, it does not depend on empirically-calibrated scaling relations like the Tully-Fisher and Fundamental Plane methods. We show that the next generation of spectroscopic galaxy redshift surveys will be able to measure the Doppler magnification effect with sufficient signal-to-noise to test GR on large scales. We illustrate this with forecasts for the constraints that can be achieved on parametrised deviations from GR for forthcoming low-redshift galaxy surveys with DESI and SKA2. Although the cross-correlation statistic considered has a lower signal to noise than RSD, it will be a useful probe of GR since it is sensitive to different systematics., Comment: Version accepted by MNRAS. Significant expansion of results and improvements in the interpretation