Covariant decomposition of the non-linear galaxy number counts and their monopole

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 work on non-linearities 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.

Observing relativistic features in large-scale structure surveys – I: Multipoles of the power spectrum

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 fNL 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 ≤ z ≤ 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.

A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology

ABSTRACT El Gordo (ACT-CL J0102-4915) is an extremely massive galaxy cluster (M200 ≈ 3 × 1015 M⊙) at redshift z = 0.87 composed of two subclusters with a mass ratio of 3.6 merging at speed Vinfall ≈ 2500 km s−1. Such a fast collision between individually rare massive clusters is unexpected in Lambda cold dark matter (ΛCDM) cosmology at such high z. However, this is required for non-cosmological hydrodynamical simulations of the merger to match its observed properties. Here, we determine the probability of finding a similar object in a ΛCDM context using the Jubilee simulation box with a side length of $6 \, h^{-1}$ Gpc. We search for galaxy cluster pairs that have turned around from the cosmic expansion with properties similar to El Gordo in terms of total mass, mass ratio, redshift, and collision velocity relative to virial velocity. We fit the distribution of pair total mass quite accurately, with the fits used in two methods to infer the probability of observing El Gordo in the surveyed region. The more conservative (and detailed) method involves considering the expected distribution of pairwise mass and redshift for analogue pairs with similar dimensionless parameters to El Gordo in the past light-cone of a z = 0 observer. Detecting one pair with its mass and redshift rules out ΛCDM cosmology at 6.16σ. We also use the results of Kraljic and Sarkar to show that the Bullet Cluster is in 2.78σ tension once the sky coverage of its discovery survey is accounted for. Using a χ2 approach, the combined tension can be estimated as 6.43σ. Both collisions arise naturally in a Milgromian dynamics (MOND) cosmology with light sterile neutrinos.

Evolution of cosmological horizons of wormhole cosmology

Recently, we solved Einstein’s field equations to obtain the exact solution of the cosmological model with the Morris–Thorne-type wormhole. We found the apparent horizons and analyzed their geometric natures, including the causal structures. We also derived the Hawking temperature near the apparent cosmological horizon. In this paper, we investigate the dynamic properties of the apparent horizons under the matter-dominated universe and lambda-dominated universe. As a more realistic universe, we also adopt the [Formula: see text]CDM universe which contains both the matter and lambda. The past light cone and the particle horizon are examined for what happens in the case of the model with wormhole. Since the spatial coordinates of the spacetime with the wormhole are limited outside the throat, the past light cone can be operated by removing the smaller-than-wormhole region. The past light cones without wormhole begin to start earlier than the past light cones with wormhole in conformal time-proper distance coordinates. The light cone consists of two parts: the information from our universe and the information from other universe or far distant region through the wormhole. Therefore, the particle horizon distance determined from the observer’s past light cone cannot be defined in a unique way.

Radiation from a D-dimensional collision of shock waves: Two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two [Formula: see text]-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Is the Universe homogeneous?

The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret observations of the cosmic microwave background (CMB) and the galaxy distribution. However, homogeneity cannot be directly observed in the galaxy distribution or CMB, even with perfect observations, since we observe on the past light cone and not on spatial surfaces. We can directly observe and test for isotropy, but to link this to homogeneity we need to assume the Copernican principle (CP). First, we discuss the link between isotropic observations on the past light cone and isotropic space–time geometry: what observations do we need to be isotropic in order to deduce space–time isotropy? Second, we discuss what we can say with the Copernican assumption. The most powerful result is based on the CMB: the vanishing of the dipole, quadrupole and octupole of the CMB is sufficient to impose homogeneity. Real observations lead to near-isotropy on large scales—does this lead to near-homogeneity? There are important partial results, and we discuss why this remains a difficult open question. Thus, we are currently unable to prove homogeneity of the Universe on large scales, even with the CP. However, we can use observations of the cosmic microwave background, galaxies and clusters to test homogeneity itself.