No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology, including: What physical process gave birth to the Universe we see today? What are the dark matter and dark energy that seem to constitute 95% of the energy density of the Universe? Do we need extensions to the standard model of particle physics and fundamental interactions? Is the ΛCDM cosmological scenario correct, or are we missing an essential piece of the puzzle? In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the CORE space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. CORE has 19 frequency channels, distributed over a broad frequency range, spanning the 60-600 GHz interval, to control astrophysical foreground emission. The angular resolution ranges from 2 to 18 , and the aggregate CMB sensitivity is about 2 µK.arcmin. The observations are made with a single integrated focal-plane instrument, consisting of an array of 2100 cryogenically-cooled, linearly-polarised detectors at the focus of a 1.2-m aperture cross-Dragone telescope. The mission is designed to minimise all sources of systematic effects, which must be controlled so that no more than 10 −4 of the intensity leaks into polarisation maps, and no more than about 1% of E-type polarisation leaks into B-type modes. CORE observes the sky from a large Lissajous orbit around the Sun-Earth L2 point on an orbit that offers stable observing conditions and avoids contamination from sidelobe pick-up of stray radiation originating from the Sun, Earth, and Moon. The entire sky is observed repeatedly during four years of continuous scanning, with a combination of three rotations of the spacecraft over different timescales. With about 50% of the sky covered every few days, this scan strategy provides the mitigation of systematic effects and the internal redundancy that are needed to convincingly extract the primordial B-mode signal on large angular scales, and check with adequate sensitivity the consistency of the observations in several independent data subsets. CORE is designed as a "near-ultimate" CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation science and cannot be obtained by any other means than a dedicated space mission. It will provide well-characterised, highly-redundant multi-frequency observations of polarisation at all the scales where foreground emission and cosmic variance dominate the final uncertainty for obtaining precision CMB science, as well as 2 angular resolution maps of high-frequency foreground emission in the 300-600 GHz frequency range, essential for complementarity w...

Abstract. It has recently been suggested by Luminet et al. (2003) that the WMAP data are better matched by a geometry in which the topology is that of a Poincaré dodecahedral model and the curvature is "slightly" spherical, rather than by an (effectively) infinite flat model. A general back-to-back matched circles analysis by Cornish et al. (2004) for angular radii in the range 25−90• , using a correlation statistic for signal detection, failed to support this. In this paper, a matched circles analysis specifically designed to detect dodecahedral patterns of matched circles is performed over angular radii in the range 1−40• on the oneyear WMAP data. Signal detection is attempted via a correlation statistic and an rms difference statistic. Extreme value distributions of these statistics are calculated for one orientation of the 36• "screw motion" (Clifford translation) when matching circles, for the opposite screw motion, and for a zero (unphysical) rotation. The most correlated circles appear for circle radii of α = 11 ± 1• , for the left-handed screw motion, but not for the right-handed one, nor for the zero rotation. The favoured six dodecahedral face centres in galactic coordinates are (l• ) and their opposites. The six pairs of circles independently each favour a circle angular radius of 11 ± 1• . The temperature fluctuations along the matched circles are plotted and are clearly highly correlated. Whether or not these six circle pairs centred on dodecahedral faces match via a 36• rotation only due to unexpected statistical properties of the WMAP ILC map, or whether they match due to global geometry, it is clear that the WMAP ILC map has some unusual statistical properties which mimic a potentially interesting cosmological signal.

We summarise some of the main observational challenges for the standard FriedmannLemaître-Robertson-Walker cosmological model and describe how results recently presented in the parallel session "Large-scale Structure and Statistics" (DE3) at the "Fourteenth Marcel Grossman Meeting on General Relativity" are related to these challenges.Keywords: large-scale structure; cosmic microwave background; statistics; generalrelativistic effects PACS numbers: 98.80.Es, 98.80.Jk, 95.36.+x, Observational Challenges for the ΛCDM ModelDespite the many well-known successes of the FLRW model with its standard parameter values, henceforth denoted the ΛCDM model, there is a wide range of observations with which it significantly disagrees. The statistical significance of these disagreements is very often debated from a Bayesian perspective. If the ΛCDM is accepted as being consistent with general relativity, then one must contend with a posteriori statistics, also called the look elsewhere effect, which globally requires ǎ Sidàk-Bonferonni correction [1] for assessing overall statistical significance. On the other hand, interpretation of structure formation within the ΛCDM model is to a large degree based on Newtonian physics-N -body simulations are widely seen as providing state-of-the-art ways of comparing the FLRW model to observational catalogues-but in comparison to general relativity, the former should be assigned an extremely weak prior.a Although precise tests of general relativity have led to * BFR: During invited lectureship. a For example, Keplerian orbits are disfavoured in relation to general-relativistic orbits at a significance level of more than 100σ [2] based on the periastron decay of the Hulse-Taylor pulsar B1913+16 [3] (See Fig. 2

A method of deriving and using merging history trees of dark matter galaxy haloes directly from pure gravity N-body simulations is presented. This combines the full nonlinearity of N-body simulations with the flexibility of the semi-analytical approach.Merging history trees derived from power-law initial perturbation spectrum simulations (for indices n = −2 and n = 0) by Warren et al. (1992) are shown. As an example of a galaxy formation model, these are combined with evolutionary stellar population synthesis, via simple scaling laws for star formation rates, showing that if most star formation occurs during merger-induced bursts, then a nearly flat faint-end slope of the galaxy luminosity function may be obtained in certain cases.Interesting properties of hierarchical halo formation are noted: (1) In a given model, merger rates may vary widely between individual haloes, and typically 20%∼30% of a halo's mass may be due to infall of uncollapsed material. (2) Small mass haloes continue to form at recent times: as expected, the existence of young, low redshift, low metallicity galaxies (e.g., Izotov et al. 1997) is consistent with hierarchical galaxy formation models. (3) For n = −2, the halo spatial correlation function can have a very high initial bias due to the high power on large scales.

One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an exactly identical copy of our Milky Way. Would we really cling on to the assumption of infinitely many identical repetitions of the same world? . . . We would be much happier with the view that these repetitions are illusory, that in reality space has peculiar connection properties so that if we leave any one cube through a side, then we immediately reenter it through the opposite side." (Schwarzschild 1900(Schwarzschild , translation 1998 Developments in the theoretical and observational sides of cosmic topology were slow for most of the century, but are now progressing rapidly, at the scale of most interest which is 1-10h −1 Gpc rather than 10kpc.The historical, mathematical and observational sides of this subject are briefly reviewed in this course. J J J J J J J J

Context. In a flat space, it has been shown heuristically that the global topology of comoving space can affect the dynamics expected in the weak-field Newtonian limit, inducing a weak acceleration effect similar to dark energy. Aims. Does a similar effect occur in the case of the Poincaré dodecahedral space, which is a candidate model of comoving space for solving the missing fluctuations problem observed in cosmic microwave background all-sky maps? Moreover, does the effect distinguish the Poincaré space from other well-proportioned spaces? Methods. The acceleration effect in the Poincaré space S 3 /I * is studied, using a massive particle and a nearby test particle of negligible mass. Calculations are made in S 3 embedded in R 4 . The weak-limit gravitational attraction on a test particle at distance r is set to be ∝[R C sin(r/R C )] −2 rather than ∝r −2 , where R C is the curvature radius, in order to satisfy Stokes' theorem. A finite particle horizon large enough to include the adjacent topological images of the massive particle is assumed. The regular, flat, 3-torus T 3 is re-examined, and two other well-proportioned spaces, the octahedral space S 3 /T * , and the truncated cube space S 3 /O * , are also studied. Results. The residual gravity effect occurs in all four cases. In a perfectly regular 3-torus of side length L a , and in the octahedral and truncated cube spaces, the highest order term in the residual acceleration is the third-order term in the Taylor expansion in powers of r/L a (3-torus), or r/R C , respectively. However, the Poincaré dodecahedral space is unique among the four spaces. The third order cancels, leaving the fifth order term ∼±300(r/R C ) 5 as the most significant. Conclusions. Not only are three of the four perfectly regular well-proportioned spaces better balanced than most other multiply connected spaces in terms of the residual gravity acceleration effect by a factor of about a million (setting r/L a = r/R C ∼ 10 −3 ), but the fourth of these spaces is about ten thousand times better balanced than the other three. This is the Poincaré dodecahedral space. Is this unique dynamical property of the Poincaré space a clue towards a theory of cosmic topology?

Context. Understanding dark energy and measuring the topology of the Universe are two of the biggest open questions in physical cosmology. It was previously shown that multiple connectedness, via the twin paradox of special relativity, provides a novel physical justification for an assumption of the standard FLRW model: it implies a favoured space-time splitting (comoving coordinates). Aims. Could cosmic topology also imply dark energy? Methods. We use a weak field (Newtonian) approximation of gravity and consider the gravitational effect from distant, multiple copies of a large, collapsed (virialised) object today (i.e. a massive galaxy cluster), taking into account the finite propagation speed of gravity, in a flat, multiply connected universe, and assume that due to a prior epoch of fast expansion (e.g. inflation), the gravitational effect of the distant copies is felt locally, from beyond the naïvely calculated horizon. Results. We find that for a universe with a T 1 × R 2 spatial section, the residual Newtonian gravitational force (to first order) provides an anisotropic effect that repels test particles from the cluster in the compact direction, in a way algebraically similar to that of dark energy. For a typical test object at comoving distance χ from the nearest dense nodes of the cosmic web of density perturbations, the pressure-to-density ratio w of the equation of state in an FLRW universe, is3 , where L is the size of the fundamental domain, i.e. of the Universe. Clearly, |w| 1. For a T 3 spatial section of exactly equal fundamental lengths, the effect cancels to zero. For a T 3 spatial section of unequal fundamental lengths, the acceleration effect is anisotropic in the sense that it will tend to equalise the three fundamental lengths. Conclusions. Provided that at least a modest amount of inflation occurred in the early Universe, and given some other conditions, multiple connectedness does generate an effect similar to that of dark energy, but the amplitude of the effect at the present epoch is too small to explain the observed dark energy density and its anisotropy makes it an unrealistic candidate for the observed dark energy.