Pierre Fleury, Chris Clarkson, Roy Maartens

The Hubble diagram is one of the cornerstones of observational cosmology. It is usually analysed assuming that, on average, the underlying relation between magnitude and redshift or distance and redshift matches the prediction of a Friedmann-Lema\^itre-Robertson-Walker model. However, the inhomogeneity of the Universe generically biases these observables, mainly due to peculiar velocities and gravitational lensing, in a way that depends on the notion of average used in theoretical calculations. In this article, we carefully derive the notion of average which correspond to the observation of the Hubble diagram. We then calculate its bias at second-order in cosmological perturbations, and estimate the consequences on the inference of cosmological parameters, for various current and future surveys. We find that this bias deeply affects direct estimations of the evolution of the dark-energy equation of state. However, errors in the standard inference of cosmological parameters remain smaller than observational uncertainties, even though they reach percent level on some parameters; they reduce to sub-percent level if an optimal distance indicator is used.

G. Risaliti, E. Lusso

The non-linear relation between X-ray and UV luminosity in quasars can be used to estimate their distance. Recently, we have shown that despite the large dispersion of the relation, a Hubble Diagram made of large samples of quasars can provide unique constraints on cosmology at high redshift. Furthermore, the dispersion of the relation is heavily affected by measurement errors: until now we have used serendipitous X-ray observations, but dedicated observations would significantly increase the precision of the distance estimates. We discuss the future role of XMM in this new field, showing (1) the fundamental contribution of the Serendipitous Source Catalogue and of large surveys, and (2) the breakthrough advancements we may achieve with the observation of a large number of SDSS quasars at high redshift: every ~10 quasars observed at z$\sim$3 would be equivalent to discovering a supernova at that redshift.

David Sloan, Pedro Ferreira

We consider a universe with an arbitrary number of extra dimensions, $N$. We present a new method for constructing the cosmological equations of motion and find analytic solutions with an explicit dependence on $N$. When we take the $N\rightarrow\infty$ limit we find novel, emergent behaviour which distinguishes it from normal Kaluza-Klein universes.

Szymon Sikora, Krzysztof Głód

In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein-de Sitter background with a periodically distributed dust overdensities. The model construction enables application of the Green-Wald averaging scheme and the Buchert averaging technique simultaneously. We compare the angular diameter distance function of the considered model to the angular diameter distances corresponding to the average space-times given by the Green-Wald and the Buchert frameworks respectively.

Jiri Novotny

Theory known as Special Galileon has recently attracted considerable interest due to its peculiar properties. It has been shown that it represents an extremal member of the set of effective field theories with enhanced soft limit. This property makes its tree-level S-matrix fully on-shell reconstructible and representable by means of the Cachazo-He-Yuan representation. The enhanced soft limit is a consequence of new hidden symmetry of the Special Galileon action, however, until now, the origin of this peculiar symmetry has remained unclear. In this paper we interpret this symmetry as a special transformation of the coset space $GAL(D,1)/SO(1,D-1)$ and show, that there exists a three-parametric family of invariant Galileon actions. The latter family is closed under duality which appears as a natural generalization of the above mentioned symmetry. We also present a geometric construction of the Special Galileon action using $D$-dimensional brane propagating in $2D$-dimensional flat pseudo-riemannian space. Within such framework, the Special Galileon symmetry emerges as an $U(1,D-1)$ symmetry of the target space, which can be treated as a $D$-dimensional K\"ahler manifold. Such a treatment allows for classification of the higher order invariant Lagrangians needed as counterterms on the quantum level. We also briefly comment on relation between such higher order Lagrangians and the Lagrangians invariant with respect to the polynomial shift symmetry.