**Relativistic n-body simulation and the averaged expansion rate**

# Parallel Session: COSMOLOGY - NUMERICAL COSMOLOGY AND SIMULATIONS (J)

## Location: Guildhall Portsmouth

#### J5 - Wednesday 14:00-15:40 (Christian Fidler, Jim Mertens)

**14:00-14:20**

**David Daverio (Theoretical Physics, University of Geneva)**

Structure formation simulation are currently still based on perturbative approaches (Newtonian, Post-Newtonian, weak field,…). It is only recently that effort have been made to develop simulation code based on numerical relativity, ence solving gravity at its fully non-linear level. In this talk, the different relativistic approaches will be discussed focusing on their advantage and drawback. Then the first results on the averaged expansion rate obtained from a fully relativistic n-body simulation will be discussed.

**Observables from Relativistic N-body Simulations**

**14:20-14:40**

**Julian Adamek (School of Physics and Astronomy, Queen Mary University of London)**

As our advanced telescopes produce ever larger and deeper maps of our Universe we need to consider that observations are taken on our past light cone and on a spacetime geometry that is pervaded by small distortions. A precise understanding of the weak-field regime of General Relativity allows one to model these aspects consistently within N-body simulations of cosmic structure formation. Within a unified relativistic picture observables can then be constructed accurately, e.g. with ray-tracing techniques. The subtle relativistic effects in cosmic structure can tell us how gravity operates on the largest scales that we observe and may hold the key to unraveling the mystery of dark energy.

**The trouble with Hubble: a general-relativistic point of view**

**14:40-15:00**

**Hayley Macpherson (DAMTP, University of Cambridge)**

The standard model adopts the cosmological principle; that our Universe is both homogeneous and isotropic on large scales. Small-scale nonlinear structures below the homogeneity scale can affect the expansion of spacetime, light propagation, and hence our observations. The extent to which our observations are affected can only be fully quantified in a general-relativistic framework. I will present simulations of the formation of cosmological large-scale structures using numerical relativity. We investigate the effect of small-scale nonlinear structures on the local expansion rate of spacetime. From this we estimate the expected variance on a local measurement of the Hubble parameter in an inhomogeneous, anisotropic Universe, purely due to the observers physical location. We use this estimate to address the tension between the locally measured and CMB-inferred Hubble parameter.

**GRAMSES: a new route to general relativistic N-body simulations in cosmology**

**15:00-15:20**

**Cristian Barrera-Hinojosa (ICC, Physics Department, Durham University)**

The implementation of general relativistic cosmological simulations has received increasing attention in the last few years, not only as a counterpart to Newtonian simulations in the era of precision cosmology, but also as a natural framework to study phenomena beyond Newtonian cosmology. In this talk, I will give an overview of the recently developed code GRAMSES, an N-body code for nonlinear, general relativistic simulations in cosmology based on RAMSES. I will discuss the key aspects behind its implementation such as the Fully Constrained Formulation of General Relativity, which maximises the number of elliptic-type equations by solving the constraints equations at each time-step and appropriate gauge conditions. I will also present the first results from GRAMSES cosmological simulations in a ΛCDM universe, and how matter, velocity and frame dragging power spectra compare with perturbation theory predictions as well as to Newtonian simulations. In addition, I will briefly discuss some aspects about the generation of initial conditions in terms of particle data for this kind of simulations.

**Turn-around time for the single mode lattice universe with pressureless matter**

**15:20-15:40**

**Chulmoon Yoo (Nagoya University)**

We simulate the time evolution of the single mode lattice universe with pressureless matter. We especially focus on the value of the linear density perturbation at the turn-around time which is given by 1.06 for the spherically symmetric top-hat collapse. The simulation has been done by using a fully general relativistic collisionless particle code. The initial condition is set as the pure growing mode when the perturbation amplitude is small enough. We found that the value of the density perturbation at the turn-around time is greater than 1.06 at the densest point in the single mode lattice universe.

#### J6 - Wednesday 16:10-17:50 (Christian Fidler, Jim Mertens)

**Spatial foliations, averaging and backreaction in relativistic cosmological models and simulations**

**16:10-16:30**

**Pierre Mourier (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Hannover, Germany)**

The late-time Universe features nonlinear regional deviations from strict homogeneity and isotropy as small-scale to large-scale matter structures form. The development of these inhomogeneities may have a non-negligible impact on the expansion dynamics at the largest scales. Such “backreaction” effects can be described in a general-relativistic picture in terms of spatial averages for scalars. The recent relativistic cosmological simulations provide a powerful tool for background-free quantitative estimates of these effects in realistic model universes. In both analytic and numerical approaches, however, particular attention often needs to be paid to the choice of “3+1” foliation of spacetime used to perform spatial averages, and to the consequences of this choice.

I will recall the context of spatial averaging and backreaction in cosmology in a simple case, before showing how such frameworks can be extended to the description of a comoving region of a general fluid source in any spatial foliation. This will allow me to discuss the foliation dependence of the resulting effective dynamics and backreaction terms, and the consequences for the analysis of cosmological simulations. This applies especially when a non–fluid-orthogonal slicing is considered, which can help dealing with instabilities associated with shell-crossings, and is necessary to handle a nonzero vorticity.

**Modelling the halo occupation distribution and clustering properties of emission line galaxies in new-generation cosmological surveys**

**16:30-16:50**

**Ginevra Favole (ICG, Portsmouth University)**

Among star-forming galaxies there is a particular population whose spectra exhibit bright nebular emission lines. These features are generated when young, massive stars in HII regions ionise the surrounding gas particles with subsequent release of high-energy photons. Emission line galaxies (ELGs) will be among the main targets of new-generation spectroscopic surveys such as DESI, Euclid, WFIRST, 4MOST, J-PAS and Subaru PFS. All these instruments will observe [OII] and Hα ELGs out to redshift z~2 to trace the Baryon Acoustic Oscillation (BAO) feature and the redshift-space distortions (RSD) in their clustering signal, measure the growth of structure, reconstruct the cosmic star formation history and fully understand the galaxy formation/evolution mechanisms. They will enable us to build 3D maps of the Universe with unprecedented accuracy and hopefully unveil the nature of dark energy. Therefore, in order to optimally exploit the upcoming missions, it is crucial to understand how to best measure and precisely model the ELG clustering properties, their bias with respect to the underlying dark matter field, and how they populate their host halos. We address these issues by interpreting state-of-the-art data using large-volume, high-resolution cosmological simulations and semi-analytic models of galaxy formation and evolution. The galaxy-halo connection is performed by modifying the standard sub-halo abundance matching (SHAM) prescription to properly account for the ELG stellar mass incompleteness. To conclude, I will also show how SHAM can be used as a powerful tool to constrain the growth history σ8(z).

**Investigating the degeneracy between modified gravity and massive neutrinos with redshift-space distortions**

**16:50-17:10**

**Bill Wright (ICG, Universiy of Portsmouth)**

There is a well known degeneracy between the enhancement of the growth of large-scale structure produced by modified gravity models and the suppression due to the free-streaming of massive neutrinos at late times. This makes the matter power-spectrum alone a poor probe to distinguish between modified gravity and the concordance ΛCDM model when neutrino masses are not strongly constrained.

In this talk, I will examine the potential of using redshift-space distortions (RSD) to break this degeneracy when the modification to gravity is scale-dependent in the form of Hu-Sawicki f(R). I will discuss our findings that if the linear growth rate can be recovered from the RSD signal, the degeneracy can be broken at the level of the dark matter field. However, this requires accurate modelling of the non-linearities in the RSD signal, and I will also introduce an extension of the standard perturbation theory-based model for non-linear RSD that includes both Hu-Sawicki f(R) modified gravity and massive neutrinos. Finally, I shall examine how we intend to develop our method to deal with biased tracers of the underlying dark matter in order to bring us closer to applying this analysis to galaxy clustering data.

**Galaxy clustering from modified gravity hydrodynamical simulations**

**17:10-17:30**

**Cesar Hernandez-Aguayo (Institute for Computational Cosmology, Durham University)**

In this talk, I will show recent results on galaxy clustering from the new SHYBONE (Simulating HYdrodynamics BeyONd Einstein) simulations. We selected a sample of galaxies ranked by stellar mass, luminosity and star formation rate. Also, I will show the shape of the HOD (halo occupation distribution) of those samples.

**Towards Cosmological Simulations Using Deep Generative Models**

**17:30-17:50**

**Andrius Tamosiunas (Institute of Cosmology and Gravitation, University of Portsmouth)**

With the recent discovery of generative adversarial networks (GANs) and variational autoencoders (VAEs) there has been a burst of research in applying these machine learning algorithms for applications in astronomy and cosmology. One exciting area of applications is using deep generative models as computationally cheap and efficient emulators of cosmological large scale structure simulations. GANs trained on N-body simulation data have been shown to produce realistic large scale structure overdensity field data in 2-D and 3-D. Our work aims to improve the currently existing algorithms by applying the newest advancements in machine learning research, such as ideas from Riemannian geometry and geometric deep learning.