<p>Inhomogeneous Cosmologies III<p>

16 Sept 2018, 09:30 → 21 Sept 2018, 17:30 Europe/Warsaw

Inhomogeneous Cosmologies III

Inhomogeneous Cosmologies meetings are small workshops (I, II) of about 40 participants which gather experts in inhomogeneous cosmology. This year it will take place during 16-21 September 2018 at the Jagiellonian University in Kraków, Poland.

Topics will include:
* exact cosmological solutions of the Einstein equations
* averaging and backreaction in cosmology
* numerical cosmological relativity
* observational tests

We will also have practical hands-on tutorials of the Einstein Toolkit and other free-licensed inhomogeneous cosmology software packages. The workshop sessions will start on the morning of Monday the 17th of September and continue to late afternoon of Friday the 21st of September.

Sunday, 16 September

18:00 → 20:00 Welcome refreshments, at the Faculty of Physics

Monday, 17 September

09:00 → 10:00 Monday Session 1

Convener: Nezihe Uzun (Ústav teoretické fyziky MFF UK)

09:00 Inhomogeneous cosmological simulations with numerical relativity

High-precision cosmological surveys are due to deliver measurements accurate to the percent level. In order to ensure we correctly interpret these data, we need to be sure that our cosmological model is accurate. The current standard model assumes that the Universe is homogeneous and isotropic. These assumptions are valid at early times and on very large scales. On smaller scales, these assumptions are called into question. Smaller-scale nonlinear structures will affect light propagation, and hence our observations. The extent our observations will be affected can only be fully addressed with numerical relativity. We use the Einstein Toolkit to perform cosmological evolutions with full numerical relativity. I will present our results of averaging a truly inhomogeneous, anisotropic matter distribution and how this compares to the equivalent FLRW model.

Speaker: Hayley Macpherson (Monash University)

09:30 Exact cosmological models with a peculiar velocity field

I examine two classes of exact solutions of Einstein's equations describing matter-energy sources in a non-comoving frame, either within a single fluid or a two fluid approach. These models can be used to test various assumptions on backreaction and to examine the observational effects of the Hubble flow.

Speaker: Roberto Sussman (ICN-UNAM)

10:00 → 11:00 Coffee Break

11:00 → 12:30 Monday Session 2

Convener: Nezihe Uzun (Ústav teoretické fyziky MFF UK)

11:00 Intrinsic average evolution of a general fluid in arbitrary foliations

Properties and dynamics of an inhomogeneous Universe can be described through regional spatial averaging of scalar observables. In relativistic cosmology, the resulting averaged quantities will depend on the choice of space-like hypersurfaces defining the spatial slices of averaging. I will present a general averaging framework that applies to any choice for such a foliation, and the resulting effective evolution equations for a region of an arbitrary source fluid. It combines a 3+1 "slicing" formalism used to define the averaging hypersurfaces with the general 1+3 "threading" that defines the fluid flow. I will stress the interest of an averaging procedure that focusses as much as possible on intrinsic properties of the fluid content. This helps avoiding artificial dependencies in the choice of foliation. I will also present an example of foliation choices that are themselves built from the fluid flow and that provide compact and transparent averaged evolution equations.

Speaker: Pierre Mourier (Centre de Recherche Astrophysique de Lyon, École Normale Supérieure de Lyon)

11:30 Extremal-foliations and foliation-(in)dependence of averaged quantities

We investigate extremal-foliations and foliation-(in)dependence of averaged space-time quantities, appearing in Buchert's scheme and generalisations hereof. For this purpose we introduce a generalised window-function for spatial hyper surface averaging, and investigate variation of the associated hypersurface-scalar. Surprisingly we find that there are foliation-independent statements to be made about certain physical integrated quantities. However, most integrated/averaged quantities are, not surprisingly, foliation dependent. We discuss methods for bounding the foliation dependence within a class of foliations, and provide physical examples of when such a bound can be useful.

Speaker: Asta Heinesen (University of Canterbury)

12:00 Dark Matter from Backreaction?

In Inhomogeneous Cosmology, restricting attention to an irrotational dust matter model, backreaction arises in terms of the deviation of the averaged spatial scalar curvature from a constant-curvature model, $\mathcal{W_D}$, and the kinematical backreaction, $\mathcal{Q_D}$. The resulting cosmological equations can be written in Friedmannian form featuring an effective scalar field in place of the backreaction, called the morphon field. A simple example for this morphon field is the class of scaling solutions where $\mathcal{W_D}$ and $\mathcal{Q_D}$ are assumed to follow a power law of the volume scale factor $a_\mathcal{D}$. The corresponding exact solutions can describe models of effective quintessence, arising with the morphon, but these and other models still assume the existence of dark matter in addition to the known sources. The contribution from backreaction, however, can change its sign to mimic dark matter-like effects. We here investigate the correspondence between the morphon field and fundamental scalar field dark matter models, in order to describe cosmological dark matter as an effective phenomenon arising from kinematical backreaction and the averaged spatial curvature of the inhomogeneous Universe. We further investigate the inverse problem by starting from exact scaling solutions and approximate solutions for structure formation and determine the properties of the corresponding morphon field.

Speaker: Quentin Vigneron (CRAL, ENSL, Université Lyon 1)

13:00 → 14:00 Lunch

14:00 → 15:00 Roadmap for inhomogeneous cosmology and backreaction

Speaker: Boudewijn Roukema (Toruń Centre for Astronomy, Nicolaus Copernicus University)

Slides https://cosmo.torun.pl/foswiki/bin/view/Cosmo/InhomCosmIII

15:00 → 15:30 Coffee Break

15:30 → 17:30 ET tutorial/workshop

Speaker: Hayley Macpherson (Monash University)

Tuesday, 18 September

09:00 → 10:00 Tuesday Session 1

Convener: Jessie Durk (Queen Mary University of London)

09:00 The most massive virialized objects in the Universe

The existence of the most massive virialized objects can be used as a tool to study properties of the Universe, such as the nature of gravity and dark sector, as well as, the Gaussianity of primordial density fluctuations. In my talk I will show the predictions for the most massive objects in the Universe using the silent universe model (Einstein field equations with no rotation and energy transfer) and the scalar averaging formalism with the Zel'dovich approximation serving as a closure condition. I will present the cosmological mass function of galaxy clusters for both cases and put them in the context of current and future astronomical sky surveys.

Speaker: Jan Ostrowski (Centre de Recherche Astrophysique de Lyon)

09:30 Preventing the Big Rip in a silent universe

The 'Big Rip' is a proposed hypothetical end to the universe where the Hubble parameter increases to infinity in a finite time. It assumes the universe contains a fluid ('dark energy' say) with an equation of state state w<-1 (pressure + density < 0). Caldwell et al give just 20 Gyr until the catastrophe, under assumptions including perfect homogeneity and isotropy, however we show inhomogeneity can prevent the Big Rip. As a rough intuition consider the edge of a galaxy, with negligible expansion inside but the Hubble expansion rate outside, say. This gradient in expansion rate implies shear, but in the Raychaudhuri equation shear reduces the expansion rate. We assume a silent universe, analyse the kinematic parameters as a dynamical system, and obtain exact qualitative results in the parameter space under certain approximations. For a local system the possibilities include collapse, a Big Rip, oscillating expansion and contraction, and various asymptotic cases. Collapse is a good thing because the Rip is prevented, it is then hoped that adding rotation will virialise the system against collapse. Research in conjunction with Krzysztof Bolejko.

Speaker: Colin MacLaurin (University of Queensland)

10:00 → 11:00 Coffee Break

11:00 → 12:30 Tuesday Session 2

Convener: Jessie Durk (Queen Mary University of London)

11:00 Covariant and observer-independent approach to geometric optics in GR

I will present a covariant and observer-independent approach to geometric optics in GR. I will discuss how one can calculate the parallax, the image distortion and magnification and the position drift, including all GR effects, of a distant source using bilocal optical operators. The formalism can be applied to any metric and has potentially important applications to cosmology and relativistic astrophysics.

Speaker: Mikołaj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences)

11:30 The distance - redshift relation in the inhomogeneous universe: improving perturbation theory

We consider an approximation scheme aiming at accounting for the effect of non-linear inhomogeneities in relativistic cosmology at all scales of interest: the perturbations in the space-time metric are considered to be small, but a different weight is given to their first and second spatial derivatives, taking into account that peculiar velocities - corresponding to first spatial derivatives - are small, but allowing the spatial curvature and the density perturbations - corresponding to second spatial derivatives - to be large. We apply this framework to light propagation and discuss the possible improvement of our approach with respect to the standard perturbative description.

Speaker: Eleonora Villa (CFT PAN)

12:00 Reciprocity and symplecticity

Reciprocity relations in physics signal the existence of potentiality of a system. Maxwell-Betti reciprocity for virtual work in elasticity, Onsager's reciprocity in thermodynamics or quantum mechanical reciprocity of the received signal all state that the observables are unchanged when the input and output agents are traversed. Those distinct systems share a similar property: they are defined under some well-defined potential. The work we present here grew out of questioning what kind of potentiality Etherington's distance reciprocity in relativity corresponds to. The outcome of such an investigation turns out to be a symplectic phase space reformulation of first order geometric optics in relativity.

Speaker: Nezihe Uzun (Ústav teoretické fyziky MFF UK)

13:00 → 14:00 Lunch

14:00 → 15:00 Gevolution hackathon

Speaker: Boudewijn Roukema (Toruń Centre for Astronomy, Nicolaus Copernicus University)

15:00 → 15:30 Coffee Break

15:30 → 17:30 Gevolution hackathon

Speaker: Boudewijn Roukema (Toruń Centre for Astronomy, Nicolaus Copernicus University)

Wednesday, 19 September

09:00 → 10:00 Wednesday Session 1

Convener: Hayley Macpherson (Monash University)

09:00 Inhomogeneous Cosmology Whitepaper

Speaker: Boudewijn Roukema (Toruń Centre for Astronomy, Nicolaus Copernicus University)

09:30 Blueshifted light from the last-scattering epoch

Some light rays emitted from the Big Bang (BB) in Lemaitre - Tolman (L-T) and Szekeres (Sz) models reach all observers with an infinite blueshift. This happens when at the emission point the BB function t_B(r) has nonzero derivative and the ray propagates radially (in L-T) or along one of two preferred directions (in Sz). Consequently, some rays emitted during the last scattering period should be reaching us with a finite blueshift. This is a prediction of general relativity, which is an otherwise well-tested theory, so it should be investigated for its consequences for observations. This author recently proposed that blueshifted rays are observed as gamma-ray bursts (GRBs). In four consecutive papers it was shown that (1) L-T-based models of GRB sources successfully account for the energies of the GRBs, the large distances to them, their multitude, and for the existence of the afterglows (but not for the durations of the GRBs and of the afterglows and for their [hypothetical] collimation into narrow jets); (2) In Sz-based models large blueshifts may arise only along two opposite directions, so the collimation is immediately accounted for; (3) A Sz model generates a stronger blueshift than an L-T model with the same BB profile; (4) The short duration of the GRBs is accounted for if the blueshifted ray, on its way to the present observer, passes through another Sz region, where it undergoes the cosmic drift (i.e. a deflection by a time-dependent angle). The last two remaining problems are (i) to account for the measured durations of the afterglows and (ii) to make the angular diameters of the sources in the model compatible with the limits imposed by observations. Work on these is in progress.

Speaker: Andrzej Krasiński (N. Copernicus Astronomical Center, Polish Academy of Sciences)

10:00 → 11:00 Coffee Break

11:00 → 12:00 Wednesday Session 2

Convener: Hayley Macpherson (Monash University)

11:00 Strict solutions in the linear theory of cosmological perturbations up to second order

We consider scalar perturbations of the spatially flat Friedmann--Lemaitre cosmological model. We formulate conditions for the metric functions under which basic gauge-invariant kinematic and dynamic fields of the perturbed model vanish at the first order of the linear perturbation theory. Then we combine these conditions to construct especially interesting perturbed models with specific properties. We particularly study the models with inhomogeneities characterized by the perfect fluid energy-momentum tensor and the models with inhomogeneities which behave monotonically with time. Finally, we perform the strict extension of the simplest cases of the considered models to the second order. We determine necessary assumptions for this development and present explicit solutions for the metric functions.

Speaker: Krzysztof Głód (Astronomical Observatory of the Jagiellonian University)

11:30 The special case of the Stephani solution for the Universe with accelerated expansion

We present the particular case of the Stephani solution for shear-free perfect fluid with uniform energy density and non-uniform pressure. Such models appeared last time as possible alternative to the consideration of the exotic forms of matter like dark energy that would cause the acceleration of the Universe expansion. These models are characterised by the spatial curvature depending on time. We analyze the properties of the cosmological model obtained on the basis of exact solution of the Stephani class and adopt it to the modern observational data. We show that despite of possible singularities, the model can describe the current stage of the Universe evolution. The spatial geometry of the model is investigated. Co-authors: Mariia Churilova, Dr., Dnipropetrovsk National University, Ukraine, Elena Kopteva, Dr., Silesian University in Opava, Czech Republic.

Speakers: Iryna Bormotova (Silesian University in Opava, Czech Republic) , Mariia Churilova (Dnipropetrovsk National University)

13:00 → 14:00 Lunch

14:00 → 15:00 Maxima tutorial

Speaker: Szymon Sikora (Astronomical Observatory, Jagiellonian University)

15:00 → 15:30 Coffee Break

15:30 → 17:30 Maxima ctensor tutorial

Speaker: Boudewijn Roukema (Toruń Centre for Astronomy, Nicolaus Copernicus University)

Thursday, 20 September

09:00 → 10:00 Thursday Session 1

Convener: Szymon Sikora (Astronomical Observatory, Jagiellonian University)

09:00 Black Hole Lattices as Exact, Inhomogeneous Cosmological Models

Black hole lattices are an interesting subset of inhomogeneous cosmologies. These are exact, fully-relativistic treatments of universes with a discretised matter content. We generalise existing lattices to include a cosmological constant and structure formation. For each new generalisation, we find a common behaviour of tending towards FLRW-like as the number of masses is increased, and for the addition of structures, we investigate the effect of gravitational interaction energies between clustered masses. When intra-cluster energies are taken into account, the discrepancy between the scales of lattice and FLRW cosmologies can be alleviated. We also discuss preliminary results of constructing black hole lattices using a simple scalar-tensor theory of gravity and find several solutions – some that admit sensible cosmologies and others that do not, which may place constraints on particular solutions.

Speaker: Jessie Durk (Queen Mary University of London)

09:30 Vacuum initial data on the three-sphere from Killing vectors

We generate initial data for vacuum spacetimes (possibly with cosmological constant) via the conformal method, with a three sphere or a ”three- donut” (the product of a two-sphere with a circle) as "seed metrics". Our motivation comes from black-hole-lattice cosmology. However, in contrast to known schemes for constructing corresponding data, we do not allow for punctures, which prevents us from changing topology. On the other hand, we include the non-linear terms ("cosmological" and "momentum") in the Lichnerowicz equation. We discuss how theorems from differential geometry (Yamabe, Obata, Premoselli) guarantee or exclude the existence of suitable solutions of this equation. We consider two examples: As a warmup, we recall the maximal Kottler (="Schwarzschild de Sitter") data on the three-donut. We then focus on the round three sphere where we take as momentum a transverse, trace-free tensor constructed algebraically out of certain pairs of the sphere’s Killing vectors and their derivatives. This endows the sphere with some "structure" - but not necessarily with black holes. This is joint work with Robert Beig and Piotr Bizo\'n.

Speaker: Walter Simon (University of Vienna)

10:00 → 11:00 Coffee Break

11:00 → 12:00 Thursday Session 2

Convener: Szymon Sikora (Astronomical Observatory, Jagiellonian University)

11:00 Expansion and topology dynamics in dust cosmology

In 2+1 Buchert's dust framework, the Gauss-Bonnet Theorem allows us to identify the Euler characteristic with a mass of topological origin, with positive or negative sign. Even though this does not extend in a straightforward manner to the 3+1 setting, a Theorem of Mess extended by Bonsante and Barbot suggest the insight extend to higher dimension. We explain how the Euler characteristic may evolve in a `sticky particle model': in dimension 2+1, a dust spacetime may be discretized to a flat spacetime with singular lines (massive point-particles); these particles may collide and we assume that at most one massive particle arises from the collision (massive particles are `sticky'). Collisions may give rise to white/black hole which change the topological type of the spacetime and, thus, the Euler characteristic of its Cauchy-surfaces. In such a scenario, Dark Energy arises through the evolution of the Euler characteristic to strongly negative values, corresponding to on average negative spatial curvature.

Speaker: Léo Brunswic (CRAL, ENSL, Université Lyon 1)

11:30 Black holes on cosmological background

In this work, we propose the way to construct the model of the cosmological black hole in the dust-filled universe on the basis of the exact solution to the Einstein equations of the Lemaitre-Tolman-Bondi class. We have found such solution as a particular case of Tolman solution with the arbitrary functions chosen in a special way such that the solution includes both the Schwarzschild and Friedmann solutions as its natural limiting cases. We have analyzed the properties of the obtained solution for the three types of spatial curvature and built the R-T-structure of the resulting spacetime, showing the horizons and singularities of the solution. We have demonstrated that in the center of symmetry of the obtained spacetime there is a region where the black hole is situated. The question of avoiding the shell-crossing in the model was solved. The trajectories of the test particles were built near the black hole for both comoving and distant observer. Although the metric for the distant observer was non-static, we have obtained the physically realistic picture of motion of the test particles around the black hole. From our analysis it follows that within the second order accuracy one will obtain the usual results, but cosmological corrections will appear in the next order. And as far as the obtained solution is exact the cosmological corrections to the Schwarzschild asymptotic may be found analytically up to any order of accuracy.

Speaker: Pavlina Jaluvkova (JINR Dubna, Russia;Silesian university in Opava, Czech Republic)

13:00 → 14:00 Lunch

14:00 → 15:00 ET tutorial/workshop

Speaker: Hayley Macpherson (Monash University)

15:00 → 15:30 Coffee Break

17:00 → 19:00 Cultural Event

19:00 → 21:00 Workshop Dinner

Friday, 21 September

10:00 → 11:00 Coffee Break

11:00 → 12:30 Friday Session 2

Convener: Krzysztof Głód (Astronomical Observatory of the Jagiellonian University)

11:00 First integrals in the cosmological perturbation equations

Darboux transformations convert the cosmological perturbation equations to the form of the d'Alembert equation. Consequently, the Noether constants (the conserved hamiltonian for instance) can be easily found. The exact form of the Darboux transformation, however, is the subject of guess (Field Shepley 1968), what strongly limitates the effectivness of the method. In the present talk we introduce an algorithm for finding the conserved quantities for perturbations. We employ the Darboux algebraic method for dynamical systems with the polynomial right hand side. We use the computer algebra. A simple package for Wolfram Mathematica is written.

Speaker: Andrzej Woszczyna (Politechnika Krakowska)

11:30 The decaying mode and the growing mode in the high order cosmological perturbation theory

During this talk, I will present the method of the construction of the approximate solutions in the framework of the cosmological perturbation theory in the order higher than two. I will restrict to the synchronous gauge and impose the particular symmetry condition by demanding that the metric is invariant under every permutation of the spatial coordinates. In this setup, I will show how to specify the metric functions so that the resulting energy-momentum tensor approximates the dust energy-momentum tensor. I will mention the results obtained with Krzysztof Głód concerning the decaying mode and present the recent results dedicated to the growing mode.

Speaker: Szymon Sikora (Astronomical Observatory, Jagiellonian University)

12:00 Backreaction of gravitational and scalar waves

Within the Green-Wald backreaction framework, one may calculate the effect of small scale inhomogeneities on the global structure of a background spacetime. I will discuss properties of a background spacetime representing cylindrically symmetric high frequency gravitational and scalar standing waves.

Speaker: Sebastian Szybka (Jagiellonian University)

13:00 → 14:00 Lunch

14:00 → 15:00 ET tutorial/workshop

Speaker: Hayley Macpherson (Monash University)

15:00 → 15:30 Coffee Break

15:30 → 16:30 Roadmap for inhomogeneous cosmology and backreaction/summary

Speaker: Thomas Buchert (Université Lyon 1)