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Advances in Research on Theories of the Dark Universe - Inhomogeneity Effects in Relativistic Cosmology

Periodic Reporting for period 2 - ARTHUS (Advances in Research on Theories of the Dark Universe - Inhomogeneity Effects in Relativistic Cosmology)

Reporting period: 2019-03-01 to 2020-08-31

The project ARTHUS aims at determining the physical origin of Dark Energy: in addition to the energy sources of the standard model of cosmology, effective terms arise through spatially averaging inhomogeneous cosmological models in General Relativity. It has been demonstrated that these additional terms can play the role of Dark Energy on large scales (but they can also mimic Dark Matter on scales of mass accumulations). The underlying rationale is that fluctuations in the Universe generically couple to spatially averaged intrinsic properties of space, such as its averaged scalar curvature, thus changing the global evolution of the effective (spatially averaged) cosmological model. At present, we understand these so-called backreaction effects only qualitatively. The project ARTHUS is directed towards a conclusive quantitative evaluation of these effects by developing generic and non-perturbative relativistic models of structure formation, by statistically measuring the key variables of the models in observations and in simulation data, and by reinterpreting observational results in light of the new models. It is to be emphasized that there is no doubt about the existence of backreaction effects; the question is whether they are even capable of getting rid of the dark sources (as some models discussed in the literature suggest), or whether their impact is substantially smaller. The project thus addresses an essential issue of current cosmological research: to find pertinent answers concerning the quantitative impact of inhomogeneity effects, a necessary, worldwide recognized step toward high-precision cosmology. If the project objectives are attained, the results will have a far-reaching impact on theoretical and observational cosmology, on the interpretation of astronomical experiments such as Planck and Euclid, as well as on a wide spectrum of particle physics theories and experiments.
For Axis A, four publications resulted: [ ],
[ ], [ ] and, since the start of the ERC postdoc of Asta Heinesen we have written a response to a vividly discussed subject in the literature [ ]: meanwhile, the standard model of cosmology is considered under `tension' (up to 5-sigma for the Hubble parameter), and a positive curvature at the CMB epoch is discussed. We provided a show case as a proof-of-concept for solving these tensions within a dark energy-free model.
Furthermore, a Letter clarifying a discussion in the community on Newtonian backreaction has been published by the PI [ ]. An editorial note has been written by the PI related to insights and a dictionary used in Axis A between Newtonian theory and general relativity [ ].

For Axis B, we developed statistical tools complementary to the Minkowski functionals. Three publications resulted, one concerning the statistics themselves [ ], the other as an application to CMB data with a discovery of a new anomaly
[ ], one further with some complementary tools
[ ].
The PI is member of and has communicated observational predictions for the forthcoming surveys Euclid and 4MOST; for 4MOST see [ ].

For Axis C, we concentrated on closure conditions of the averaged equations using topological constraints [ ].
Also, for Axis C, we have already found two key-answers to important questions of the project. We could answer two criticisms that were raised in the community, namely (i) the dependence on this foliation choice and (ii) the covariance of the averaged equations.
To (i): the Letter [ ] provides an astonishingly simple answer to a general treatment of foliations. The Letter is based on a large paper that has been published as
`Editor's Choice Research Article' [ ].
To (ii): the covariance, built into the scheme, but now explicitly demonstrated with a four-dimensional averaging scheme that has potential for further applications [ ].

For Axes A and C, we further already attacked the question of whether dark matter could be explained by backreaction effects [ ]. We also pursued another approach for the question of closure in terms of a numerical realization of the `silent universe hypothesis’ (Jan Ostrowski) [ ]. ERC postdoc Nezihe Uzun aims to achieve even model-independent distance relations
[ ]. Furthermore, an invited conference paper that covers all aspects of the project has been written by the PI: [ ].
One main result forms a breakthrough on a key-question of ARTHUS: Is the averaging formalism covariant, and does the result strongly depend on how we foliate the space-time ? The article [ ] provides the answer 'yes', demonstrated explicitly by using a four-dimensional averaging scheme, and the article [ ] demonstrates a weak dependence of the results on the foliation of space-time on cosmological scales, contrary to what has been claimed in the literature based on non-covariant schemes.
The latter reference has been highlighted by the journal with an insight comment
[ ], and the results cumulated in a longer article that has been awarded the status of 'Editor's Choice Research Article'
[ ].

A further key-question of ARTHUS could be substantially advanced. We succeeded, along a 'high-risk route', to obtain a unique further equation that governs the evolution of those 'backreaction terms' that potentially replace the dark components in the standard model of cosmology. This route went deep into the mathematical discipline of topology pursued with the mathematician Léo Brunswic (ERC postdoc) [ ]. With these results we also found two links to results of Axis A. While closure is not achieved yet, these results form a significant (and unexpected) step forward to justify our optimism of achieving our goal - a general description of the average evolution of the Universe.

A direct answer to the main question of ARTHUS, i.e. whether we can explain observations without the need for dark energy, has been given with the astonishing outcome that not only we find a dark energy-free model to explain supernova observations
[ ], but also that we simultaneously solved further questions that were recently raised in the community [ ].

Until the end of the project we shall aim at enhancing and finalizing the results above.
We have furthermore obtained many 'solid' results on models and statistical tools, their application falling into the second mid-term of ARTHUS. Here, we concentrate on the morpho-statistical analysis of observational data (Cosmic Microwave Background for finite universe models, analysis of galaxy catalogs and new interpretations of the catalogs with distance measures that account for the curvature evolution, updated supernova catalogs to improve our results).
an illustration of non-Gaussianity in Cosmic Microwave Background simulations and Planck data
an illustration of topological analysis tools for the Cosmic Microwave Background
an illustration of the evolution of curvature and backreaction that can replace dark matter
an illustration of Cosmic MIcrowave Background simulations