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

Project Information

ARTHUS

Grant agreement ID: 740021

DOI

10.3030/740021

Project closed

EC signature date 18 April 2017

Start date 1 September 2017

End date 31 August 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 091 000,00

EU contribution

€ 2 091 000,00

Coordinated by

UNIVERSITE LYON 1 CLAUDE BERNARD
France

Periodic Reporting for period 4 - ARTHUS (Advances in Research on Theories of the Dark Universe - Inhomogeneity Effects in Relativistic Cosmology)

Reporting period: 2022-03-01 to 2023-08-31

Summary of the context and overall objectives of the project

The project ARThUs aimed at determining the physical origin of Dark Energy and Dark Matter: 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 the beginning of this project, we understood these so-called backreaction effects only qualitatively. The project ARThUs was directed towards a conclusive quantitative evaluation of these effects by developing generic and nonperturbative 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, or whether their impact is substantially smaller. The project thus addressed 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. In the case where the project objectives were fully attained, the results have the potential of 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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Concluding this project, most of the objectives have been attained (i) in terms of the construction of models that quantify backreaction having an architecture that goes well beyond currently employed models and simulations, (ii) in terms of the development of advanced statistical methods and their application to a variety of observational data, all showing the limits of the standard model by quantifying the significance of anomalies, e.g. for the deviations from hemispherical isotropy, by matching finite-volume universe models with a better fit to observational data than the standard model could achieve, and through the application of model-independent methods to distance measurements in inhomogeneous cosmologies. Finally, they have been attained (iii) in terms of the development of fully general averaging formalisms of Einstein's equations both for spatial foliations of spacetime and for finite bundles of light rays, together with closure conditions for the resulting hierarchy of averaged equations both through generic modeling strategies and through global topological theorems. As show-cases of the successes of our understanding of inhomogeneity effects, we could provide Dark Energy-free models that simultaneously explain various conundrums of the standard model while matching observational data, and we could provide a quantitative replacement of Dark Matter through emerging curvature during the collapse process of cluster-scale structure.
As a further conclusion, we can envisage new routes and synergies resulting from these outcomes, including the possibility of a knowledge transfer of ARThUs' results to a new research field that heads towards advanced propulsion systems through spacetime engineering, a subject of considerable interest of researchers at space agencies. The ERC PoC project GRAMMAR has been submitted by the PI.

The project resulted in 75 publications, out of which peer-reviewed 46 with on average 30 journal pages each, 3 submitted to peer review, 3 invited papers, 1 book, 1 insight comment, 5 preprints, 3 PhD theses, and 13 internship reports. There are furthermore 9 papers in preparation. These publications are either available in green or gold open access, except the internship reports and the book.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

We followed a solid gain pace by investigating Lagrangian models in general relativity and applying them to a variety of problems, e.g. to gravitational waves. In individual papers we could also identify break-throughs, but here we just emphasize the unexpected breakthrough at the end of this series of papers: by comparing with classes of exact solutions in general relativity, we first found restrictions that are common to all models and simulations in contemporary cosmological modeling. But we were then able to generalize our Lagrangian models to get rid of this restriction, providing the break-through of having generic models that are capable of quantifying global backreaction, a main goal in the project.
We also provided an explicit Dark Energy-free model that can fit the supernova data and explain the Hubble tension, two major themes in contemporary cosmology.

We investigated a direct correspondence between Newtonian theory and general relativity, which we consider as a break-through, since this result appears to have impact on many research fields where the Newtonian "limit" is taken as an important reference, including classical problems like the deflection of light, the perihelion precession, orbits in Schwarzschild Black Holes, etc. where the Newtonian theory in traditional calculations appears to fall short. We actually applied elements of this correspondence in constructing our Lagrangian schemes, but we only realized at the end that this correspondence bears the fundamental insight that Newtonian theory is more general than expected or exposed in textbooks.

We investigated spatial averaging of Einstein's equations in general foliations of spacetime and for general energy-momentum tensors. The unexpected outcome here was that we expected more complex results for this fully general setting. However, the break-through came as we realized that a foliation of spacetime into proper time hypersurfaces made the final general result as transparent as the simplest case of a flow-orthogonal foliation. This implies that the resulting effective cosmological equations (the so-called Buchert equations in the most general setting) acquire a compact and easy to apply form and allow for a global cosmological time.
We also investigated light cone averaging. Here, this work sets out a general formalism to treat extended light bundles in a generic inhomogeneous spacetime, a result that was not available before.

We have exploited mathematical theorems in global topology, with deep insights into the hierarchy of the Einstein equations and their averages. Two unexpected new routes emerged: (i) looking at local topology changes, e.g. due to the formation of Black Holes, a complementary understanding of Dark Energy-like effects emerged. This promising route will be continued; (ii) looking at morphological characteristics of domain boundaries of the domains of averaging, we could link Einstein's evolution equations to integral-geometric properties. This opens the door for a new closure possibility in terms of the Euler characteristic of the boundary: a conservation law for the topology of the boundary may lead us finally to achieve closure of the averaged Einstein equations. Also this route will be continued beyond ARThUs.

Illustration of the averaging problem on the light cone, from REF 47.

Illustrations of topological analysis of the Cosmic Microwave Background, from REF 9.

Illustration of the effect of curvature that can replace Dark Matter, from REF 10.

Illustration of Lagrangian models controlled by exact solutions, from REF 48.

Illustration of the complexity of structures in the collapse phase, from REF 46.