Schedule

Official Opening:

Opening words by selected representatives

Lavinia Heisenberg (ETH Zürich, Zürich, Switzerland):

The Trinity of Gravity

Following the geometrical interpretation of gravity, I will introduce the geometrical trinity of General Relativity, where it is represented in three independent formulations based on curvature, torsion and non-metricity. Stepping more into the field theoretical interpretation of gravity I will introduce the trinity of gravity based on tensor, vector and scalar representation. After having gained an systematical overview about consistent-looking constructions of effective field theories of gravity, I will discuss different ways of assessing them by means of theoretical and cosmological consistency.

Jutta Kunz (University of Oldenburg, Oldenburg, Germany):

Compact objects in gravity theories

Compact objects such as black holes and neutron stars allow to study the effects of strong gravity and thus to test Einstein's theory of general relativity and its contenders by comparison with observations, since alternative theories of gravity may lead to distinct features of black holes and neutron stars, like hair or spontaneous scalarization. Quasi-normal mode analysis of these compact objects allows to make contact with gravitational wave observations.

Fawad Hassan (Stockholm University, Stockholm, Sweden):

On the current status of theories of multiple spin-2 fields

Theories of spin-2 fields interacting with gravity are highly constrained by consistency conditions, including the requirement of absence of ghost instabilities. This talk will describe the current status of theories of two and multiple spin-2 fields commonly known as bimetric and multimetric theories. In particular I will focus on the structure of ghost free bimetric and multimetric interactions and on the notions of space and time in such theories. Finally I will comment on attempts at further generalizations and incorporation of extra symmetries.

Aleksei Starobinsky (Landau Institute for Theoretical Physics RAS, Moscow, Russia):

Inflation and pre-inflation in $f(R)$ and related modified gravity theories

Several new results on inflation and pre-inflationary evolution of homogeneous cosmological models in $f(R)$ and related modified gravity theories are presented. The $R + R^2$ (Starobinsky) model where $R$ is the Ricci scalar, augmented by small one-loop quantum gravitational corrections, represents the pioneer inflationary model [1] which still remains viable. It contains only one adjustable parameter taken from observations, has a graceful exit from inflation and a natural mechanism for creation and heating of matter after its end, and it produces a very good fit to existing observational data on the power spectrum of primordial scalar (adiabatic density) perturbations. More generally, all viable slow-roll inflationary models in $f(R)$ gravity should be close to this model over some range of $R$. It also represents a dynamical attractor for slow-rolling scalar fields strongly coupled to gravity, as well as for the mixed $R^2$-Higgs inflationary model [2]. We consider the inverse problem of reconstruction of inflationary models in $f(R)$ gravity using information on the power spectrum of scalar perturbations only, ambiguity in this procedure and how it can be fixed by some aesthetic assumptions on the absence of new physical scales during and after inflation. The forms of $f(R)$ for which exact constant-roll solutions generalizing slow-roll ones can be realized are found [3]. As follows from observational data on the primordial scalar (matter density) perturbation spectrum, running of the dimensionless coefficient in front of the $R^2$ term with curvature due to loop quantum-gravitational corrections is small and does not exceed a few percent [4]. The same refers to the $R\Box R$ correction considered perturbatively, without increasing the number of degrees of freedom [5]. Also studied is the problem of inflation formation from preceding generic classical curvature singularity, and which conditions are needed for this [6]. Some exact anisotropic solutions describing it are presented. Since this process is generic, too, for inflation to begin inside a patch including the observable part of the Universe, causal connection inside the whole patch is not necessary. However, it becomes obligatory for a graceful exit from inflation in order to have practically the same number of e-folds during inflation inside this patch.

1. A. A. Starobinsky, Phys. Lett. B 91, 99 (1980).
2. M. He, A. A. Starobinsky and J. Yokoyama, JCAP 1805, 064 (2018); arXiv:1804.00409.
3. H. Motohashi and A. A. Starobinsky, Eur. Phys. J. C 77, 538 (2017); arXiv:1704.08188.
4. L.-H. Liu, T. Prokopec and A. A. Starobinsky, Phys. Rev. D 98, 043505 (2018); arXiv:1806.05407.
5. A. R. R. Castellanos, F. Sobreira, I. L. Shapiro and A. A. Starobinsky, JCAP 1812, 007 (2018); arXiv:1810.07787.
6. D. Muller, A. Ricciardone, A. A. Starobinsky and A. Toporensky, Eur. Phys. J. C 78, 311 (2018); arXiv:1710.08753.

Public Lecture

The public lecture by Lavinia Heisenberg will take place in the Old Observatory.

Claus Lämmerzahl (University of Bremen, Bremen, Germany):

Testing alternative matter and gravity models with accretion disks

Accretion disks come very close to Black Holes and are, thus, an ideal tool to test gravity in its strong field regime. Based on a general framework for thick accretion disks in axially symmetric space-times, we will report in particular on a study of testing regular Black Hole geometries which arise in the context of the coupling of nonlinear electrodynamics to Einstein gravity. We investigate the shape of neutral as well as of charged disks. While the effect on the motion of stars in such geometries is comparably small due to the large distance to the Black Hole, the effect on accretion disks seems to be significant.

Salvatore Capozziello (Università di Napoli "Federico II", Naples, Italy):

Cosmography as a tool to discriminate between dark energy and modified gravity

We discuss the cosmographic approach to cosmological evolution adopting various polynomial series for the luminosity function. Their convergence properties give hints to discriminate among concurring dark energy and modified gravity scenarios.

Syksy Räsänen (University of Helsinki, Helsinki, Finland):

The gravity track of Higgs inflation

Using the Standard Model Higgs as the inflation is attractively economical. However, apart from quantum corrections, the predictions depend on the chosen formulation of general relativity: metric, Palatini, teleparallel, etc. I will discuss how these differences manifest in cosmological observables, in particular how non-metricity can affect the inflationary potential.

Alexey Golovnev (Saint Petersburg State University, Saint Petersburg, Russia):

Playing with flat spin connections: degrees of freedom in $f(T)$ and beyond

It might seem that introducing a flat spin connection for covariantizing modified teleparallel gravity is impractical since it increases the number of variables without changing the physical content. However, I will argue that this procedure is very convenient for figuring out many tricky issues including the infamous puzzle of the extra degrees of freedom in $f(T)$ gravity.

Topical Discussion:

Teleparallel Gravity

Topical Discussion:

Scalar-Tensor Gravity

Topical Discussion:

Bimetric Gravity

Topical Discussion:

Cosmology

Derek Wise (Denver, United States):

Cartan Geometry and Observer Space

General Panel Discussion:

What are the most important questions to be pursued?