Лекции

A.A. Starobinsky (Landau ITP, Moscow, Russia)
New results on inflation and its origin from curvature singularity
New results on inflation and preceding evolution of a universe in f(R) gravity are presented. f(R) gravity where R is the Ricci scalar represents the simplest purely geometrical generalization of the Einstein general theory of relativity without undesirable ghosts. For a RLRW spatially flat isotropic cosmological model in the absence of matter, its equations can be reduced to one first order differential equation that first shown in Starobinsky (1980) for the special case of the R+R^2 model (even with some additional geometric term). This model represents the pioneer inflationary model, too. 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 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. 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 the exact constant-roll solutions generalizing slow-roll ones can be realized are found. Also studied is the problem of inflation formation from preceding generic classical curvature singularity, and which conditions are needed for this. 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.

I.F. Bikmaev (KFU, Kazan, Russia)
Scientific tasks of the Spectrum-Roentgen-Gamma project
During the period 2018-2025 Kazan Federal University will participate in the ground based support of the Russian-German 'Spectrum-Roentgen-Gamma (SRG) ' orbital observatory by using 1.5-meter optical telescope in Turkey (RTT-150). The main scientific tasks and technical performances of RTT-150 and SRG will be discussed in this lecture.

V.M. Mostepanenko (Pulkovo Central Astronomical Observatory, St. Petersburg, Russia)
The Casimir effect in cosmology and on a laboratory table
We discuss the vacuum polarization and forces which arise due to the presence of zero-point and thermal fluctuations of quantized fields in the restricted quantization volumes and in spaces with non-Euclidean topology. Starting from simply calculated model examples, we consider the recent experiments on precise measurements of the Casimir force including some fundamental unresolved problems. Then we pass to cosmological applications taking into account the results which are already verified on a laboratory table.

G.L. Klimchitskaya (Pulkovo Central Astronomical Observatory, St. Petersburg, Russia)
Constraints on an axion and on non-Newtonian gravity from the Casimir effect
Recent precise measurements of the Casimir force allow obtaining strong constraints on the parameters of the Yukawa-type corrections to Newtonian gravity which have been predicted due to exchange of light elementary particles between atoms of two macrobodies and by the unification schemes with a low-energy compactification scale. The same measurements have been recently used to obtain new constraints on the coupling constants of axions to nucleons. We discuss the most strong constraints obtained in this way, and also some prospects in connection with the problem of dark matter. 

K.A. Bronnikov (RUDN University, Moscow, Russia)
Wormholes and regular black holes. The stability problem.
We review the properties of static, spherically symmetric configurations of general relativity with minimally coupled scalar fields. Special attention is given to scalar fields whose kinetic energy is negative in a restricted (strong-field) region of space and positive outside it. This "trapped ghost'' concept may in principle explain why no ghosts are observed under usual, weak-field conditions. The configurations considered are wormholes and regular black holes without a center, in particular, black universes (black holes with an expanding cosmology beyond the event horizon). Spherically symmetric perturbations of these objects are considered, and it is stressed that, due to the universal shape of the effective potential near a transition surface from canonical to phantom behavior of the scalar field, such surfaces restrict the possible perturbations and play a stabilizing role.

S.V. Chervon (Ulyanovsk State Pedagogical University, Russia)
Scalar field cosmologies
The lectures are devoted to investigations performed in Friedmann Universe, which is filled by the scalar field. Much attention is paid to methods of exact solution construction of cosmology dynamic equations.
The fact that the presentation of the scalar field dynamic equations in terms of the Hubble parameter as the function of the scalar field was derived firstly by G. Ivanov in 1981 and then it independently was derived by D. Salopec and J. Bond in 1990. The generating function for solving the scalar cosmology equation in the form of Ivanov-Salopec-Bond (ISB) presentation reproduces various exact solutions found for the special choice of the potential. The list of the potentials includes exponential, power-law, inverse-power, trigonometric and Higgs type of potentials. The original approach for solving ISB equation suggested by A. Muslimov in 1990 that is based on intermediate hyperbolic function is discussed as well.
Detailed des­cription of the methods of exact solutions construction is considered. With the help of fine tuning of the potential method, firstly introduced by G. Ellis and M. Madsen in 1991, it was demonstrated how to obtain the inflationary solutions for power-law, exponential, power-law-exponential and hyperbolic expansion of the Universe. In addition, it is considered fine tuning of the potential method in a conformally flat spacetime. The method of solution construction from a scalar field evolution, firstly suggested by J. Barrow in 1994, is discussed as well.
Finally, we will discuss the way in which the exact solution construction methods for GR scalar field cosmology can be applied for scalar field cosmology in modified theories of gravity.

S. Capozziello (Napoli University, Italia)
Addressing the missing matter problem in galaxies through a new fundamental gravitational radius
We demonstrate that the existence of a Noether symmetry in f(R) theories of gravity gives rise to a further gravitational radius, besides the standard Schwarzschild one, determining the dynamics at galactic scales. By this feature, it is possible to explain the baryonic Tully–Fisher relation and the rotation curve of gas-rich galaxies without
the dark matter hypothesis.

Francisco Lobo (Universidade de Lisboa, Lisboa, Portugal)
Lecture 1: Generalized curvature-matter couplings in modified gravity
In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit non-minimal couplings, for instance, between an arbitrary function of the scalar curvature and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and consequently leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified des­cription of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra-terms in the gravitational field equations modify the equations of motion of test particles, and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions, and for explaining the late-time cosmic acceleration.

Lecture 2: Hybrid metric-Palatini gravity
Recently, the phenomenology of f(R) gravity has been scrutinized motivated by the possibility to account for the self-accelerated cosmic expansion without invoking dark energy sources. It has been established that both metric and Palatini versions of these theories have interesting features but also manifest severe and different downsides. A hybrid combination of theories, containing elements from both these two formalisms, turns out to be also very successful accounting for the observed phenomenology and is able to avoid some drawbacks of the original approaches. This talk reviews the formulation of this hybrid metric-Palatini approach and its main achievements in passing the local tests and in applications to astrophysical and cosmological scenarios, where it provides a unified approach to the problems of dark energy and dark matter.

M.S. Volkov (Tour University, France)
Weyl metrics and wormholes
We study solutions  obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. These solutions have  wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly  flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Such wormholes can be obtaining by taking the zero mass limit of the Kerr metric. 

E. Elizalde (ICREA, Barcelona, Spain)
On a renormalization group improved accelerating cosmological scenario
At the begining of my talk, I will discuss the crucial issue that the actual concept of Big Bang is in need of some up­date or specification. Quantum and inflationary additions to the celebrated singularity theorems by Penrose, Geroch, Hawking and others led to the subsequent theorems by Borde, Guth and Vilenkin, and corresponding corrections to the Einstein equations have originated, in particular, R^2 and f(R) gravities. However, high-curvature corrections to GR, although well motivated by quantum considerations, are at best multiplicatively renormalizable. As the Hilbert-Einstein action for GR is non-renormalizable, it is then compulsory to consider an effective improved action with an ultraviolet completion at high-energy scale, which might eventually lead to renormalizability. As a starting step in this direction, we have recently considered a rather simple, kind of phenomenological model for renormalizable quadratic gravity, by the addition of a logarithmic correction to the cosmological-constant parameter of the exponential F(R)-modified gravity term appearing in the action. It seems to adjust well the basic cosmological parameters resulting from the latest analysis of the PLANCK astronomical data.

S.D. Odintsov (ICREA, Barcelona, Spain)
Accelerating cosmology in modified gravity
We review modified gravity cosmology paying attention specially to F(R) gravity. Some other theories like modified Gauss-Bonnet gravity are briefly discussed. Inflation in viable F(R) gravity is described. Different possibilities like singular inflation and constant roll inflation are mentioned. The account of higher-derivative quantum gravity is made. It is shown that QG induced terms may provide very consistent unification of the early-time inflation with late-time acceleration. The examples of such unified modified gravity cosmology is presented. The possibility of bounce in F(R) gravity is also discussed.

M. Sami (Centre for Theoretical Physics, New Delhi, India)
Quintessential inflation
We review the basics of quintessential inflation. IN this talk focus will be on the model independent aspects of the paradigm. The model building blocks required to unify late time acceleration with inflation will be presented.  The alternative reheating mechanism will also be described in brief. Last but not least, we shall present a successful model of quintessential inflation.

J.C. Fabris (Universidade Federal do Espírito Santo, Vitoria, Brasil)
Quantum Cosmology in Scalar-Tensor Theories
We review some general properties of scalar-tensor theories at classical and quantum level. As one specific example, the Brans-Dicke theory is considered. At quantum level, an effective Hamiltonian is obtained by introducing the time coordinate through matter fields. The self-adjoint character of the Hamiltonian both in the Einstein and in the Jordan frames is studied. In both cases we determine the wave-function solutions in order to obtain concrete predictions for the evolution of the Universe Singularity free solutions are obtained. Moreover, the specific cosmological scenarios depend very weakly on the conditions of having a self-adjoint operator. The problem of equivalence between Einstein and Jordan frames is considered, and it is shown that this equivalence implies a specific ordering parameter, as well as a particular choice of the physical variables.

H. Velten (Universidade Federal do Espirito Santo, Vitoria, Brasil)
Anomalous gravitational wave speed: Constraints on modified gravity from binary pulsars
By using observations of the Hulse-Taylor pulsar we constrain the gravitational wave (GW) speed to the level of 10^{−2}. We apply this result to scalar-tensor theories that generalize Galileon 4 and 5 models, which display anomalous propagation speed and coupling to matter for GWs. We argue that this effect survives conventional screening due to the persistence of a scalar field gradient inside virialized overdensities, which effectively "pierces" the Vainshtein screening. In specific branches of solutions, our result allows to directly constrain the cosmological couplings in the effective field theory of dark energy formalism.

A.V. Toporensky (Moscow University, Russia)
Compactification scenario in multidimensional Gauss-Bonnet cosmology
In this talk cosmological dynamics in Einstein-Gauss-Bonnet gravity with a perfect fluid source in arbitrary dimension is studied. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely one for the three dimensional space and one for the extra dimensional space, is found that a regime exists where the two scale factors tend to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the (3+1)-dimensional Friedmann model with perfect fluid is recovered. In the second part of the talk we study the influence of initial anisotropy. Our study reveals that the transition from Gauss-Bonnet Kasner regime to anisotropic exponential expansion (with expanding three and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces. Combining the two described affects allows us to construct a scenario, where isotropisation of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.

Ernazar Abdikamalov (Nazarbayev University, Astana, Kazakhstan)
The Explosions of Massive Stars
Massive stars end their lives as spectacular explosions known as core-collapse supernovae. They play a crucial role in the evolution of the Universe, producing most elements heavier than iron and leading to the formation of neutron stars and black holes. Despite their importance, the details of how they explode are still unclear. In this talk, I will review the recent progress in our understanding of the explosion mechanism, with an emphasis on the role of multi-dimensional hydrodynamic instabilities in facilitating an explosion.

Edvard Musaev (Max-Planck-Institute for Gravitational Physics, Potsdam, Germany)
Exotic branes in string and M-theory
Despite the name string theory describes dynamics of not only strings but also Dp-branes, extended p-dimensional objects interacting with p-form gauge potential. Certain observations suggest that string theory spectrum should contain additional objects interacting with exotic potentials. In this lecture dynamics of such objects will described as well as the corresponding supergravity backgrounds and their application in cosmological models.