49thWinter School of Theoretical Physics

Cosmology and non-equilibrium statistical mechanics

Lądek-Zdrój, Poland, February 10-16, 2013

Recent developments in:

  • F(R) gravity & cosmology
  • Relativistic statistical mechanics
  • Dark matter & dark energy

Aim and Scope:

The recent studies of dark matter and dark energy problems rely on (independent) modifications of both sides of the Einstein equations in order to explain current cosmic acceleration. The winter school will concern with both sides of the Einstein equations. The Einstein tensor determines the energy-momentum tensor of a fluid. In general, the relativistic fluid is more complex than just an ideal fluid. At the conference the statistical mechanics of such fluids and their consequences for the large scale cosmic evolution will be discussed. The school will be held in the mountain resort in the south-west of Poland. This is a continuation of the tradition of the Karpacz Winter schools which were organized for almost half a century.

Organizing Committee:

Z. Haba (Head), A. Borowiec, Z. Popowicz, P. Ługiewicz (Secretary), A. Błaut (Treasurer), P. Gusin, M. Kamionka, A. Wojnar

Contact: karp49 [at] ift.uni.wroc.pl,
zhab [at] ift.uni.wroc.pl, borow [at] ift.uni.wroc.pl
Phone: (+48) 71 375 94 32, (+48) 71 375 94 06
Fax: (+48) 71 321 44 54
Institute of Theoretical Physics, Wroclaw University,
pl. M. Borna 9; 50-204 Wroclaw; Poland

List of invited speakers: (click for abstract)

H. Andreasson (Chalmers Inst., Goeteborg)

F. Becattini (Univ. of Florence)

O. Bertolami (Univ. of Porto)

S. Calogero (Univ. of Granada)

S. Capozziello (Univ. of Napoli)

M. Francaviglia (Torino Univ.)

Title of talk:



The so called Ehlers-Pirani-Schild (EPS) analysis of spacetime properties and structure for a coherent theory of gravitation show that there is much more space that what happens in General Relativity. In particular EPS shows that a "gravitationally coherent" spacetime should admit a Conformal Structure that governs causality but may admit a free fall dictated by an independent (possibly non-metric) connection. One of the conformal metrics determines metric relations in spacetime (rods and clocks). Compatibility conditions relate of course the Conformal Structure and the free fall, but they do not imply that the connection is the Levi-Civita connection of one of the conformal metrics. Much less is in fact required for coherence. Reasonable toy examples can be easily constructed for standard fluid matter in any curved spacetime, in which curvature arises directly from the fluid. Recent failures of General Relativity, especially at extra-galactic and Cosmological scale, suggest that the Universe does not obey Einstein Equations as they are, unless one adds a large amount of (largely unseen) Dark Matter and Dark Energy. It has been shown that a possible alternative way consists in adopting an EPS-compatible framework (so called "Extended Theories of Gravitation") based on so called "Palatini's variational technique". Applications to f(R) theories governed by Lagrangians that are non-linear in the scalar curvature do show interesting properties, since they are EPS-compatible and they imply that a scalar field arises, tuned up by "standard matter" hidden in the "standard stress tensor" (observed or assumed a priori in spacetime). The given metric that appears in the Lagrangian (in a sense the one we locally observe in Solar System) is thence changed to a new conformal metric, that in far regions might be rather more curved than in the Solar System. The conformal factor depends in fact on Curvature, and near the Solar System it is approximately constant. This could provide at least a partial explanation of the Dark side of our Universe. It also suggests that measurements of time and space should be carefully revised when performing extra-galactic and cosmological tests for gravity. Moreover a mechanism for generating mass out of breaking the conformal invariance appears naturally, so that an alternative mechanism to explain Higg's Boson properties might be suggested.

R. A. Janik (Jagiellonian Univ.)

G.M. Kremer (Univ. of Parana)

Title of talk:



The aim of this work is to derive macroscopic field equations for relativistic fluids from the Boltzmann equation in the context of special and general relativity. The description of the relativistic fluid is based on five scalar fields of particle number density, four-velocity and temperature, which are characterized by the balance equations of the particle four-flow and energy-momentum tensor. The non-equilibrium pressure, the traceless part of the pressure tensor and the heat flux are constitutive quantities in the five-field theory and are determined by using the Chapman-Enskog method applied to the Boltzmann equation. From the system of field equations for a gas in special relativity the solutions corresponding to small perturbations from an equilibrium state related with the propagation of forced and free waves are analyzed. In general relativity two cases are investigated, the first one refers to a gas in a homogeneous and isotropic Universe where irreversible processes are present during its evolution. The responsible for the irreversible processes is the non-equilibrium pressure which is determined from the Anderson and Witting model of the Boltzmann equation by using the Chapman-Enskog method. The other case refers to a gas, which is not a source of the gravitational field, under the influence of a Schwarzschild metric. Explicit expression for the momentum density balance equation in terms of the relativistic character of gas and of the potential energy of the gravitational field is given. Furthermore, the limiting case of a non-relativistic gas in a weak gravitational field is also discussed.

S.D. Odintsov (Univ. of Barcelona)

D. Pavon (Univ. of Barcelona)

E.A. Spiegel (Columbia Univ.)

A.A. Starobinsky (Landau Inst., Moscow)

Title of talk:



f(R) gravity where R is the Ricci scalar is the simplest non-perturbative generally covariant generalization of the Einstein gravity where it is possible to avoid the appearance of new ghost and tachyon degrees of freedom. Thus, this theory can be considered at the same level of generality as general relativity, not in some perturbative regime only. It represents a particular case of scalar-tensor gravity in the limit of the zero Brans-Dicke parameter, but with a non-zero scalar field (dubbed scalaron) potential. Its most interesting applications in cosmology are related to the possibility to use it for description of both types of dark energy which have appeared during the Universe evolution: primordial dark energy driving inflation in the early Universe and present dark energy which has much smaller effective energy density. In the case of inflation, the simplest f(R)=R+R2 model proposed already in 1980 is internally consistent, has a graceful exit to the radiation-dominated FRW stage via an intermediate period of the scalaron decay during which all matter in the Universe arises as a result of gravitational particle creation, and remains in agreement with the most recent observational data. Moreover, this form of f(R) may be justified by a number of microscopic models. In particular, it describes the gravitational sector of the Higgs inflation. It is possible to construct models describing the present dark energy in f(R) gravity which satisfy all present observational tests. However, these models require a much more complicated form of f(R) and a very low energy scale, so there is no microscopic justification of them at present. More critical is that these models generically cannot reproduce the correct evolution of the Universe in the past due to formation of additional weak singularities and other problems. Thus, to construct complete cosmological models of present dark energy not destroying all previous achievements of the early Universe cosmology including the recombination, the correct BBN and inflation of any kind, one has to change the behaviour of f(R) at large positive R and to extend f(R) to the region of negative R.Combined description of primordial and present dark energy using one f(R) function is possible, too, if the quantum effect of gravitational particle creation is taken into account, similar to the case of purely inflationary models in f(R) gravity. However, the post-inflationary evolution in such combined models is totally different and strongly non-linear oscillations of R occur during it.

M. Szydłowski (Jagiellonian Univ.)

B. Zegarliński (Imperial College)

Title of talk:




W. Zimdahl (Univ. Espirito Santo)

Title of talk:



Since the interpretation of the SNIa observations by the SCP (Supernova Cosmology Project) and HZT (High-z Supernova Search Team) collaborations as evidence for an accelerated expansion of our present Universe, cosmologists have been challenged to provide a physically consistent description of this phenomenon. Although there exists a standard model, the ΛCDM model, which grosso modo seems able to account for the observed dynamics, there remain good reasons to study alternative models both within GR and in the context of alternative gravity. In standard descriptions the matter content of the Universe is modeled in terms of perfect fluids (and/or minimally coupled scalar fields) with simple equations of state. However, if dynamically dominating components deviate from being separately conserved perfect fluids and have a more complicated internal structure, the cosmic evolution, in particular the perturbation dynamics, may differ from that of the standard model. After briefly reviewing basic principles of relativistic fluid dynamics and kinetic theory we discuss, on the mentioned background, different phenomenological models of the cosmological dark sector and confront them with observational data. Among them are viscous models and models in which dark matter and dark energy are non-gravitationally coupled to each other. Potential interactions result in corrections to the dynamics of non-interacting models. Moreover, there are models in which an interaction is crucial and accelerated expansion may be an interaction phenomenon. Examples are specific holographic models and models of transient acceleration. We also comment on scenarios with a future evolution different from that of the standard ΛCDM model.

We are planning to publish all lectures in conference proceedings.
Contact: karp49 [at] ift.uni.wroc.pl

Contact phones:
Z. Haba:    mobile +48 601 767 937    office: +48 71 375 94 32
A. Borowiec:  mobile +48 665 596 186    office: +48 71 375 94 06