The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on cosmological time, or another suitably chosen time parameter. Consequently, the field equations can always be cast into the form of a dynamical system, a successful approach to study such models. We propose a perspective that is applicable to many different modified gravity models and relies on the standard cosmological density parameters only, making our choice of variables model independent. The drawback of our approach is a more complicated constraint equation. We demonstrate our procedure studying various modified gravity models and show how much generic information can be extracted before a specific model is considered.

United Kingdom

Christian Böhmer

Erik Jensko

Spain

Ruth Lazkoz

Cosmological dynamical systems in modified gravity

In this work, we further study a metric modified theory of gravity which contains a non-minimal coupling to matter, more precisely, we assume two functions of the scalar curvature,  $$f_1$$  <math> <msub> <mi>f</mi> <mn>1</mn> </msub> </math>   and  $$f_2$$  <math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math>  , where the first one generalises the Hilbert–Einstein action, while the second couples to the matter Lagrangian. On the one hand, assuming a  $$\varLambda $$  <math> <mi>Λ</mi> </math>  CDM background, we calculate analytical solutions for the functions  $$f_1$$  <math> <msub> <mi>f</mi> <mn>1</mn> </msub> </math>   and  $$f_2$$  <math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math>  . We consider two setups: on the first one, we fix  $$f_2$$  <math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math>   and compute  $$f_1$$  <math> <msub> <mi>f</mi> <mn>1</mn> </msub> </math>   and on the second one, we fix  $$f_1$$  <math> <msub> <mi>f</mi> <mn>1</mn> </msub> </math>   and compute  $$f_2$$  <math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math>  . Moreover, we do the analysis for two different energy density contents, a matter dominated universe and a general perfect fluid with a constant equation of state fuelling the universe expansion. On the other hand, we complete our study by performing a cosmographic analysis for  $$f_1$$  <math> <msub> <mi>f</mi> <mn>1</mn> </msub> </math>   and  $$f_2$$  <math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math>  . We conclude that the gravitational coupling to matter can drive the accelerated expansion of the universe.

María Ortiz-Baños

Mariam Bouhmadi-López

Poland

Vincenzo Salzano

$$\varLambda $$  <math> <mi>Λ</mi> </math>  CDM suitably embedded in f(R) with a non-minimal coupling to matter

The study of the dynamics of a two-body system in modified gravity constitutes a more complex problem than in Newtonian gravity. Numerical methods are typically needed to solve the equations of geodesics. Despite the complexity of the problem, the study of a two-body system in f(R) gravity leads to a new exciting perspective hinting the right strategy to adopt in order to probe modified gravity. Our results point out some differences between the semiclassical (Newtonian) approach, and the relativistic (geodesic) one thus suggesting that the latter represents the best strategy for future tests of modified theories of gravity. Finally, we have also highlighted the capability of forthcoming observations to serve as smoking gun of modified gravity revealing a departure from GR or further reducing the parameter space of f(R) gravity.

Russia

Italy

Germany

Mariafelicia Laurentis

Ivan Martino

Modified gravity revealed along geodesic tracks

It is a very well established matter nowadays that many modified gravity models can offer a sound alternative to General Relativity for the description of the accelerated expansion of the universe. But it is also equally well known that no clear and sharp discrimination between any alternative theory and the classical one has been found so far. In this work, we attempt at formulating a different approach starting from the general class of f ( R ) theories as test probes: we try to reformulate f ( R ) Lagrangian terms as explicit functions of the redshift, i.e., as f ( z ). In this context, the f ( R ) setting to the consensus cosmological model, the Λ CDM model, can be written as a polynomial including just a constant and a third-order term. Starting from this result, we propose various different polynomial parameterizations f ( z ), including new terms which would allow for deviations from Λ CDM, and we thoroughly compare them with observational data. While on the one hand we have found no statistically preference for our proposals (even if some of them are as good as Λ CDM by using Bayesian Evidence comparison), we think that our novel approach could provide a different perspective for the development of new and observationally reliable alternative models of gravity.

f ( R ) gravity modifications: from the action to the data

The cosmological redshift drift could lead to the next step in high-precision cosmic geometric observations, becoming a direct and irrefutable test for cosmic acceleration. In order to test the viability and possible properties of this effect, also called Sandage–Loeb (SL) test, we generate a model-independent mock data set in order to compare its constraining power with that of the future mock data sets of Type Ia Supernovae (SNe) and Baryon Acoustic Oscillations (BAO). The performance of those data sets is analyzed by testing several cosmological models with the Markov chain Monte Carlo (MCMC) method, both independently as well as combining all data sets. Final results show that, in general, SL data sets allow for remarkable constraints on the matter density parameter today Ωm on every tested model, showing also a great complementarity with SNe and BAO data regarding dark energy parameters.

Iker Leanizbarrutia

Forecast and analysis of the cosmological redshift drift

In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H ( z ) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means â¼2.8 Â Gyrs from the present time.

France

Jose Beltrán Jiménez

Portugal

Diego Sáez-Gómez

Observational constraints on cosmological future singularities

We review the appropriateness of using SNIa observations to detect potential signatures of anisotropic expansion in the Universe. We focus on Union2 and SNLS3 SNIa datasets and use the hemispherical comparison method to detect possible anisotropic features. Unlike some previous works where non-diagonal elements of the covariance matrix were neglected, we use the full covariance matrix of the SNIa data, thus obtaining more realistic and not underestimated errors. As a matter of fact, the significance of previously claimed detections of a preferred direction in the Union2 dataset completely disappears once we include the effects of using the full covariance matrix. Moreover, we also find that such a preferred direction is aligned with the orthogonal direction of the SDSS observational plane and this suggests a clear indication that the SDSS subsample of the Union2 dataset introduces a significant bias, making the detected preferred direction unphysical. We thus find that current SNIa surveys are inappropriate to test anisotropic features due to their highly non-homogeneous angular distribution in the sky. In addition, after removal of the highest inhomogeneous sub-samples, the number of SNIa is too low. Finally, we take advantage of the particular distribution of SNLS SNIa sub-sample in the SNLS3 data set, in which the observations were taken along four different directions. We fit each direction independently and find consistent results at the 1 σ level. Although the likelihoods peak at relatively different values of Ωm , the low number of data along each direction gives rise to large errors so that the likelihoods are sufficiently broad as to overlap within 1 σ .

Belgium

Anisotropic expansion and SNIa: An open issue

In this work we investigate if a small fraction of quarks and gluons, which escaped hadronization and survived as a uniformly spread perfect fluid, can play the role of both dark matter and dark energy. This fluid, as developed in [1] , is characterized by two main parameters: β , related to the amount of quarks and gluons which act as dark matter; and γ , acting as the cosmological constant. We explore the feasibility of this model at cosmological scales using data from type Ia Supernovae (SNeIa), Long Gamma-Ray Bursts (LGRB) and direct observational Hubble data. We find that: (i) in general, β cannot be constrained by SNeIa data nor by LGRB or H(z) data; (ii) γ can be constrained quite well by all three data sets, contributing with ≈78% to the energy–matter content; (iii) when a strong prior on (only) baryonic matter is assumed, the two parameters of the model are constrained successfully.