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Gravitational theories differing from General Relativity may explain the accelerated expansion of the Universe without a cosmological constant. However, to pass local gravitational tests, a screening mechanism is needed to suppress, on small scales, the fifth force driving the cosmological acceleration. We consider the simplest of these theories, i.e. a scalar-tensor theory with first-order derivative self-interactions, and study isolated (static and spherically symmetric) non-relativistic and relativistic stars. We produce screened solutions and use them as initial data for non-linear numerical evolutions in spherical symmetry. We find that these solutions are stable under large initial perturbations, as long as they do not cause gravitational collapse. When gravitational collapse is triggered, the characteristic speeds of the scalar evolution equation diverge, even before apparent black-hole or sound horizons form. This casts doubts on whether the dynamical evolution of screened stars may be predicted in these effective field theories.
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We propose a modified gravity theory that propagates only two local gravitational degrees of freedom and that does not have an Einstein frame. According to the classification in JCAP 01 (2019) 017 [arXiv:1810.01047 [gr-qc]], this is a type-II minimally modified gravity theory. The theory is characterized by the gravitational constant $G_{rm N}$ and a function $V(phi)$ of a non-dynamical auxiliary field $phi$ that plays the role of dark energy. Once one fixes a homogeneous and isotropic cosmological background, the form of $V(phi)$ is determined and the theory no longer possesses a free parameter or a free function, besides $G_{rm N}$. For $V(phi) = 0$ the theory reduces to general relativity (GR) with $G_N$ being the Newtons constant and $V=const.$ being the cosmological constant. For $V(phi) e 0$, it is shown that gravity behaves differently from GR but that GR with $G_{rm N}$ being the Newtons constant is recovered for weak gravity at distance and time scales sufficiently shorter than the scale associated with $V(phi)$. Therefore this theory provides the simplest framework of cosmology in which deviations from GR can be tested by observational data.
We study new FRW type cosmological models of modified gravity treated on the background of Palatini approach. These models are generalization of Einstein gravity by the presence of a scalar field non-minimally coupled to the curvature. The models employ Starobinskys term in the Lagrangian and dust matter. Therefore, as a by-product, an exhausted cosmological analysis of general relativity amended by quadratic term is presented. We investigate dynamics of our models, confront them with the currently available astrophysical data as well as against LCDM model. We have used the dynamical system methods in order to investigate dynamics of the models. It reveals the presence of a final sudden singularity. Fitting free parameters we have demonstrated by statistical analysis that this class of models is in a very good agreement with the data (including CMB measurements) as well as with the standard LCDM model predictions. One has to use statefinder diagnostic in order to discriminate among them. Therefore Bayesian methods of model selection have been employed in order to indicate preferred model. Only in the light of CMB data the concordance model remains invincible.
We investigate the cosmological applications of a bi-scalar modified gravity that exhibits partial conformal invariance, which could become full conformal invariance in the absence of the usual Einstein-Hilbert term and introducing additionally either the Weyl derivative or properly rescaled fields. Such a theory is constructed by considering the action of a non-minimally conformally-coupled scalar field, and adding a second scalar allowing for a nonminimal derivative coupling with the Einstein tensor and the energy-momentum tensor of the first field. At a cosmological framework we obtain an effective dark-energy sector constituted from both scalars. In the absence of an explicit matter sector we extract analytical solutions, which for some parameter regions correspond to an effective matter era and/or to an effective radiation era, thus the two scalars give rise to mimetic dark matter or to dark radiation respectively. In the case where an explicit matter sector is included we obtain a cosmological evolution in agreement with observations, that is a transition from matter to dark energy era, with the onset of cosmic acceleration. Furthermore, for particular parameter regions, the effective dark-energy equation of state can transit to the phantom regime at late times. These behaviours reveal the capabilities of the theory, since they arise purely from the novel, bi-scalar construction and the involved couplings between the two fields.
We perform a phase space analysis of a generalized modified gravity theory with nonminimally coupling between geometry and matter. We apply the dynamical system approach to this generalized model and find that in the cosmological context, different choices of Lagrangian density will apparently result in different phases of the Universe. By carefully choosing the variables, we prove that there is an attractor solution to describe the late time accelerating universe when the modified gravity is chosen in a simple power-law form of the curvature scalar. We further examine the temperature evolution based on the thermodynamic understanding of the model. Confronting the model with supernova type Ia data sets, we find that the nonminimally coupled theory of gravity is a viable model to describe the late time Universe acceleration.
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.
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