We discuss a class of phantom $(p<\mathrm{}-\varrho )$ cosmological models. Except for the phantom we admit various forms of standard types of matter and discuss the problem of singularities for these cosmologies. The singularities are different from those of standard matter cosmology since they appear for infinite values of the scale factor. We also find an interesting relation between the phantom models and standard matter models which is like the duality symmetry of string cosmology.

We classify singularities in FRW cosmologies, which dynamics can be reduced to the dynamical system of the Newtonian type. This classification is performed

Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting \(\Lambda \) CDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative—the \(\Lambda \) CDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam’s principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), \(h(z)\) , baryon acoustic oscillation, the Alcock–Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting \(\Lambda \) CDM model when compared to the \(\Lambda \) CDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the \(\Lambda \) CDM model. Given the weak or almost non-existing support for the interacting \(\Lambda \) CDM model and bearing in mind Occam’s razor we are inclined to reject this model.

We investigate evolutional paths of an extended quintessence with a nonminimally coupled phantom scalar field $\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasioscillatory and monotonic trajectories approach the attractor which represents the Friedmann-Robertson-Walker model with the cosmological constant. We demonstrate that the dynamical system admits an invariant two-dimensional submanifold and discuss that which cosmological scenario is realized depends on the behavior of the system on the phase plane $(\psi ,{\psi }^{\prime })$. We formulate simple conditions on the value of the coupling constant $\xi$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. We also investigate the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.

In this paper we study the flat ($k=0$) cosmological Friedmann-Robertson-Walker model with holonomy corrections of loop quantum gravity. The considered universe contains a massless scalar field and the cosmological constant $\Lambda$. We find analytical solutions for this model in different configurations and investigate its dynamical behavior in the whole phase space. Such an approach might be significant e.g. as a phenomenological reference for a further, fully quantum treatment. We show the explicit influence of $\Lambda$ on the qualitative and quantitative character of solutions. Even in the case of positive $\Lambda$ the oscillating solutions without the initial and final singularity appear as a generic case for some quantization schemes.