arXiv subjects
Publications and source records attributed to Aneta Wojnar.
A new simple expression for the circular velocity of spiral galaxies is proposed and tested against HI Nearby Galaxy Survey (THINGS) data set. Its accuracy is compared with the one coming from MOND.
We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).
We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et {\it al}. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman-Oppenheimer-Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar-tensor gravity.
The main subjects of the PhD dissertation concern cosmological models considered in Palatini f(R) gravity and scalar-tensor theories. We introduce a simple generalization of the LCDM model based on Palatini modified gravity with quadratic Starobinsky term. A matter source is provided by generalized Chaplygin gas. The statistical analysis of our model is investigated. We use dynamical system approach to study the evolution of the Universe. The model reaches a very good agreement with the newest experimental data and yields an inflationary epoch caused by a singularity of the type III. The present-day accelerated expansion is also provided by the model. We also show that the Lie and Noether symmetry approaches are very useful tools in cosmological considerations. We examine two other models of Extended Theories of Gravity (ETGs): the novel hybrid metric-Palatini gravity and a minimally coupled to gravity scalar field. The first one is applied to homogeneous and isotropic model while in the scalar-tensor theory we study anisotropic universes. We use the symmetries in order to find unknown forms of potential and to solve classical field equations in both models. The symmetries also are very helpful in searching exact and invariant solutions of Wheeler-DeWitt equations. In the last part we are interested in equilibrium configurations and stability conditions of relativistic stars in the framework of scalar-tensor theories. Firstly, we show that TOV-like form of the equilibrium equations can be obtained for a wide class of ETGs if generalized energy density and pressure are defined. According to our studies, a neutron star is a stable system for the minimally coupled scalar field model. There is a supplement including notes on symmetries as well as dynamical systems approach. The illustrative examples of applications are also provided.
We investigate further (cf. arXiv:1512.01199, JCAP01 (2016) 040) Starobinsky cosmological model $R+γR^2$ in the Palatini formalism with Chaplygin gas and baryonic matter as a source. For this aim we use dynamical system theory. The dynamics is reduced to the 2D sewn dynamical system of a Newtonian type (a piecewise-smooth dynamical system). We classify all evolutional paths in the model as well as trajectories in the phase space. We demonstrate the presence of a degenerate freeze singularity (glued freeze type singularities) for the positive $γ$. In this case it is a generic feature of early evolution of the universe. We point out that a degenerate type III of singularity can be considered as an endogenous model of inflation between the matter dominating epoch and the dark energy phase. We also investigate cosmological models with negative $γ$. It is demonstrated that $γ$ equal zero is a bifurcation parameter and dynamics qualitatively changes in comparison to positive $γ$. Instead of the big bang the sudden bounce singularity of a finite scale factor appears and there is a generic class of bouncing solutions sewn along the line $a=a_{\text{sing}}$. And we argue that the presence of sudden singularities in an evolutional scenario of the Universe falsifies the negative $γ$ in the Palatini cosmology. Only very small values of $Ω_γ$ parameter are admissible if we requires that agreements physics with the $Λ$CDM model. From the statistical analysis of astronomical observations, we deduce that the case of negative values of $Ω_γ$ can be rejected even if it may fit better to the data.
We present a simple generalisation of the $Λ$CDM model which on the one hand reaches very good agreement with the present day experimental data and provides an internal inflationary mechanism on the other hand. It is based on Palatini modified gravity with quadratic Starobinsky term and generalized Chaplygin gas as a matter source providing, besides a current accelerated expansion, the epoch of endogenous inflation driven by type III freeze singularity. It follows from our statistical analysis that astronomical data favors negative value of the parameter coupling quadratic term into Einstein-Hilbert Lagrangian and as a consequence the bounce instead of initial Big-Bang singularity is preferred.
We test a free {\it ad hoc} parametrization of the Tolman-Oppenheimer-Volkoff (TOV) equation. We do not have in mind any specific extended theory of gravity (ETG) but each new parameter introduced has a physical interpretation. Our aim is fully pedagogical rather than a proposal for a new ETG. Given a realistic neutron star equation of state we map the contributions of each new parameter into a shift in trajectories of the mass-radius diagram. This exercise allows us to make the correspondence between each TOV sector with possible modifications of gravity and clarifies how neutron star observations are helpful for distinguishing theories.
Symmetries play a crucial role in physics and, in particular, the Noether symmetries are a useful tool both to select models motivated at a fundamental level, and to find exact solutions for specific Lagrangians. In this work, we consider the application of point symmetries in the recently proposed metric-Palatini Hybrid Gravity in order to select the $f({\cal R})$ functional form and to find analytical solutions for the field equations and for the related Wheeler-DeWitt (WDW) equation. We show that, in order to find out integrable $f({\cal R})$ models, conformal transformations in the Lagrangians are extremely useful. In this context, we explore two conformal transformations of the forms $dτ=N(a) dt$ and $dτ=N(ϕ) dt$. For the former conformal transformation, we found two cases of $f({\cal R})$ functions where the field equations admit Noether symmetries. In the second case, the Lagrangian reduces to a Brans-Dicke-like theory with a general coupling function. For each case, it is possible to transform the field equations by using normal coordinates to simplify the dynamical system and to obtain exact solutions. Furthermore, we perform quantization and derive the WDW equation for the minisuperspace model. The Lie point symmetries for the WDW equation are determined and used to find invariant solutions.
The notion of relativistic observer is confronted with Naveira's classification of (pseudo-)Riemannian almost-product structures on space-time manifolds. Some physical properties and their geometrical counterparts are shortly discussed.