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In this paper, our objective is to explore a time-machine space-time formulated in general relativity, as introduced by Li (Phys. Rev. D {\bf 59}, 084016 (1999)), within the context of modified gravity theories. We consider Ricci-inverse gravity of all Classes of models, {\it i.e.}, (i) Class-{\bf I}: $f(\mathcal{R}, \mathcal{A})=(\mathcal{R}+{\kappa\,\mathcal{R}^2}+\beta\,\mathcal{A})$, (ii) Class-{\bf II}: $f(\mathcal{R}, A^{\mu\nu}\,A_{\mu\nu})=(\mathcal{R}+{\kappa\,\mathcal{R}^2}+\gamma\,A^{\mu\nu}\,A_{\mu\nu})$ model, and (iii) Class-{\bf III}: $f(\mathcal{R}, \mathcal{A}, A^{\mu\nu}\,A_{\mu\nu})=(\mathcal{R}{\kappa\,\mathcal{R}^2}+\beta\,\mathcal{A}+\delta\,\mathcal{A}^2+\gamma\,A^{\mu\nu}\,A_{\mu\nu})$ model, where $A^{\mu\nu}$ is the anti-curvature tensor, the reciprocal of the Ricci tensor, $R_{\mu\nu}$, $\mathcal{A}=g_{\mu\nu}\,A^{\mu\nu}$ is its scalar, and $\beta, {\kappa}, \gamma, \delta$ are the coupling constants. Moreover, we consider $f(\mathcal{R})$ modified gravity theory and investigate the same time-machine space-time. In fact, we show that Li time-machine space-time serve as valid solutions both in Ricci-inverse and $f(\mathcal{R})$ modified gravity theories. Thus, both theory allows the formation of closed time-like curves analogue to general relativity, thereby representing a possible time-machine model in these gravity theories theoretically., Comment: 23 pages, 4 figures

Our focus is on a specific type-N space-time that exhibits closed time-like curves in general relativity theory within the framework of Ricci-inverse gravity model. The matter-energy content is solely composed of a pure radiation field, and it adheres to the energy conditions while featuring a negative cosmological constant. One of the key findings in this investigation is the non-zero determinant of the Ricci tensor ($R_{\mu\nu}$), which implies the existence of an anti-curvature tensor ($A^{\mu\nu}$) and, as a consequence, an anti-curvature scalar ($A \neq R^{-1}$). Furthermore, we establish that this type-N space-time serves as a solution within modified gravity theories via the Ricci-inverse model, which involves adjustments to the cosmological constant ($\Lambda$) and the energy density ($\rho$) of the radiation field expressed in terms of a coupling constant. As a result, our findings suggest that causality violations remain possible within the framework of this Ricci-inverse gravity model, alongside the predictions of general relativity., Comment: 15 pages, accepted for publication in AOP

In this paper, Ricci-inverse gravity is investigated. It is an alternative theory of gravity that introduces into the Einstein-Hilbert action an anti-curvature scalar that is obtained from the anti-curvature tensor which is the inverse of the Ricci tensor. An axially symmetric spacetime with causality violation is studied. Two classes of the model are discussed. Different sources of matter are considered. Then a direct relation between the content of matter and causality violation is shown. Our results confirm that Ricci-inverse gravity allows the existence of Closed Time-like Curves (CTCs) that lead to the violation of causality. Furthermore, a comparison is made between the results of general relativity and Ricci-inverse gravity. Other spacetimes, such as G\"{o}del and G\"{o}del-type universes, which are exact solutions of general relativity and allow for causality violations, are also explored in Ricci-inverse gravity framework., Comment: 11 pages, accepted for publication in EPJC

We constrain scattering length parameters in a Bose-Einstein condensate dark matter model by using galaxy clusters radii, with the implementation of a method previously applied to galaxies. At the present work, we use a sample of 114 clusters radii in order to obtain the scattering lengths associated with a dark matter particle mass in the range $10^{-6}-10^{-4}\, {\rm eV}$. We obtain scattering lengths that are five orders of magnitude larger than the ones found in the galactic case, even when taking into account the cosmological expansion in the cluster scale by means of the introduction of a small cosmological constant. We also construct and compare curves for the orbital velocity of a test particle in the vicinity of a dark matter cluster in both the expanding and the non-expanding cases., Comment: 11 pages, 5 figures; v2: 12 pages, matches published version

We show that the galactic dark matter halo, considered composed of an axionlike particles Bose-Einstein condensate \cite{pir12} trapped by a self-graviting potential \cite{boh07}, may be stable in the Thomas-Fermi approximation since appropriate choices for the dark matter particle mass and scattering length are made. The demonstration is performed by means of the calculation of the potential, kinetic and self-interaction energy terms of a galactic halo described by a Boehmer-Harko density profile. We discuss the validity of the Thomas-Fermi approximation for the halo system, and show that the kinetic energy contribution is indeed negligible., Comment: 10 pages, 2 figures; v.2: 11 pages, 3 figures, references added, matches published version in JCAP

We assume that the galactical dark matter halo, considered composed of an axionlike particles Bose-Einstein condensate \cite{pir12}, can present topological defects, namely domain walls, arising as the dark soliton solution for the Gross-Pitaevskii equation in a self-graviting potential. We investigate the influence that such substructures would have in the gravitational interactions within a galaxy. We find that, for the simple domain wall model proposed, the effects are too small to be identified, either by means of a local measurement of the gradient of the gravitational field or by analysing galaxy rotation curves. In the first case, the gradient of the gravitational field in the vicinity of the domain wall would be $10^{-31}\; (m/s^2)/m$. In the second case, the ratio of the tangential velocity correction of a star due to the presence of the domain wall to the velocity in the spherical symmetric case would be $10^{-8}$., Comment: 11 pages; 6 figures; v.2: 12 pages, matches published version in JCAP

We propose here the dark matter content of galaxies as a cold bosonic fluid composed of Weakly Interacting Slim Particles (WISPs), represented by spin-0 axion-like particles and spin-1 hidden bosons, thermalized in the Bose-Einstein condensation state and bounded by their self-gravitational potential. We analyze two zero-momentum configurations: the polar phases in which spin alignment of two neighbouring particles is anti-parallel and the ferromagnetic phases in which every particle spin is aligned in the same direction. Using the mean field approximation we derive the Gross-Pitaevskii equations for both cases, and, supposing the dark matter to be a polytropic fluid, we describe the particles density profile as Thomas-Fermi distributions characterized by the halo radii and in terms of the scattering lengths and mass of each particle. By comparing this model with data obtained from 42 spiral galaxies and 19 Low Surface Brightness (LSB) galaxies, we constrain the dark matter particle mass to the range $10^{-6}-10^{-4} eV$ and we find the lower bound for the scattering length to be of the order $10^{-14} fm$., Comment: 13 pages; 6 figures; references added; v.3: typo corrected in the abstract, published in JCAP

In this work we extend the first order formalism for cosmological models that present an interaction between a fermionic and a scalar field. Cosmological exact solutions describing universes filled with interacting dark energy and dark matter have been obtained. Viable cosmological solutions with an early period of decelerated expansion followed by late acceleration have been found, notably one which presents a dark matter component dominating in the past and a dark energy component dominating in the future. In another one, the dark energy alone is the responsible for both periods, similar to a Chaplygin gas case. Exclusively accelerating solutions have also been obtained., Comment: 14 pages, 4 figures;v.4: published version

An analysis of the solutions for the field equations of generalized scalar-tensor theories of gravitation is performed through the study of the geometry of the phase space and the stability of the solutions, with special interest in the Brans-Dicke model. Particularly, we believe to be possible to find suitable forms of the Brans-Dicke parameter omega and potential V of the scalar field, using the dynamical systems approach, in such a way that they can be fitted in the present observed scenario of the Universe., Comment: revtex, 2 pages, 4 eps figures, to appear in Brazilian Journal of Physics (proceedings of the Conference 100 Years of Relativity, Sao Paulo, Brazil, August 2005)