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Here we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed. Sometimes this leads to an unwanted doubling of the results. In this paper we illustrate this issue with the example of two apparently different gravitational theories: (i) the (minimally coupled) Einstein-massless-scalar system and (ii) the S\'aez-Ballester theory. We demonstrate that the latter is not a scalar-tensor theory of gravity, as widely acknowledged. Moreover, S\'aez-Ballester theory is identified with the Einstein-massless-scalar theory. As illustrations of this identification we show that several known solutions of S\'aez-Ballester theory are also solutions of the Einstein-massless-scalar system and viceversa. Cosmological arguments are also considered. In particular, a dynamical systems-based demonstration of the dynamical equivalence between these theories is given. The study of the asymptotic dynamics of the S\'aez-Ballester based cosmological model shows that there are not equilibrium points which could be associated with accelerated expansion, unless one includes a cosmological constant term or a self-interacting scalar field. This is a well-known result for cosmological models which are based in the Einstein-self-interacting-scalar theory, also known as quintessence., Comment: 12 pages, 4 eps figures. We include a demonstration of the dynamical equivalence between SBT and EMS system based on the dynamical systems tools applied in the FRW cosmological context. This version matches the one accepted by the Int. J. Modern Phys. D

In this paper we perform a thorough dynamical systems analysis of the cubic galileon model non-minimally coupled to the dark matter. Three well-known classes of interacting models are considered where the energy exchange between the dark components is a function of the dark matter density and of the dark energy density: $Q_1=3\alpha H\rho_m$, $Q_2=3\beta\rho_m\dot{\phi}$ and $Q_3=3 \epsilon H \rho_\phi$, respectively. We are able to show the global asymptotic dynamics of the model for the exponential potential in a homogeneous and isotropic background. The cosmological implications of the proposed scenarios are explored and it is found that, in addition to the appearance of new equilibrium configurations that do not appear neither in the non-interacting cubic galileon model nor in the interacting quintessence model, there is a significant impact of the non-minimal coupling through modification of the stability properties of the critical points. The resulting cosmological scenario provides a bigbang origin of the cosmic expansion, an early transient stage of inflationary expansion, as well as matter-scaling late time stable state of the universe, among other solutions of lesser cosmological interest. This work extends previous studies of coupled dark energy to a broader class of gravitational theories., Comment: 22 pages, 6 figures. Version that matches the one published

Electrification by rubbing different materials is a well known phenomenon with a history that begun more than five centuries BC. However, simple experiments can lead to contradictory or inconsistent results and the history of this phenomena is plagued with non-intuitive results. For example, triboelectric charging by rubbing identical materials is possible. In this work we want to highlight some historical aspects of triboelectricity that could enrich the discussion of electrostatics in an undergraduate physics course. We will focus on the effect of strain on the triboelectric properties of a sample, which we think is not well known to physics teachers. We will show that it is possible to obtain robust polarities by rubbing identical rubber balloons of different radii and we will also show that this charging method can be very useful in introductory physics courses.

In this paper we show that an equivalence between Horndeski and beyond Horndeski theories and general relativity with an effective imperfect fluid can be formally established. The formal equivalence is discussed for several particular cases of interest. Working in the cosmological framework, it is shown that, while the effective stress-energy tensor of viable Horndeski theories is formally equivalent to that of an imperfect fluid with anisotropic stresses and vanishing heat flux vector, the effective stress-energy tensor of beyond Horndeski theories is equivalent to the one of a perfect fluid instead., Comment: 17 pages, no figures. Several bibliographic references added

In the bibliography a certain confusion arises in what regards to the classification of the gravitational theories into scalar-tensor theories and general relativity with a scalar field either minimally or non-minimally coupled to matter. Higher-derivatives Horndeski and beyond Horndeski theories that at first sight do not look like scalar-tensor theories only add to the confusion. To further complicate things, the discussion on the physical equivalence of the different conformal frames in which a given scalar-tensor theory may be formulated, makes even harder to achieve a correct classification. In this paper we propose a specific criterion for an unambiguous identification of scalar-tensor theories and discuss its impact on the conformal transformations issue. The present discussion carries not only pedagogical but also scientific interest since an incorrect classification of a given theory as a scalar-tensor theory of gravity may lead to conceptual issues and to the consequent misunderstanding of its physical implications., Comment: 22 pages, no figures. Version that matches the one accepted by the IJMPD. arXiv admin note: substantial text overlap with arXiv:1901.08690

In this paper we generalize the dynamical systems analysis of the cubic galileon model previously investigated in \cite{rtgui} by including self-interaction potentials beyond the exponential one. It will be shown that, consistently with the results of \cite{rtgui}, the cubic self-interaction of the galileon vacuum appreciably modifies the late-time cosmic dynamics by the existence of a phantom-like attractor (among other super-accelerated solutions that are not of interest in the present investigation). In contrast, in the presence of background matter the late-time cosmic dynamics remains practically the same as in the standard quintessence scenario. This means that we can not recover the cubic galileon vacuum continuously from the more general cubic quintessence with background matter, by setting to zero the matter energy density (and the pressure). This happens to be a kind of cosmological vDVZ discontinuity that can be evaded by means of the cosmological version of the Vainshtein screening mechanism., Comment: 25 pages, 3 figures. Version that matches the one published by CQG

In this paper we investigate the so called "phantom barrier crossing" issue in a cosmological model based in the scalar-tensor theory with non-minimal derivative coupling to the Einstein's tensor. Special attention will be paid to the physical bounds on the squared sound speed. The numeric results are geometrically illustrated by means of a qualitative procedure of analysis that is based on the mapping of the orbits in the phase plane onto the surfaces that represent physical quantities in the extended phase space, that is: the phase plane complemented with an additional dimension relative to the given physical parameter. We find that the cosmological model based in the non-minimal derivative coupling theory -- this includes both the quintessence and the pure derivative coupling cases -- has serious causality problems related with superluminal propagation of the scalar and tensor perturbations. Even more disturbing is the finding that, despite that the underlying theory is free of the Ostrogradsky instability, the corresponding cosmological model is plagued by the Laplacian (classical) instability related with negative squared sound speed. This instability leads to an uncontrollable growth of the energy density of the perturbations that is inversely proportional to their wavelength. We show that independent of the self-interaction potential, for the positive coupling the tensor perturbations propagate superluminally, while for the negative coupling a Laplacian instability arises. This latter instability invalidates the possibility for the model to describe the primordial inflation., Comment: 26 pages, 27 eps figures. Version accepted by the CQG journal