On the effect of the cosmological expansion on the gravitational lensing by a point mass

We analyze the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a pointlike lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter $H$ we derive and approximately solve the null geodesic equations, finding an expression for the bending angle $\delta$, which we expand in powers of the mass-to-closest approach distance ratio and of the impact parameter-to-lens distance ratio. It turns out that the leading order of the aforementioned expansion is the same as the one calculated for the Schawarzschild metric and that cosmological corrections contribute to $\delta$ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of $H$ constant and find that they provide a correction of order $10^{-11}$ on the lens mass estimate.Comment: 10 pages, 7 figures (created with tikz

Gravitational potential evolution in Unified Dark Matter Scalar Field Cosmologies: an analytical approach

We investigate the time evolution of the gravitational potential Phi for a special class of non-adiabatic Unified Dark matter Models described by scalar field lagrangians. These models predict the same background evolution as in the LambdaCDM and possess a non-vanishing speed of sound. We provide a very accurate approximation of Phi, valid after the recombination epoch, in the form of a Bessel function of the first kind. This approximation may be useful for a future deeper analysis of Unified Dark Matter scalar field models.Comment: 5 pages, 6 figure

Scalar-Tensor gravity with system-dependent potential and its relation with Renormalization Group extended General Relativity

We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the potential is not necessarily fixed at the action level, and show that this extended ST theory formally contains the Renormalization Group case. We also propose here a Renormalization Group scale setting identification that is explicitly covariant and valid for arbitrary relativistic fluids.Comment: 29 pages, 2 figs. v2: small changes in text and ref's. v3: further details on the relation between this work and others on the Renormalization Group. Version to appear in JCA

Scalar models for the unification of the dark sector

We review the difficulties of the generalized Chaplygin gas model to fit observational data, due to the tension between background and perturbative tests. We argue that such issues may be circumvented by means of a self-interacting scalar field representation of the model. However, this proposal seems to be successful only if the self-interacting scalar field has a non-canonical form. The latter can be implemented in Rastall's theory of gravity.Comment: Latex file, 8 pages, 3 figures in eps format. To appear in the proceedings of the CosmoSul conference, held in Rio de Janeiro, Brazil, 01-05 august of 201

Unified Dark Matter scalar field models with fast transition

We investigate the general properties of Unified Dark Matter (UDM) scalar field models with Lagrangians with a non-canonical kinetic term, looking specifically for models that can produce a fast transition between an early Einstein-de Sitter CDM-like era and a later Dark Energy like phase, similarly to the barotropic fluid UDM models in JCAP1001(2010)014. However, while the background evolution can be very similar in the two cases, the perturbations are naturally adiabatic in fluid models, while in the scalar field case they are necessarily non-adiabatic. The new approach to building UDM Lagrangians proposed here allows to escape the common problem of the fine-tuning of the parameters which plague many UDM models. We analyse the properties of perturbations in our model, focusing on the the evolution of the effective speed of sound and that of the Jeans length. With this insight, we can set theoretical constraints on the parameters of the model, predicting sufficient conditions for the model to be viable. An interesting feature of our models is that what can be interpreted as w_{DE} can be <-1 without violating the null energy conditions.Comment: Slightly revised version accepted for publication in JCAP, with a few added references; 27 pages, 13 figure

The Step-Harmonic Potential

We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. For high energies we recover the classical half-period limit.Comment: 19 pages, 7 figure

Einstein e sua famosa fórmula E = mc²

Uma das equações mais populares da física é a famosa fórmula da energia de repouso, E = mc2, deduzida por Albert Einstein no desenvolvimento da teoria da relatividade restrita. O artigo onde as ideias que dão origem a essa equação são discutidas por Einstein é apresentado aqui em uma tradução direta do alemão para o português.One of the most popular equations of physics is the famous rest energy formula, E = mc2, derived by Albert Einstein while developing the special relativity theory. The article where the ideas that give origin to this equation are discussed by Einstein is presented here in a direct translation from German to Brazilian Portugues