Estamos vivenciando um período de extrema efervescência intelectual na área da cosmologia. Um volume enorme de dados observacionais em quantidade e qualidade sem precedência e um arcabouço teórico mais consistente, impeliram a cosmologia para uma era da precisão, transformando a disciplina em área de ponta da ciência contemporânea. Observações com Supernovas do tipo Ia (SNe Ia) mostraram que o Universo está expandindo aceleradamente, um fato sem explicação no modelo desacelerado tradicional. Identificar a causa dessa aceleração é hoje o problema mais fundamental da área. Tal como ocorreu no renascimento científico, a solução norteará os rumos da disciplina no futuro próximo e as possíveis respostas (se energia escura, alguma extensão da relatividade geral ou um mecanismo ainda desconhecido) deverão também alavancar o desenvolvimento da física. Nesse contexto, sem abdicar de uma abordagem pedagógica, apresentamos uma visão geral tanto dos principais resultados teóricos quanto das descobertas observacionais mais significativas da cosmologia nos últimos 100 anos. A saga da cosmologia moderna será apresentada numa trilogia. Neste artigo (Parte I), com base nos artigos de Einstein, de Sitter, Friedmann, Lemaître e Hubble, descreveremos o período decorrido entre as origens da cosmologia e a descoberta da expansão Universal (1929). Na Parte II veremos o período de 1930–1997, finalizando com o velho modelo padrão desacelerado. A Parte III será inteiramente dedicada ao modelo acelerado do Universo, o paradigma cósmico do século XXI.

We are experiencing a period of extreme intellectual effervescence in the area of cosmology. A huge volume of observational data in unprecedented quantity and quality and a more consistent theoretical framework propelled cosmology to an era of precision, turning the discipline into a cutting-edge area of contemporary science. Observations with type Ia Supernovae (SNe Ia), showed that the expanding Universe is accelerating, an unexplained fact in the traditional decelerated model. Identifying the cause of this acceleration is the most fundamental problem in the area. As in the scientific renaissance, the solution will guide the course of the discipline in the near future and the possible answers (whether dark energy, some extension of general relativity or a still unknown mechanism) should also leverage the development of physics. In this context, without giving up a pedagogical approach, we present an overview of both the main theoretical results and the most significant observational discoveries of cosmology in the last 100 years. The saga of cosmology will be presented in a trilogy. In this article (Part I), based on the articles by Einstein, de Sitter, Friedmann, Lemaître and Hubble, we will describe the period between the origins of cosmology and the discovery of Universal expansion (1929). In Part II we will see the period from 1930 to 1997, closing with the old standard decelerated model. The Part III will be entirely devoted to the accelerated model of the universe, the cosmic paradigm of the XXI century.

O chamado princípio da relatividade é capaz de determinar uma transformação geral de coordenadas que difere da forma lorentziana padrão por um velocidade desconhecida que não pode, em princípio, ser identificada com a velocidade da luz. Com base em uma nova análise do experimento de Michelson-Morley, usando esta transformação estendida, mostramos que tal velocidade invariante é determinada analíticamente, sem qualquer referência às equações de Maxwell e questões conceituais relacionadas a procedimentos de sincronização, definição de tempo e causalidade. Tal resultado demonstra de uma maneira pedagógica que a constância da velocidade da luz não precisa ser suposta como um postulado básico da teoria da relatividade especial, uma vez que ela pode ser deduzida diretamente a partir de um experimento óptico em combinação com o princípio da relatividade. O método apresentado aqui resulta numa dedução das transformações de Lorentz que é simples e elucidativa, apropriada para um curso introdutório sobre teoria da relatividade especial.

The so-called principle of relativity is able to fix a general coordinate transformation which differs from the standard Lorentzian form only by an unknown speed which cannot in principle be identified with the light speed. Based on a reanalysis of the Michelson-Morley experiment using this extended transformation we show that such unknown speed is analytically determined regardless of the Maxwell equations and conceptual issues related to synchronization procedures, time and causality definitions. Such a result demonstrates in a pedagogical manner that the constancy of the speed of light does not need to be assumed as a basic postulate of the special relativity theory since it can be directly deduced from an optical experiment in combination with the principle of relativity. The approach presented here provides a simple and insightful derivation of the Lorentz transformations appropriated for an introductory special relativity theory course.

Abstract: A new method is proposed to infer the Hubble constant Ho through the ob served mean transmitted flux from high-redshift quasars and the baryon acoustic oscillations (BAOs). A semi-analytical model for the cosmological-independent vol ume density distribution function was adopted; it allowed us to obtain constraints on the cosmological parameters once a moderate knowledge of the Inter Galactic Medium (IGM) parameters is assumed. Our analysis, based on two different sam ples of Lyman-α forest and the BAO measurement, restricts (h,Ω m) to the intervals 0.19 ≤ Ω m ≤ 0.23 and 0.53 ≤ h ≤ 0.82 (1σ). Although the constraints are weaker compared with other estimates, we point out that, with a bigger sample and a better knowledge of the IGM, this method could provide complementary results to measure the Hubble constant independently of the cosmic distance ladder.

Resumen: Se propone un nuevo método para inferir el valor de la constante de Hubble. Ho, mediante el flujo medio observado de cuásares de alto corrimiento al rojo y las oscilaciones acústicas de los bariones (BAOs). Se adopta un modelo semianalítico para la distribución de densidad volumétrica independiente de la cosmología que nos permite obtener límites para los parámetros cosmológicos una vez que se cuenta con una aceptable estimación de los parámetros del medio intergaláctico (IGM). Basado en dos muestras diferentes del bosque de Lyman-α y en la medición de las BAOs, nuestro análisis restringe (h,Ω m) a los intervalos 0.19 ≤ Ω m ≤ 0.23 y 0.53 ≤ h ≤ 0.82. Si bien estos límites son menos estrictos que los que se obtienen por otros métodos, señalamos que con muestras más numerosas y con un mejor conocimiento del IGM nuestro método podría aportar resultados complementarios para la determinación de la constante de Hubble, independientemente de la escala cósmica de distancias.

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, V(q) = alphaq n, where alpha and n are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of alpha, n and the total energy E. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem t(q). A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of n, it leads to a simple harmonic oscillator if E > 0, an "anti-oscillator" if E < 0, or a free particle if E = 0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of n. For n >> 1, it is found that the correction is just twice that one deduced for the simple harmonic oscillator (n = 2), and does not depend on the specific value of n.

We propose a new analytic approximation for the luminosity function of galaxies. The suggested expression behaves like the Schechter function at the faint end (f ~ La) but departs considerably at the bright end (L >> L*). We argue here that such a behavior may provide a better fit for the current observational data than does the Schechter function. Its practical interest is stressed by considering roughly the data set provided by the Stromlo-APM redshift survey. Implications on the estimates of the matter density parameter from mass-to-light ratio are also briefly discussed.

A large number of recent observational data strongly suggest that we live in a flat, accelerating Universe composed of ~ 1/3 of matter (baryonic + dark) and ~ 2/3 of an exotic component with large negative pressure, usually named Dark Energy or Quintessence. The basic set of experiments includes: observations from SNe Ia, CMB anisotropies, large scale structure, X-ray data from galaxy clusters, age estimates of globular clusters and old high redshift galaxies (OHRG's). It is now widely believed that such results provide the remaining piece of information connecting the inflationary flatness prediction (W T = 1) with astronomical observations. From a theoretical viewpoint, they have also stimulated the current interest for more general models containing an extra component describing this unknown dark energy, and simultaneously accounting for the present accelerating stage of the Universe. In this review we present a simplified picture of the main results and discuss briefly some difficulties underlying the emerging dark energy paradigm.

Old high-z galaxies are important tools for understanding the structure formation problem and may become the key to determine the ultimate fate of the Universe. In this paper, the inferred ages of the three oldest galaxies at high redshifts reported in the literature are used to constrain the first epoch of galaxy formation and to reanalyse the high-z time scale crisis. The lower limits on the formation redshift z f depends on the quantity of cold dark matter in the Universe. In particular, if omegam > or = 0.37 these galaxies are not formed in FRW cosmologies with no dark energy. This result is in line with the Supernovae type Ia measurements which suggest that the bulk of energy in the Universe is repulsive and appears like an unknown form of dark energy component. In a complementar analysis, unlike recent claims favoring the end of the age problem, it is shown that the Einstein-de Sitter model is excluded at high-z by 3sigma.

We analyse the planetary perihelion precession and the deffection of light in the Schwarzschild field modified by a conical defect. By using observational results from solar system tests of general relativity, we obtain limits on the conical defect parameter <img src="http:/img/fbpe/bjp/v30n2/ses.gif">. For the physical case of a cosmic string the quoted limits are one and three orders weaker than the cosmological bounds.

A general proof of the energy equipartition theorem is given. Our derivation holds for any distribution function depending on the phase space variables only through the Hamiltonian of the system. This approach generalizes the standard theorem in two main directions. On the one hand, it considers the contribution to the total mean energy of homogeneous functions having a more general type than the ones usually discussed in the literature. On the other hand, our proof does not rely on the assumption of a Boltzmann-Gibbs exponential distribution.