We investigate the possibility of detecting the Podolsky generalized electrodynamics constant a. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis, et al (Phys. Rev. Lett. 99, (2007) 200401) who looked for deviations from Coulomb's inverse-square law in the context of Proca model. Our results show that this experiment has not enough precision for measurements of a. In order to set up bounds for a we investigate the influence of Podolsky's electrostatic potential on the ground state of the Hydrogen atom. The value of the ground state energy of the Hydrogen atom requires Podolsky's constant to be smaller than 5.6 fm, or in energy scales larger than 35.51 MeV.

The high precision attained by cosmological data in the last few years has increased the interest in exact solutions. Analytic expressions for solutions in the Standard Model are presented here for all combinations of Λ = 0 , Λ = 0, κ = 0 and κ = 0, in the presence and absence of radiation and nonrelativistic matter. The most complete case (here called the ΛγCDM Model) has Λ = 0, κ = 0, and supposes the presence of radiation and dust. It exhibits clearly the recent onset of acceleration. The treatment includes particular models of interest such as the ΛCDM Model (which includes the cosmological constant plus cold dark matter as source constituents).

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature.We analyze the form of the second field strenght, G = ∂F + f AF , in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his Generalized Electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behaviour at short distances as well as a meso-large distance modification.

In this work, the hydrogen's ionization energy was used to constrain the free parameter b of three BornInfeld-like electrodynamics namely Born-Infeld itself, Logarithmic electrodynamics and Exponential electrodynamics. An analytical methodology capable of calculating the hydrogen ground state energy level correction for a generic nonlinear electrodynamics was developed. Using the experimental uncertainty in the ground state energy of the hydrogen atom, the bound b > 5.37 × 10 20 K V m , where K = 2, 4 √ 2/3 and √ π for the Born-Infeld, Logarithmic and Exponential electrodynamics respectively, was established. In the particular case of Born-Infeld electrodynamics, the constraint found for b was compared with other constraints present in the literature.

The Reduced Relativistic Gas (RRG) is a simplified version of the ideal relativistic gas, which assumes that all particles have the same momentum magnitude. Although this is a very idealized situation, the resulting model preserves the phenomenology of Maxwell-Boltzmann distribution and, in some situations, can be described as a perfect fluid, without introducing large errors in both cosmological background and first-order perturbations. The perfect fluid description of RRG model was already used to study the warmness of dark matter, massive neutrinos and interaction of baryons and photons before recombination, showing very good agreement with previous works based on the full Einstein-Boltzmann system of equations. In order to understand these results and construct a more general and formal framework for RRG, we develop a theoretical description of first-order cosmological perturbations of RRG, based on a distribution function which encodes the simplifying assumption that all particles have the same momentum magnitude. The full set of Einstein-Boltzmann equations for RRG distribution are derived and quantities beyond the perfect fluid approximation are studied. Using RRG to describe warm dark matter, we show that, for particles with m ∼ keV, the perfect fluid approximation is valid on scales k < 10 h/Mpc, for most of the universe evolution. We also determine initial conditions for RRG in the early universe and study the evolution of potential in a toy model of universe composed only by RRG.