A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = ∂F + f AF arises besides the one of the first order treatment, F = ∂A − ∂A + f AA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is LP ∝ G 2 . In this application the photon mass is estimated. The SU (N ) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.

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.

We analyse the Klein–Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.

We propose a cosmological scenario involving a scalar field, ϕ, that is a source of Dark Matter as well as of Dark Energy. Besides ϕ, the Lagrangian of the field theory envisaged in our scenario contains a second field χ, for simplicity assumed to be a scalar, too. For fixed values of χ, the potential term decays exponentially at large positive values of ϕ. While ϕ is not coupled to Standard Model fields, χ is assumed to be coupled to them, and the Green functions of χ depend on the cosmological redshift in the expanding universe. We assume that the term in the Lagrangian coupling χ to ϕ is such that, at redshifts z larger than some critical redshift zc, ϕ is trapped near ϕ = 0, and oscillations of ϕ about ϕ = 0 describing massive scalar particles give rise to Dark Matter. At redshifts below zc, the field ϕ is no longer trapped near the origin and starts to "roll" towards large field values. A homogenous component of ϕ emerges that acts as Dark Energy. Within over-dense regions, such as galaxies and galaxy clusters, the redshifting of χ stops, and ϕ therefore remains trapped near ϕ = 0 as long as zc is smaller than the redshift when structures on galactic scales decouple from the Hubble flow. Thus, at the present time, ϕ describes both Dark Energy and Dark Matter. * Electronic address: rhb@physics.mcgill.ca † Electronic address: cuzinatto@hep.physics.mcgill.ca ‡ Electronic address: juerg@phys.ethz.ch § Electronic address: namba@physics.mcgill.ca 1 The energy scale of supersymmetry breaking is chosen such that one can explain, for example, the hierarchy problem in particle

An extension of the Starobinsky model is proposed. Besides the usual Starobinsky Lagrangian, a term proportional to the derivative of the scalar curvature, ∇µR∇ µ R, is considered. The analyzis is done in the Einstein frame with the introduction of a scalar field and a vector field. We show that inflation is attainable in our model, allowing for a graceful exit. We also build the cosmological perturbations and obtain the leading-order curvature power spectrum, scalar and tensor tilts and tensor-to-scalar ratio. The tensor and curvature power spectrums are compared to the most recent observations from BICEP2/Keck collaboration. We verify that the scalar-to-tensor rate r can be expected to be up to three times the values predicted by Starobinsky model.Hence, the fluid represented by Eq. (9) has no contribution from viscous shear components, which are null here. Notice that the heat flux vector exists solely due to the higher order term -were it absent, the theory would be reduced to Starobinsky's model and, therefore, would be represented by a perfect fluid energy-momentum tensor. The above equations are specified in FLRW spacetime in the next section.

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure × energy density equations of state p(ρ). The usual approach in cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the statistical mechanics of real fluids, is proposed to include them. A toy model is presented which shows how such interaction terms could be applied to engender significant cosmological effects.