Abstract: General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordinary ability to regularise the gravitational dynamics, leading to non-singular cosmologies and regular black hole spacetimes in a very robust manner and without resorting to quantum gravity effects. This has boosted the interest in these theories in applications to stellar structure, compact objects, inflationary scenarios, cosmological singularities, and black hole and wormhole physics, among others. We review the motivations, various formulations, and main results achieved within these theories, including their observational viability, and provide an overview of current open problems and future research opportunities.

Abstract: This work is a brief presentation of the theory based on the SU(3)(c) circle times SU(3)(L) circle times U(1)(X) gauge group in the presence of heavy leptons. Recent studies [1] have considered a set of four possible variants for the 3-3-1HL, whose content arises according to the so-denoted variable beta. Since it has been argued about the presence of stable charged particles in this sort of model, we divide the different sectors of the Lagrangian between universal and specific vertices, and conclude that the omission of beta-dependent terms in the potential may induce discrete symmetry for the versions defined by vertical bar beta vertical bar = root 3 . In the context of vertical bar beta vertical bar = 1/root 3, where the new degrees of freedom have the same standard electric charges, additional Yukawa interactions may create decay channels into the SM sector. Furthermore, motivated by a general consequence of the Goldstone theorem, a method of diagonalization by parts is introduced in the Scalar sector and provides a clarification on the definition of mass eigenstates. In summary, we develop the most complete set of terms allowed by the symmetry group and resolve their definitive pieces in order to justify the model description present in the literature.

Abstract: We report measurements of charm-mixing parameters based on the decay-time-dependent ratio of D-0 -> K+pi(-) to D-0 -> K-pi(+) rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of 5.0 fb(-1) recorded by the LHCb experiment from 2011 through 2016. Assuming charge-parity (CP) symmetry, the mixing parameters are determined to be x'(2) = (3.9 +/- 2.7) x 10(-5), y' = (5.28 +/- 0.52) x 10(-3), and R-D = (3.454 +/- 0.031) x 10(-3). Without this assumption, the measurement is performed separately for D-0 and (D) over bar (0) mesons, yielding a direct CP-violating asymmetry A(D) = (-0.1 +/- 9.1) x 10(-3), and magnitude of the ratio of mixing parameters 1.00 < vertical bar q/p vertical bar < 1.35 at the 68.3% confidence level. All results include statistical and systematic uncertainties and improve significantly upon previous single-measurement determinations. No evidence for CP violation in charm mixing is observed.