Abstract: We study the generation of primordial perturbations in a (single-field) slow-roll inflationary Universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a nonzero variance Delta(2) (k, t). However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize Delta(2) (k, t). This can (and should) be achieved by proper renormalization in an expanding Universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the cosmic microwave background anisotropies is significantly altered. We find a nontrivial change in the consistency condition that relates the tensor-to-scalar ratio r to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n(t) = 0, is now compatible with a nonzero ratio r approximate to 0.12 +/- 0.06, which is forbidden by the standard prediction (r = -8n(t)). The influence of relic gravitational waves on the cosmic microwave background may soon come within the range of planned measurements, offering a nontrivial test of the new predictions.

Abstract: Inspired by the peculiarities of the effective geometry of crystalline structures, we reconsider thick brane scenarios from a metric-affine perspective. We show that for a rather general family of theories of gravity, whose Lagrangian is an arbitrary function of the metric and the Ricci tensor, the background and scalar field equations can be written in first-order form, and tensorial perturbations have a non negative definite spectrum, which makes them stable under linear perturbations regardless of the form of the gravity Lagrangian. We find, in particular, that the tensorial zero modes are exactly the same as predicted by Einstein's theory regardless of the scalar field and gravitational Lagrangians.

Abstract: The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r = 2 M, while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.

Abstract: We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist. The incorporation of nonlinearities in the electromagnetic field may effectively reduce their mass spectrum by many orders of magnitude. As a consequence, these objects could be within (or near) the reach of current particle accelerators. We provide an exactly solvable model to support this idea.

Abstract: The optical appearance of a body compact enough to feature an unstable bound orbit, when surrounded by an accretion disk, is expected to be dominated by a luminous ring of radiation enclosing a central brightness depression typically known as the shadow. Despite observational limitations, the rough details of this picture have been now confirmed by the results of the Event Horizon Telescope (EHT) Collaboration on the imaging of the M87 and Milky Way supermassive central objects. However, the precise characterization of both features-ring and shadow-depends on the interaction between the background geometry and the accretion disk, thus being a fertile playground to test our theories on the nature of compact objects and the gravitational field itself in the strong-field regime. In this work we use both features in order to test a continuous family of solutions interpolating between regular black holes and horizonless compact objects, which arise within the Eddington-inspired Born-Infeld theory of gravity, a viable extension of Einstein's general relativity (GR). To this end we consider seven distinctive classes of such configurations (five black holes and two traversable wormholes) and study their optical appearances under illumination by a geometrically and optically thin accretion disk, emitting monochromatically with three analytic intensity profiles previously suggested in the literature. We build such images and consider the sub-ring structure created by light rays crossing the disk more than once and existing on top of the main ring of radiation. We discuss in detail the modifications as compared to their GR counterparts, the Lyapunov exponents of unstable nearly-bound orbits, as well as the differences between black hole and traversable wormholes for the three intensity profiles. In addition we use the claim by the EHT Collaboration on the radius of the bright ring acting (under proper calibrations) as a proxy for the radius of the shadow itself to explore the parameter space of our solutions compatible with such a result.