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In this paper, we delve into the significance of local scale symmetry and the role of the associated noether current, within gravitational theories which are based in non-riemannian background space. Our focus is in Weyl and in Riemann-Cartan geometry based gravitational theories. We show that local scale symmetry is associated with vanishing noether current whenever there are not new propagating gravitational degrees of freedom beyond the two polarizations of the massless graviton. In contrast, in local scale invariant theories where there are more than two propagating gravitational degrees of freedom, local scale symmetry is associated with nonvanishing noether current. The known result that Weyl symmetry has vanishing noether current, is generalized to non-riemannian gravitational theories. An exception are the local scale invariant gravitational theories with vectorial nonmetricity, where the associated noether current is nonvanishing., Comment: 16 pages, version matching the published one on PRD

Building on the success of the Starobinsky model in describing the inflationary period of the universe, we investigate two simple generalizations of this model and their constraints imposed by the reheating epoch. The first generalization takes the form $R^{2p}$, while the second is the $\alpha$-Starobinsky model. We first focus on the case where $p=1$ or equivalently, $\alpha=1$, which corresponds to the original Starobinsky model. We derive exact consistency relations between observables and cosmological quantities, without neglecting any terms, and impose the reheating condition $0 < \omega_{re} < 0.25$, where $\omega_{re}$ is the equation of state parameter at the end of reheating. This allows us to obtain new bounds for $n_s$ and $r$ that satisfy this condition and apply them to other observables and cosmological quantities. We repeat this process for the cases where $p \neq 1$ and $\alpha \neq 1$ and find that these generalizations only result in minor modifications of the Starobinsky model, including the potential and the bounds on observables and cosmological quantities., Comment: 17 pages, 2 figures. Accepted for publication in JCAP

Scalar fields are widely and popularly used in cosmology in order to explain different phenomena among which, inflation and dark energy are two of the most popular ones. Specifically, in recent years, scale invariance in the gravitational sector has gained interest due to its simplicity, ability to model inflation and the dynamical generation of the Planck scale. In this paper, motivated by a non minimally coupled scale invariant $R^{2}$ gravitational model originally proposed by M.Rinaldi and L. Vanzo, we investigate how the inclusion of a vector scalar interaction that respects the scale invariance of the original model may affect the early and late time dynamics. We employ dynamical analysis tools in order to find the fixed points of the system and the local solutions for each variable around each fixed point finding out that the early universe solution of the extended model is compatible with that found in the original model with the exception of a new unstable fixed point appearing in the extended model. This new fixed point however has the same linealized solutions as the unstable fixed point found for the original model. We later employ numerical calculations in order to check that the analytical approach holds. Furthermore we show how the dynamical generation of the Planck mass is unaffected by the new field content of the model. Finally, we motivate and investigate a reduced version of the extended model finding out that, at late times, the extended model has only stable de Sitter fixed points where the scalar field becomes constant taking the role of the cosmological constant and the vector field is washed out., Comment: 26 pages, 8 figures

We present a simple procedure to obtain universal bounds for quantities of cosmological interest, such as the number of $e$-folds during inflation, reheating, and radiation, as well as the reheating temperature. The main assumption is to represent each of the various epochs of evolution of the universe as being due to a single substance changing instantaneously into the next, describing a new era of evolution of the universe. This assumption, commonly used to obtain solutions of the Friedmann equations for simple cosmological models, is implemented here to find model-independent bounds on cosmological quantities of interest. In particular, we find that the bound $N_k\approx 56$ for $-\frac{1}{3} < \omega_{re} < \frac{1}{3}$ is very robust as an upper bound on the number of $e$-folds during inflation and also as a lower bound when $\omega_{re} > \frac{1}{3}$, where $\omega_{re}$ is the effective equation of state parameter during reheating. These are model-independent results that any single-field model of inflation should satisfy. As an example, we illustrate the two approaches with the basic $\alpha$ attractor model and show how they complement each other., Comment: 17 pages, 3 figures, 3 tables. Accepted for publication in JCAP

In recent years, gravitational models motivated by quantum corrections to gravity which introduce higher order terms like $R^{2}$ or terms in which the Riemann tensor is not symmetric have been studied by several authors in the form of a general Brans-Dicke type model containing the Ricci scalar, the Holst term and the Nieh-Yan invariant. In this paper we focus on the less explored Jordan frame of such theories and in the comparison between both this frame and the Einstein one. Furthermore, we discuss the role of the transformation of the torsion under conformal transformations and show that the transformation proposed in this paper (extended conformal transformation) contains a special case of the projective transformation of the connection used in some of the papers that motivated this work. We discuss the role and advantages of the extended conformal transformation and show that this new approach can have interesting consequences by working with different variables such as the metric and torsion. Moreover, we study the stability of the system via a dynamical analysis in the Jordan frame, this in order to analyze whether or not we have the fixed points that can be later identified as the inflationary attractor and the unstable fixed point where inflation could take place. Finally we study the scale invariant case of the general model in the Jordan frame. We find out that both the scalar spectral index and the tensor-to-scalar ratio are in agreement with the latest Planck results., Comment: 25 pages, references added and improved manuscript. Accepted for publication in EPJP

Using a hyperbolic complex plane, we study the realization of the underlying hyperbolic symmetry as an internal symmetry that enables the unification of scalar fields of cosmological and particle physics interest. Such an unification is achieved along the universal prescriptions used in physics, avoiding the use of concepts as Euclideanization, non-canonical Lagrangians and hidden structures, that have appeared in other approaches. The scalar potentials constructed within the present scheme are bounded from below, and the realization of the spontaneous symmetry breaking of the aforementioned noncompact symmetry is studied. The profiles of these potentials with exact/broken hyperbolic symmetry replicate qualitative aspects of those ones used in inflationary models, and then a detailed com\-pa\-ri\-son is made. Moreover, the homotopy constraints of the topology induced on the corresponding vacuum manifolds, restricts the existence of topological defects associated with continuous symmetries, allowing only those defects associated with discrete symmetries; the consistency of these results is contrasted with current observational tests from the LIGO/Virgo collaboration, and terrestrial experiments based on a synchronized network of atomic magnetometers. At the end, the nonre\-la\-tivistic limit of the model is identified with a hyperbolic version of the nonlinear Schr\"odinger equation.

The strong interaction of antikaons (K-) with nucleons and nuclei in the low energy regime represents an active research field connected intrinsically with few-body physics. There are important open questions like the question of antikaon nuclear bound states - the prototype system being K-pp. A unique and rather direct experimental access to the antikaon-nucleon scattering lengths is provided by precision X-ray spectroscopy of transitions in low-lying states of light kaonic atoms like kaonic hydrogen isotopes. In the SIDDHARTA experiment at the electron-positron collider DA?NE of LNF-INFN we measured the most precise values of the strong interaction observables, i.e. the strong interaction on the 1s ground state of the electromagnetically bound K-p atom leading to a hadronic shift and a hadronic broadening of the 1s state. The SIDDHARTA result triggered new theoretical work which achieved major progress in the understanding of the low-energy strong interaction with strangeness. Antikaon-nucleon scattering lengths have been calculated constrained by the SIDDHARTA data on kaonic hydrogen. For the extraction of the isospin-dependent scattering lengths a measurement of the hadronic shift and width of kaonic deuterium is necessary. Therefore, new X-ray studies with the focus on kaonic deuterium are in preparation (SIDDHARTA2). Many improvements in the experimental setup will allow to measure kaonic deuterium which is challenging due to the anticipated low X-ray yield. Especially important are the data on the X-ray yields of kaonic deuterium extracted from a exploratory experiment within SIDDHARTA., Comment: Proc. Few Body 21, 4 pages, 2 figures

The AMADEUS experiment aims to provide unique quality data of $K^-$ hadronic interactions in light nuclear targets, in order to solve fundamental open questions in the non-perturbative strangeness QCD sector, like the controversial nature of the $\Lambda(1405)$ state, the yield of hyperon formation below threshold, the yield and shape of multi-nucleon $K^-$ absorption, processes which are intimately connected to the possible existence of exotic antikaon multi-nucleon clusters. AMADEUS takes advantage of the DA$\Phi$NE collider, which provides a unique source of monochromatic low-momentum kaons and exploits the KLOE detector as an active target, in order to obtain excellent acceptance and resolution data for $K^-$ nuclear capture on H, ${}^4$He, ${}^{9}$Be and ${}^{12}$C, both at-rest and in-flight. During the second half of 2012 a successful data taking was performed with a dedicated pure carbon target implemented in the central region of KLOE, providing a high statistic sample of pure at-rest $K^-$ nuclear interactions. For the future dedicated setups involving cryogenic gaseous targets are under preparation., Comment: 14 pages, 6 figures

The X-ray transition yields of kaonic atoms produced in Kapton polyimide (C22H10N2O5) were measured for the first time in the SIDDHARTA experiment. X-ray yields of the kaonic atoms with low atomic numbers (Z = 6, 7, and 8) and transitions with high principal quantum numbers (n = 5-8) were determined. The relative yield ratios of the successive transitions and those of carbon-to-nitrogen (C:N) and carbon-to-oxygen (C:O) were also determined. These X-ray yields provide important information for understanding the capture ratios and cascade mechanisms of kaonic atoms produced in a compound material, such as Kapton., Comment: Accepted in Nucl. Phys. A (2013)

The strong-interaction shift of kaonic 3He and 4He 2p states was measured using gaseous targets for the first time in the SIDDHARTA experiment. The determined shift of kaonic 4He is much smaller than the values obtained in the experiments performed in 70's and 80's. Thus, the problems in kaonic helium (the "kaonic helium puzzle") was definitely solved by our measurements. The first observation of the kaonic 3He X-rays was also achieved. The shift both of kaonic 3He and 4He was found to be as small as a few eV., Comment: Proc of Hadron2011