Corrections to the apparent value of the cosmological constant due to local inhomogeneities
Supernovae observations strongly support the presence of a cosmological constant, but its value, which we will call apparent, is normally determined assuming that the Universe can be accurately described by a homogeneous model. Even in the presence of a cosmological constant we cannot exclude nevertheless the presence of a small local inhomogeneity which could affect the apparent value of the cosmological constant. Neglecting the presence of the inhomogeneity can in fact introduce a systematic misinterpretation of cosmological data, leading to the distinction between an apparent and true value of the cosmological constant. We establish the theoretical framework to calculate the corrections to the apparent value of the cosmological constant by modeling the local inhomogeneity with a ΛLTB solution. Our assumption to be at the center of a spherically symmetric inhomogeneous matter distribution correspond to effectively calculate the monopole contribution of the large scale inhomogeneities surrounding us, which we expect to be the dominant one, because of other observations supporting a high level of isotropy of the Universe around us. By performing a local Taylor expansion we analyze the number of independent degrees of freedom which determine the local shape of the inhomogeneity, and consider the issue of central smoothness, showing how the same correction can correspond to different inhomogeneity profiles. Contrary to previous attempts to fit data using large void models our approach is quite general. The correction to the apparent value of the cosmological constant is in fact present for local inhomogeneities of any size, and should always be taken appropriately into account both theoretically and observationally.

title: Scale dependent non gaussianity from generalized features of the inflaton potential
abstract: We study the effects of a general class of features of the inflaton potential on the spectrum and bispectrum of primordial curvature perturbations. These features correspond to a discontinuity in the $n-th$ order derivative of the potential. We provide fully numerical calculations and analytical approximations for the spectrum and the bispectrum, which are in good agreement with each other. The spectrum of primordial perturbations has oscillations around the scale $k_0$ which leaves the horizon at the time $\tau_0$ when the feature occurs, with the amplitude and phase of the oscillations determined by the size and the order of the discontinuity. Both in the squeezed and equilateral large scale limit the bispectrum has an oscillatory behavior whose phase depends on the parameters determining the discontinuity, and whose amplitude is inversely proportional to the scale. The small scale bispectrum in the squeezed and equilateral limits have a very similar form and are quadratically suppressed. Given the generality of this class of features it could be used to model phenomenologically different types of non gaussian features encountered in observational data such as the cosmic microwave background radiation or large scale structure.

title: Mimicking the cosmological constant for more than one observable with large scale inhomogeneities
abstract: Assuming the definition of the inversion problem (IP) as the exact matching of the terms in the low redshift expansion of cosmological observables calculated for different cosmological models, we solve the IP for D L (z) and the redshift spherical shell mass density mn(z) for a central observer in a Lemaitre-Tolman-Bondi (LTB) space without cosmological constant and a generic ACDM model. We show that the solution of the IP is unique, corresponds to a matter density profile which is not smooth at the center, and that the same conclusions can be reached expanding self-consistently to any order all the relevant quantities. Contrary to the case of a single observable inversion problem, it is impossible to solve the IP (LTB vs ACDM) for both mn(z) and D L ( Z ) while setting one of the two functions k(r) or t b (r) to zero, even allowing nonsmooth matter profiles. Our conclusions are general, since they are exclusively based on comparing directly physical observables in redshift space, and do not depend on any special ansatz or restriction for the functions defining a LTB model.

title: Can smooth LTB models mimicking the cosmological constant for the luminosity distance also satisfy the age constraint?
abstract: The central smoothness of the functions defining a LTB solution plays a crucial role in their ability to mimic the effects of the cosmological constant. Even if non-smoothness is not physically inconsistent with the theory of general relativity, smoothness is still an important geometrical property characterizing the solution of the Einstein’s equations. So far attention has been focused on $$C^{1}$$C1 models while in this paper we approach it in a more general way, investigating the implications of higher order central smoothness conditions for LTB models reproducing the luminosity distance of a $$\Lambda CDM$$ΛCDM Universe. Our analysis is based on a low red-shift expansion, and extends previous investigations by including also the constraint coming from the age of the Universe and re-expressing the equations for the solution of the inversion problem in a manifestly dimensionless form which makes evident the freedom to accommodate any value of $$H_0$$H0 as well. Higher order smoothness conditions strongly limit the number of possible solutions respect to the first order condition. Neither a $$C^{1}$$C1 or a $$C^{i}$$Ci LTB model can both satisfy the age constraint and mimic the cosmological constant for the luminosity distance. This implies that it is not necessary to include any additional observable to distinguish mathematically the theoretical predictions of a smooth LTB model from a $$\Lambda CDM$$ΛCDM. One difference is in the case in which the age constraint is not included and the bang function is zero, in which there is a unique solution for $$C^1$$C1 models but no solution for the $$C^{i}$$Ci case. Another difference is in the case in which the age constraint is not included and the bang function is not zero, in which the solution is undetermined for both $$C^1$$C1 and $$C^{i}$$Ci models, but the latter ones have much less residual parametric freedom. Our results imply that any LTB model able to fit luminosity distance data and satisfy the age constraint is either not mimicking exactly the $$\Lambda CDM$$ΛCDM red-shift space theoretical predictions or it is not smooth.

title: Redshift spherical shell energy in isotropic Universes
abstract: We introduce the redshift spherical shell energy, which can be used to test in the redshift space the radial inhomogeneity of an isotropic universe, providing additional constraints for Lemaitre-Tolman-Bondi models, and a more general test of cosmic homogeneity.

title: Effect of inhomogeneities on apparent cosmological acceleration

title: Leptonic decays and kaon identification at the NA62 experiment at CERN
abstract: A study of the radiative leptonic K\(^+\) \(\rightarrow\) e\(^+\)v\(_e\) \(\gamma\) kaon decay is reported, using a partial sample of data collected by the NA62 experiment at CERN in 2007. The signal event selection, the study of trigger efficiencies and the measurement of form factors are presented. The main systematic uncertainties associated to the analysis are discussed and preliminary results on form factor parameters are obtained: 
 
V\(_0\) = 0.0946 \(\pm\) 0.0018\(_{stat}\) \(\pm\) 0.0170\(_{syst}\) 
\(\lambda\) = 0.521 \(\pm\) 0.055\(_{stat}\) \(\pm\) 0.052\(_{syst}\) 
 
with a statistical correlation between parameters of 0.94 and ~ 100% correlation between systematic errors. 
 
The outcome of a test run performed at CERN in October 2011 for the commissioning of a Cherenkov differential counter to be used for the charged kaon identification in the near-future NA62 research programme, is reported. The counter’s ability to distinguish between kaons and pions is validated by pressure scan results. Tests of various combinations of standard and new read-out technology and electronics are presented. The time resolution of the new photon detector technology (Hamamatsu R7400-U03 PMT) to be replaced for the detector upgrade in NA62 is measured: 
 
\(\sigma\)T =(251 \(\pm\)2)ps.