On a principle of cosmological uncertainty
We show that cosmological observations are subject to an intrinsic uncertainty which can be expressed in the form of an uncertainty relation similar to the Heisenberg principle. This is a consequence of the fact that the four dimensional space-time metric information is projected into the one-dimensional observational red-shift space, implying a limit on the amount of information which can be extracted about the underlying geometry. Since multiple space-time configurations can lead to the same red-shift, there is an unavoidable uncertainty about the determination of the space-time geometry. This suggests the existence of a limit about of the amount of information that cosmological observations can reveal about our Universe that no experiment could ever overcame, conceptually similar to what happens in quantum mechanics.

title: Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?
abstract: As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test such an hypothesis we calculate the low redshift expansion of the luminosity distance DL(z) and the redshift spherical shell mass density mn(z) for a central observer in a LTB space without cosmological constant and show how they cannot fit the observations implied by a ΛCDM model if the conditions to avoid a weak central singularity are imposed, i.e. if the matter distribution is smooth everywhere. Our conclusions are valid for any value of the cosmological constant, not only for ΩΛ > 1/3 as implied by previous proofs that qapp0 has to be positive in a smooth LTB space, based on considering only the luminosity distance. The observational signatures of smooth LTB matter dominated models are fundamentally different from the ones of ΛCDM models not only because it is not possible to reproduce a negative apparent central deceleration qapp0, but because of deeper differences in their space-time geometry which make impossible solve the inversion problem when more than one observable is considered, and emerge at any redshift, not only for z = 0.

title: What could the value of the cosmological constant tell us about the future variation of the fine structure constant
abstract: Motivated by reported claims of the measurements of a variation of the fine structure constant $\alpha$ we consider a theory where the electric charge, and consequently $\alpha$, is not a constant but depends on the Ricci scalar $R$. %We then show how this can be considered a particular case of the Bekenstein theory in which there is no need to %introduce an additional kinetic term for the scalar field associated to the electric charge, since the Einstein's% %equations are sufficient to determine the geometry and, consequently the Ricci scalar. We then study the cosmological implications of this theory, considering in particular the effects of dark energy and of a cosmological constant on the evolution of $\alpha$. Some low-red shift expressions for the variation of $\alpha(z)$ are derived, showing the effects of the equation of state of dark energy on $\alpha$ and observing how future measurements of the variation of the fine structure constant could be used to determine indirectly the equation of state of dark energy and test this theory. In the case of a $\Lambda CDM$ Universe, according to the current estimations of the cosmological parameters, the present value of the Ricci scalar is $\approx 10%$ smaller than its future asymptotic value determined by the value of the cosmological constant, setting also a bound on the future asymptotic value of $\alpha$.

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: Low-redshift effects of local structure on the Hubble parameter in presence of a cosmological constant
abstract: In order to estimate the effects of a local structure on the Hubble parameter we calculate the low-redshift expansion for H(z) and $$\frac{\delta H}{H}$$δHH for an observer at the center of a spherically symmetric matter distribution in the presence of a cosmological constant. We then test the accuracy of the formulas comparing them with fully relativistic non-perturbative numerical calculations for different cases for the density profile. The low-redshift expansion we obtain gives results more precise than perturbation theory since it is based on the use of an exact solution of Einstein’s field equations. For larger density contrasts the low-redshift formulas accuracy improves respect to the perturbation theory accuracy because the latter is based on the assumption of a small density contrast, while the former does not rely on such an assumption. The formulas can be used to take into account the effects on the Hubble expansion parameter due to the monopole component of the local structure. If the H(z) observations will show deviations from the $$\Lambda CDM$$ΛCDM prediction compatible with the formulas we have derived, this could be considered an independent evidence of the existence of a local inhomogeneity, and the formulas could be used to determine the characteristics of this local structure.

title: Corrections to the apparent value of the cosmological constant due to local inhomogeneities
abstract: 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: 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.