Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such ...modifications lead to new uncertainty relations that are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows us to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min entropy is exactly 1 bit.
In the early universe, neutrinos are slightly coupled when electron–positron pairs annihilate transferring their entropy to photons. This process originates non-thermal distortions on the neutrino ...spectra which depend on neutrino flavour, larger for
ν
e
than for
ν
μ
or
ν
τ
. We study the effect of three-neutrino flavour oscillations on the process of neutrino decoupling by solving the momentum-dependent kinetic equations for the neutrino spectra. We find that oscillations do not essentially modify the total change in the neutrino energy density, giving
N
eff
=
3.046
in terms of the effective number of neutrinos, while the small effect over the production of primordial
4He is increased by
O
(
20
%
)
, up to
2.1
×
10
−4
. These results are stable within the presently favoured region of neutrino mixing parameters.
We discuss in detail the evolutionary properties of low-mass stars (M < 1 M sub(o)) having metallicity lower than Z = 10 super(-6) from the pre-main sequence up to (almost) the end of the early ...asymptotic giant branch phase. We also discuss the possibility that the large C/Fe, N/Fe observed on the surface of the most iron-poor star currently known, HE 0107-5240, could be attributed to the autopollution induced by the penetration of the He convective shell into the H-rich mantle during the He core flash of a low-mass, very low metallicity star. On the basis of a quite detailed analysis, we conclude that the autopollution scenario cannot be responsible for the observed chemical composition of HE 0107-5240.
The most general case of self-induced neutrino flavor evolution is described by a set of kinetic equations for a dense neutrino gas evolving in both space and time. Solutions of these equations have ...been typically worked out assuming that either the time (in the core-collapse supernova environment) or space (in the early Universe) homogeneity in the initial conditions is preserved through the evolution. In these cases, one can gauge away the homogeneous variable and reduce the dimensionality of the problem. In this paper, we investigate whether small deviations from an initial postulated homogeneity can be amplified by the interacting neutrino gas, leading to a new flavor instability. To this end, we consider a simple two-flavor isotropic neutrino gas evolving in time, and initially composed by only nu sub(e) and nu sub(e) with equal densities. In the homogeneous case, this system shows a bimodal instability in the inverted mass hierarchy scheme, leading to the well-studied flavor pendulum behavior. This would lead to periodic pair conversions nu sub(e)nu sub(e) left right arrow nu sub(x)nu sub(x). To break space homogeneity, we introduce small amplitude space-dependent perturbations in the matter potential. By Fourier transforming the equations of motion with respect to the space coordinate, we then numerically solve a set of coupled equations for the different Fourier modes. We find that even for arbitrarily tiny inhomogeneities, the system evolution runs away from the stable pendulum behavior: the different modes are excited and the space-averaged ensemble evolves towards flavor equilibrium. We finally comment on the role of a time decaying neutrino background density in weakening these results.
We derive here a robust bound on the effective number of neutrinos from constraints on primordial nucleosynthesis yields of deuterium and helium. In particular, our results are based on very weak ...assumptions on the astrophysical determination of the helium abundance, namely that the minimum effect of stellar processing is to keep constant (rather than increase, as expected) the helium content of a low-metallicity gas. Using the results of a recent analysis of extragalactic HII regions as upper limit, we find that Delta N sub(effless-than-or-equals, slant1 at 95% C.L., quite independently of measurements on the baryon density from cosmic microwave background anisotropy data and of the neutron lifetime input. In our approach, we also find that primordial nucleosynthesis alone has no significant preference for an effective number of neutrinos larger than the standard value. The inline imageinline image hint sometimes reported in the literature is thus driven by CMB data alone and/or is the result of a questionable regression protocol to infer a measurement of primordial helium abundance.)
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