Abstract:
The total lepton asymmetry $l=\sum_f l_f$ in our universe is only poorly constrained by theories and experiments. It might be orders of magnitudes larger than the observed baryon asymmetry $b\simeq {\cal O}(10^{-10})$, $|l|/b \leq {\cal O}(10^{9})$. We found that the dynamics of the cosmic QCD transition changes for large asymmetries. Predictions for asymmetries in a single flavour $l_f$ allow even larger values. We find that asymmetries of $l_f\leq {\cal O}(1)$ in a single or two flavours change the relic abundance of WIMPs. However, large lepton and large individual lepton flavour asymmetries influences significantly the dynamics of the early universe.

Abstract:
We study the influence of lepton asymmetry on the evolution of the early Universe. The lepton asymmetry $l$ is poorly constrained by observations and might be orders of magnitude larger than the baryon asymmetry $b$, $|l|/b \leq 2\times 10^8$. We find that lepton asymmetries that are large compared to the tiny baryon asymmetry, can influence the dynamics of the QCD phase transition significantly. The cosmic trajectory in the $\mu_B-T$ phase diagram of strongly interacting matter becomes a function of lepton (flavour) asymmetry. Large lepton asymmetry could lead to a cosmic QCD phase transition of first order.

Abstract:
Recent observations of the cosmic microwave background (CMB) at smallest angular scales and updated abundances of primordial elements, indicate an increase of the energy density and the helium-4 abundance with respect to standard big bang nucleosynthesis with three neutrino flavour. This calls for a reanalysis of the observational bounds on neutrino chemical potentials, which encode the number asymmetry between cosmic neutrinos and anti-neutrinos and thus measures the lepton asymmetry of the Universe. We compare recent data with a big bang nucleosynthesis code, assuming neutrino flavour equilibration via neutrino oscillations before the onset of big bang nucleosynthesis. We find a slight preference for negative neutrino chemical potentials, which would imply an excess of anti-neutrinos and thus a negative lepton number of the Universe. This lepton asymmetry could exceed the baryon asymmetry by orders of magnitude.

Abstract:
We investigate how large lepton asymmetries affect the evolution of the early universe at times before big bang nucleosynthesis and in particular how they influence the relic density of WIMP dark matter. In comparison to the standard calculation of the relic WIMP abundance we find a decrease, depending on the lepton flavour asymmetry. We find an effect of up to 20 per cent for lepton flavour asymmetries $l_f= {\cal O}(0.1)$.

Abstract:
A poorly constrained parameter in the Standard Model of Cosmology is the lepton asymmetry l = \sum_f l_f=\sum_f(n_f+n_{\nu_f})/s. Each flavour asymmetry l_f with f=e, \mu, {\tau} is the sum of the net particle density of the charged leptons n_f and their corresponding neutrinos, normalized with the entropy density s. Constraints on l_f \leq O(0.1) from BBN and CMB allow for lepton flavour asymmetries orders of magnitudes larger then the baryon asymmetry b ~ 10^{-10}. In this article we show how such large lepton (flavour) asymmetries influence the early universe, in particular the freeze out of WIMPs and the cosmic QCD transition.

Abstract:
The largest fluctuation in the observed CMB temperature field is the dipole, its origin being usually attributed to the Doppler Effect - the Earth's velocity with respect to the CMB rest frame. The lowest order boost correction to temperature multipolar coefficients appears only as a second order correction in the temperature power spectrum, $C_{\ell}$. Since v/c - 10-3, this effect can be safely ignored when estimating cosmological parameters [4-7]. However, by cutting our galaxy from the CMB sky we induce large-angle anisotropies in the data. In this case, the corrections to the cut-sky $C_{\ell}$s show up already at first order in the boost parameter. In this paper we investigate this issue and argue that this effect might turn out to be important when reconstructing the power spectrum from the cut-sky data.

Abstract:
The importance of vision in guiding a leader and an organization is paramount. Given the importance of vision, leaders will often seek assistance from tools in order to amplify their vision. Big data is one of the primary tools commonly sought. In this brief article, the advantages and disadvantages of relying on big data are explored. Plato’s allegory of the cave is used to advance the position that a proper vision ought to dwell in experience first and only secondarily resort to abstraction.

Abstract:
Over the past years, risk measurement and therewith risk measures became more and more important in economics. While in the past risk measures were already adopted at the deposit of credit and shareholders equity, the approach now generates two hybrid decision models and applies them to the reinsurance business. The two introduced models implement a convex combination of risk measures and with it provide the possibility of modelling risk attitudes. By doing that, for the two hybrid decision models on the one hand can be shown, which risk attitude leads to the acceptance of a reinsurance contract and on the other hand, a deductible of which height an insurer is willing to undertake. Hence the possibility exists to identify the risk attitude of an insurer. In return, due to the knowledge of risk attitudes, under similar conditions the possibility arises to establish recommendations about the extent of the deductible at reinsurance contracts.

Abstract:
Despite its age quantum theory remains ill-understood, which is partially to blame on its deep interwovenness with the mysterious concept of quantization. In this article we argue that a quantum theory recoursing to quantization algorithms is necessarily incomplete. To provide a new axiomatic foundation, we give a rigorous proof showing how the Schr\"odinger equation follows from the Madelung equations, which are formulated in the language of Newtonian mechanics. We show how the Schr\"odinger picture relates to this Madelung picture and how the "classical limit" is directly obtained. This suggests a reformulation of the correspondence principle, stating that a quantum theory must reduce to a probabilistic version of Newtonian mechanics for large masses. We then enhance the stochastic interpretation developed by Tsekov, which speculates that quantum mechanical behavior is caused by random vibrations in spacetime. A new, yet incomplete model of particle creation and annihilation is also proposed.

Abstract:
We generalize the notion of Gaussian bridges by conditioning Gaussian processes given that certain linear functionals of the sample paths vanish. We show the equivalence of the laws of the unconditioned and the conditioned process and by an application of Girsanov's theorem, we show that the conditioned process follows a stochastic differential equation (SDE) whenever the unconditioned process does. In the Markovian case, we are able to determine the coefficients in the SDE of the conditioned process explicitly. Our main example is Brownian motion on $[0,1]$ pinned down in 0 at time 1 and conditioned to have vanishing area spanned by the sample paths.