Motivated by a recent application of the Kolmogorov-Johnson-Mehl-Avrami sKJMAd model to the study of DNA replication, we consider the one-dimensional s1Dd version of this model. We generalize previous work to the case where the nucleation rate is an arbitrary function Istd and obtain analytical results for the timedependent distributions of various quantities ssuch as the island distributiond. We also present improved computer simulation algorithms to study the 1D KJMA model. The analytical results and simulations are in excellent agreement.

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Nucleation and growth in one dimension. I. The generalized Kolmogorov-Johnson-Mehl-Avrami model

The cosmological QCD phase transition revisited

As predicted by quantum chromodynamics (QCD), at around $T\ensuremath{\sim}190\text{ }\text{ }\mathrm{MeV}$ in the early Universe, the QCD transition occurs during which the quarks are combined into the massive hadrons. This process reduces the effective relativistic degree of freedom and causes a change in the expansion behavior of the Universe. Similarly, the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation occurred around $T\ensuremath{\sim}0.5\text{ }\text{ }\mathrm{Mev}$ and has the same kind of effect. Besides, the dark energy also drives the present stage accelerating expansion. We study these combined effects on the relic gravitational waves (RGWs). In our treatment, the QCD transition and the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation are each, respectively, represented by a short period of expansion inserted into the radiation era. Incorporating these effects, the equation of RGWs is analytically solved for a spatially flat universe, evolving from the inflation up to the current acceleration, and the spectrum of RGWs is obtained, covering the whole range of frequency $g{10}^{\ensuremath{-}19}\text{ }\text{ }\mathrm{Hz}$. It is found that the QCD transition causes a reduction of the amplitude of RGWs by $\ensuremath{\sim}20%$ in the range $g{10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{Hz}$, and the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation causes a reduction of $\ensuremath{\sim}10%$ in the range $g{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{Hz}$. In the presence of the dark energy, the combination of the QCD transition and the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation causes a larger reduction of the amplitude by $\ensuremath{\sim}30%$ for the range $g{10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{Hz}$, which covers the bands of operation of LIGO and LISA. By analysis, it is shown that RGWs will be difficult to detect by the present LIGO, but can be tested by LISA for certain inflationary models.

Modifications by the QCD transition and e + e - annihilation of the analytic spectrum of relic gravitational waves in the accelerating universe

The QCD phase diagram might exhibit a first order phase transition for large baryochemical potentials. We explore the cosmological implications of such a QCD phase transition in the early universe. We propose that the large baryon-asymmetry is diluted by a little inflation where the universe is trapped in a false vacuum state of QCD. The little inflation is stopped by bubble nucleation which leads to primordial production of the seeds of extragalactic magnetic fields, primordial black holes and gravitational waves. In addition the power spectrum of cold dark matter can be affected up to mass scales of a billion solar masses. The imprints of the cosmological QCD phase transition on the gravitational wave background can be explored with the future gravitational wave detectors LISA and BBO and with pulsar timing.

The Cosmological QCD Phase Transition Revisited

In this paper, we have improved the calculation of the relic gravitational waves (RGW) in two aspects. First, we investigate the transfer function by taking into consideration the redshift-suppression effect, the accelerating expansion effect, the damping effect of free-streaming relativistic particles, and the damping effect of cosmic phase transition, and give a simple approximate analytic expression, which clearly illustrates the dependence on the cosmological parameters. Second, we develop a numerical method to calculate the primordial power spectrum of RGW in a very wide frequency range, where the observed constraints on ns (the scalar spectral index) and PS(k0) (the amplitude of primordial scalar spectrum) and the Hamilton–Jacobi equation are used. This method is applied to two kinds of inflationary models, which satisfy the current constraints on ns, α (the running of ns) and r (the tensor–scalar ratio). We plot them in the r - Ωg diagram, where Ωg is the strength of RGW, and study their measurements from the cosmic microwave background (CMB) experiments and laser interferometers.

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Improved calculation of relic gravitational waves

The sequence of phase transitions during the hot history of the universe is followed within a phenomenological framework. Particular emphasis is put on the QCD confinement transition, which is at reach under earth laboratory conditions. A tepid inflationary scenario on the GUT scale with bubble growth at moderate supercooling is discussed.

Cosmic phase transitions

The sequence of phase transitions during the hot history of the universe is followed within a phenomenological framework. Particular emphasis is put on the QCD confinement transition, which is at reach under earth laboratory conditions. A tepid inflationary scenario on the GUT scale with bubble grow at moderate supercooling is discussed.

Cosmic Phase Transitions

The Nambu-Jona-Lasinio model as a particular model of quark flavour dynamics is bosonized in the low-energy regime using a generalized heat kernel expansion with local mass scale. The resulting effective meson Lagrangian defines a chiral soliton model, the solutions of which show a partial restoration of chiral symmetry inside the soliton.



Chirales Solitonenmodell mit dynamischer Restauration der chiralen Symmetrie aus der Quark-Flavour-Dynamik



Das Nambu-Lona-Lasinio-Modell als ein spezielles Modell fur die Quark-Flavour-Dynamik wird im Niederenergiebereich bosonisiert, indem eine verallgemeinerte Heat-Kernel-Entwicklung mit lokaler Massenskala verwendet wird. Die resultierende effektive Meson-Lagrange-Dichte definiert ein chirales Solitonen-Modell, dessen Losungen eine partielle Restauration der chiralen Symmetrie im Zentrum des Solitons aufweisen.

Burkhard Kampfer

Papers

Cosmic phase transitions

Cosmic Phase Transitions

Chiral Soliton Model with Dynamical Restoration of Chiral Symmetry from Quark Flavour Dynamics