The Quark-Hadron Transition in Cosmology and Dark Energy

Neşever BALTACI1

1 Umraniye Anatolia I.H.High School –Istanbul –Turkiye
e-mail : nesever@yahoo.com





Dark sides and golden ages Astronomers first started talking about a "golden age" of astrophysics and cosmology in the late 1990s. • Ironically, the outstanding questions in the golden age concern the dark side of the universe - what are the "dark matter" and the "dark energy" that cannot be seen but which make themselves known through their gravitational influence? •
But dark matter and dark energy are just two puzzles, albeit two extremely difficult and important ones, in a galaxy of questions that still new evidence has confirmed that the expansion of the universe is accelerating under the influence of a gravitationally repulsive form of energy that makes up two-thirds of the cosmos.
It is an irony of nature that the most abundant form of energy in the universe is also the most mysterious. Since the breakthrough discovery that the cosmic expansion is accelerating, a consistent picture has emerged indicating that two-thirds of the cosmos is made of "dark energy" - some sort of gravitationally repulsive material.



But is the evidence strong enough to justify exotic new laws of nature? Or could there be a simpler, astrophysical explanation for the results? The dark-energy story begins in 1998, when two independent teams of astronomers were searching for distant supernovae, hoping to measure the rate at which the expansion of the universe was slowing down. They were in for a shock: the observations showed that the expansion was speeding up





In fact, the universe started to accelerate long ago, some time in the last 10 billion years. Like detectives, cosmologists around the world have built up a description of the culprit responsible for the acceleration: it accounts for two-thirds of the cosmic energy density; it is gravitationally repulsive; it does not appear to cluster in galaxies; it was last seen stretching space–time apart; and it goes by the assumed name of "dark energy".
Many theorists already had a suspect in mind: the cosmological constant. It certainly fits the accelerating-expansion scenario. But is the case for dark energy airtight? The existence of gravitationally repulsive dark energy would have dramatic consequences for fundamental physics.
The most conservative suggestions are that the universe is filled with a uniform sea of quantum zero-point energy, or
a condensate of new particles that have a mass that is 10-39 times smaller than that of the electron.
Some researchers have also suggested changes to Einstein's general theory of relativity, such as a new long-range force that moderates the strength of gravity.




But there are shortcomings with even the leading conservative proposals. For instance, the zero-point energy density would have to be precisely tuned to a value that is an unbelievable factor of 10120 below the theoretical prediction. Until recently the supernova data were the only direct evidence for the cosmic acceleration, and the only compelling reason to accept dark energy. Precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have recently provided circumstantial evidence for dark energy. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS)now a second witness has testified.
By combining data from WMAP, SDSS and other sources, four independent groups of researchers have reported evidence for a phenomenon known as the integrated Sachs-Wolfe effect. The case for the existence of dark energy has suddenly become a lot more convincing. One of the prime methods for measuring extragalactic distances is to use "standard candles" such as Cepheid variable stars , the total amount of matter in universe - including all the dark matter - accounts for just one-third of the total energy. This has been confirmed by surveys such as the 2DF and SDSS projects, which have mapped the positions and motions of millions of galaxies. But general relativity predicts that there is a precise connection between the expansion and the energy content of the universe. We therefore know that the collective energy density of all the photons, atoms, dark matter and everything else ought to add up to a certain critical value determined by the Hubble constant: ρcritical = 3H02/8π G, where G is the gravitational constant. The snag is that they do not. Mass, energy and the curvature of space-time are intimately related in relativity.


One explanation is therefore that the gap between the critical density and the actual matter density is filled by the equivalent energy density of a large-scale warping of space that is discernable only on scales approaching c/H0 (about 4000 Mpc).
In a universe where the full critical energy density comes from atoms and dark matter only, the weak gravitational potentials on very long length scales - which correspond to gentle waves in the matter density - evolve too slowly to leave a noticeable imprint on the CMB photons., gravitational collapse is slowed by the repulsive dark energy.
Consequently, gravitational potentials grow shallower and photons gain energy as they pass by. Similarly, photons lose energy passing through underdense regions. Negative pressure; to examine this strange property of dark energy it is helpful to introduce a quantity w = pdark/ρdark, where pdark is the mean pressure and ρdark is the density of dark energy in the universe. The rate of change in the cosmic expansion is proportional to -(ρtotal + 3ptotal), where ρtotal is the density of all the matter and energy in the universe and ptotal is the corresponding pressure. To account for the accelerated expansion, however, this quantity must be positive. Since ρtotal is a positive quantity, and the mean pressure due to both ordinary and dark matter is negligible because it is cold or non-relativistic, we arrive at the requirement that 3w x ρdark + ρtotal < 0 for an accelerating expansion. Since ρdark ~ 2/3ρtotal, we find that
w≥-1/2, so the pressure of the dark energy is not just a little negative but a lot negative!






Cartan torsion (The non-Riemannian geometry of macroscopic spin distributions in thermodynamics and ferromagnetism is obtained from the respective partition functions. An expression for the Cartan torsion in terms of the chemical potential is obtained. Analogies with the Einstein-Cartan theory of gravitation are discussed. From the partition function of ferromagnetism a spin-torsion relation analogous to the one obtained in Einstein-Cartan theory is given where piezomagnetic effects are taken into account) contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed. From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as 10^{16} mks units.The spin-density fluctuations at the hadron era (the Big Bang era when the Universe was matter-dominated, containing many hadrons in equilibrium with the radiation field and when kT ≈ mπ. The hadron era ended when the characteristic photon energy fell below the rest mass of a pion or π-meson (270 electron masses), and very few hadrons remained (about one hadron for every 108 photons).) is shown to coincide with the anisotropy temperature fluctuations
A transition from normal hadronic matter (such as protons and neutrons) to quark-gluon matter is expected at both high temperatures and densities. In physical situations, this transition may occur in heavy ion collisions, the early universe, and in the cores of neutron stars. Astrophysics and cosmology can be greatly affected by such a phase transition. With regard to the early universe, big bang nucleosynthesis, the theory describing the primordial origin of the light elements, can be affected by inhomogeneities produced during the transition. A transition to quark matter in the interior by neutron stars further enhances our uncertainties regarding the equation of state of dense nuclear matter and neutron star properties such as the maximum mass and rotation frequencies. Difficulties : higher energy scales
Planck era : ~ 10*77 GeV*4 GUT : ~ 10*64 GeV*4 Electroweak : ~ 10*8 GeV*4 QCD : ~ 10*-4 GeV*4
Puzzle Why rDE is so small ???



Quark-hadron phase transition The standard picture of cosmology assumes that a phase transition (associated with chiral symmetry breaking following the electroweak transition) occurred at approximately after the Big Bang to convert a plasma of free quarks and gluons into hadrons. Although this transition can be of significant cosmological importance, it is not known with certainty whether it is of first order or higher, and what the astrophysical consequences might be on the subsequent state of the Universe. For example, the transition may play a potentially observable role in the generation of primordial magnetic fields. The QCD transition may also give rise to important baryon number inhomogeneities which can affect the distribution of light element abundances from primordial Big Bang nucleosynthesis. The distribution of baryons may be influenced hydrodynamically by the competing effects of phase mixing and phase separation, which arise from any inherent instability of the interface surfaces separating regions of different phase. Unstable modes, if they exist, will distort phase boundaries and induce mixing and diffusive homogenization through hydrodynamic turbulence



In an effort to support and expand theoretical studies, a number of one-dimensional numerical simulations have been carried out to explore the behavior of growing hadron bubbles and decaying quark droplets in simplified and isolated geometries. For example, Rezolla et al. considered a first order phase transition and the nucleation of hadronic bubbles in a supercooled quark-gluon plasma, solving the relativistic Lagrangian equations for disconnected and evaporating quark regions during the final stages of the phase transition. They investigated numerically a single isolated quark drop with an initial radius large enough so that surface effects can be neglected. The droplet evolves as a self-similar solution until it evaporates to a sufficiently small radius that surface effects break the similarity solution and increase the evaporation rate. Their simulations indicate that, in neglecting long-range energy and momentum transfer (by electromagnetically interacting particles) and assuming that baryon number is transported with the hydrodynamical flux, the baryon number concentration is similar to what predicted by chemical equilibrium calculations.


Kurki-Suonio and Laine studied the growth of bubbles and the decay of droplets using a one-dimensional spherically symmetric code that accounts for a phenomenological model of the microscopic entropy generated at the phase transition surface. Incorporating the small scale effects of finite wall width and surface tension, but neglecting entropy and baryon flow through the droplet wall, they simulate the process by which nucleating bubbles grow and evolve to a similarity solution. They also compute the evaporation of quark droplets as they deviate from similarity solutions at late times due to surface tension and wall effects. Ignatius et al. carried out parameter studies of bubble growth for both the QCD and electroweak transitions in planar symmetry, demonstrating that hadron bubbles reach a stationary similarity state after a short time when bubbles grow at constant velocity. They investigated the stationary state using numerical and analytic methods, accounting also for preheating caused by shock fronts.

Figure 1:






Image sequence of the scalar field from a 2D calculation showing the interaction of two deflagration systems (one planar wall propagating from the right side, and one spherical bubble nucleating from the center). The physical size of the grid is set to and resolved by zones. The run time of the simulation is about two sound crossing times, where the sound speed is , so the shock fronts leading the condensing phase fronts travel across the grid twice. The hot quark (cold hadron) phases have smaller (larger) scalar field values and are represented by black (color) in the colormap.





Figure 2:





Image sequence of the scalar field from a 2D calculation showing the interaction of two detonation systems (one planar wall propagating from the right side, and one spherical bubble nucleating from the center). The physical size of the grid is set to and resolved by zones. The run time of the simulation is about two sound crossing times.



Figure 3:








Image sequence of the scalar field from a 2D calculation showing the interaction of shock and rarefaction waves with a deflagration wall (initiated at the left side) and a detonation wall (starting from the right). A shock and rarefaction wave travel to the right and left, respectively, from the temperature discontinuity located initially at the grid center (the right half of the grid is at a higher temperature). The physical size of the domain is set to and resolved by zones. The run time of the simulation is about two sound crossing times.









Fragile and Anninos performed two-dimensional simulations of first order QCD transitions to explore the nature of interface boundaries beyond linear stability analysis, and determine if they are stable when the full nonlinearities of the relativistic scalar field and hydrodynamic system of equations are accounted for. They used results from linear perturbation theory to define initial fluctuations on either side of the phase fronts and evolved the data numerically in time for both deflagration and detonation configurations. No evidence of mixing instabilities or hydrodynamic turbulence was found in any of the cases they considered, despite the fact that they investigated the parameter space predicted to be potentially unstable according to linear analysis. They also investigated whether phase mixing can occur through a turbulence-type mechanism triggered by shock proximity or disruption of phase fronts. They considered three basic cases (see image sequences in Figures 1, 2, and 3 above): interactions between planar and spherical deflagration bubbles, collisions between planar and spherical detonation bubbles, and a third case simulating the interaction between both deflagration and detonation systems initially at two different thermal states. Their results are consistent with the standard picture of cosmological phase transitions in which hadron bubbles expand as spherical condensation fronts, undergoing regular (non-turbulent) coalescence, and eventually leading to collapsing spherical quark droplets in a medium of hadrons. This is generally true even in the detonation cases which are complicated by greater entropy heating from shock interactions contributing to the irregular destruction of hadrons and the creation of quark nuggets.

However, Fragile and Anninos also note a deflagration ‘instability’ or acceleration mechanism evident in their third case for which they assume an initial thermal discontinuity in space separating different regions of nucleating hadron bubbles. The passage of a rarefaction wave (generated at the thermal discontinuity) through a slowly propagating deflagration can significantly accelerate the condensation process, suggesting that the dominant modes of condensation in an early Universe which super-cools at different rates within causally connected domains may be through supersonic detonations or fast moving (nearly sonic) deflagrations. A similar speculation was made by Kamionkowski and Freese who suggested that deflagrations become unstable to perturbations and are converted to detonations by turbulent surface distortion effects. However, in the simulations, deflagrations are accelerated not from turbulent mixing and surface distortion, but from enhanced super-cooling by rarefaction waves. In multi-dimensions, the acceleration mechanism can be exaggerated further by upwind phase mergers due to transverse flow, surface distortion, and mode dissipation effects, a combination that may result in supersonic front propagation speeds, even if the nucleation process began as a slowly propagating deflagration.







The Higgs is Different! All the matter particles are spin-1/2 fermions. All the force carriers are spin-1 bosons.
Higgs particles are spin-0 bosons. The Higgs is neither matter nor force; The Higgs is just different.
This would be the first fundamental scalar ever discovered. The Higgs field is thought to fill the entire universe.
Could give some handle of dark energy(scalar field)? Many modern theories predict other scalar particles like the Higgs.
Why, after all, should the Higgs be the only one of its kind? LHC and ILC can search for new scalars with precision.














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