QCD Phase Transition in the Inhomogeneous Universe

Abstract

We investigate a new mechanism for the cosmological QCD phase transition: inhomogeneous nucleation. The primordial temperature fluctuations, measured to be δT /T ∼ 10 −5 , are larger than the tiny temperature interval, in which bubbles would form in the standard picture of homogeneous nucleation. Thus the bubbles nucleate at cold spots. We find the typical distance between bubble centers to be a few meters. This exceeds the estimates from homogeneous nucleation by two orders of magnitude. The resulting baryon inhomogeneities may affect primordial nucleosynthesis. 98.80.Cq, 12.38.Mh, 64.60.Qb A separation of cosmic phases during a first-order QCD transition [1] could give rise to inhomogeneous nucleosynthesis [2][3][4][5]. During a thermal first-order phase transition in a homogeneous medium bubbles nucleate due to statistical fluctuations (homogeneous nucleation). Their mean separation at nucleation introduces a scale for isothermal inhomogeneities in the early Universe, which may influence the local neutron-to-proton ratio, providing inhomogeneous initial conditions for nucleosynthesis. The baryon inhomogeneities may survive until the time of neutron freeze-out, if the mean bubble nucleation distance, d nuc , exceeds the diffusion length of the proton. Comparing those scales at the time of the QCD transition, assuming a thermodynamic transition temperature T c = 150 MeV, gives d nuc > 2 m [4]. The causal scale is set by the Hubble distance at the QCD transition, d H ≡ c/H ∼ 10 km.The order of the QCD transition and the values of its parameters are still under debate. Nevertheless there are indications from lattice QCD calculations [6][7][8][9][10]. For the physical masses of the quarks the order of the transition is still unclear [6,7]. Quenched QCD (no dynamical quarks) shows a first-order phase transition with a small latent heat, compared to the bag model, and a small surface tension, compared to dimensional arguments [8]. We assume that the QCD transition is of first order and that the values from quenched lattice QCD (scaled appropriately by the number of degrees of freedom) are typical for the physical QCD transition. Based on these values and homogeneous bubble nucleation a small supercooling, ∆ sc ≡ 1−T f /T c ∼ 10 −4 , and a tiny bubble nucleation distance, d nuc ∼ 1 cm, follow [11]. The actual nucleation temperature is denoted by T f .We argue that the assumption of homogeneous nucleation is violated in the early Universe by the inevitable density perturbations from inflation or from other seeds for structure formation. Those fluctuations in density and temperature have been measured by COBE [12] to have an amplitude of δT /T ∼ 10 −5 . The effect of the QCD transition on density perturbations [13,14] and gravitational waves [15] has been studied previously, while we investigate the effect of the density perturbations on the QCD phase transition here. We conclude that a first order QCD transition induces an inhomogeneity scale of a few meters. In comparison with heterogeneous nucleation via ad hoc d...

Quark-hadron phase transitions in the viscous early universe

“…The density fluctuations amplified by the vanishing sound velocity effect during the quark-hadron phase transition could lead to QGP lumps decoupled from the expansion, which rapidly transform to quark nuggets [24]. The inhomogeneous nucleation, as a new mechanism for the cosmological QCD phase transition, was proposed by Ignatius and Schwartz [25]. In this model the typical distance between bubble centers is of the order of a few meters.…”

Cosmological Consequences of QCD Phase Transition(s) in Early Universe

“…According to [17], the second scenario can be fulfilled, if the rms temperature fluctuations > 10 −5 . In that case, the scale of inhomogeneity in baryon distribution [18] can be related to the scale of inhomogeneity in radiation fluid after the QCD phase transition.…”

“…Candidates for such "cosmic" bubbles would be primordial monopoles, cosmic strings, black holes, etc. As there is so far no verification for any of these objects, we have to look for other consequences, like primordial temperature fluctuations [17] and inhomogeneities forming dark matter clumps, etc.…”

Phase transitions in the early and the present Universe: from the big bang to heavy ion collisions

“…Larger values of d nucl can arise from inhomogeneous nucleation seeded by "impurities" [25]. These inhomogeneities can be produced by primordial black holes (see below) as proposed by [25] or by primordial density fluctuations as suggested by [26].…”

“…However as recognized in the literature [24,25,26] much more needs to be understood about the phase structure of QCD before a quantitatively reliable statement can be made. Of particular importance are details of the equation of state (Eos), surface tension, which determines the size of the nucleating bubbles, and also the (in medium) mass of the strange quark.…”