Baryon density

The primordial Li abundance was sought primarily because of its ability to constrain the baryon to photon ratio in the Universe, or equivalently the baryon contribution to the critical density. In this way, Li was able to complement estimates from 4He, the primordial abundance of which varied only slightly with baryon density. Li also made up for the fact that the other primordial isotopes, 2H (i.e. D) and 3He, were at that time difficult to observe and/or interpret. During the late 1990 s, however, measurements of D in damped Lyman alpha systems (high column-density gas believed to be related to galaxy discs) provided more reliable constraints on the baryon density than Li could do (e.g. [19]). Even more recently, the baryon density has been inferred from the angular power spectrum of the cosmic microwave background radiation, for example from the WMAP measurements [26]. We consider the role of Li plateau observations post WMAP. 

Fig. 1. The baryon density parameter, r/10, inferred from SBBN and the relic abundances of D, 3He, 4He, and 7Li (filled circles), along with the non-BBN determination from WMAP (filled triangle). See the text for details.

After e annihilation during the early evolution of the Universe, the ratio of baryons to photons is, to a very good approximation, preserved down to the present. The baryon density parameter is defined to be this ratio (at present) r] = n /n r/io =... 

Fig. 4. A summary of the time evolution of primordial 4He abundance determinations (mass fraction Yp) from observations of metal-poor, extragalactic Hu regions (see the text for references). The solid horizontal line is the SBBN-predicted 4He abundance expected for the WMAP (and/or D) inferred baryon density. The two dashed lines show the la uncertainty in this prediction.

F. Hoyle, D. N. Schramm, G. Steigman and others, which assumes standard cosmology and particle physics and a uniform baryon density, has been very successful in several respects, e.g. ... 

The number rj, together with the known background temperature Tyf), measures the cosmological baryon density today ... 

The deuterium abundance, on the other hand, is a steeply decreasing function because it is destroyed by two-body reactions with p, n, D and 3He. 3He declines more gently because this nucleus is more robust. 7Li has a bimodal behaviour because at low baryon densities it is synthesized from 3H by reaction (Eq. 4.46) and both nuclei are destroyed by two-body reactions, whereas at higher densities it... 

Because of the destruction of D when interstellar gas is recycled through stars, its present-day abundance is a firm lower limit to the primordial one. Adopting the local bubble value as representative of the Galaxy places an upper limit on the baryonic density parameter,... 

SBBN theory has been remarkably successful and does not seem to be in need of any modification except just possibly in the case of 7Li. The limits that it sets on baryonic density are most robust in the case of deuterium (2 < 105D/H < 4) implying... 

Deuterium discovered in interstellar gas (Copernicus satellite) and quantitatively estimated in early Solar System, restricting baryonic density in Big Bang nucleosynthesis (BBNS) theory. 

Abstract The equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions is considered, in particular the region of medium excitation energy given by the temperature range T < 30 MeV and the baryon density range ps < 1014 2 g/cm3. In this region, in addition to the mean-field effects the formation of few-body correlations, in particular light bound clusters up to the alpha-particle (1 < A < 4) has been taken into account. The calculation is based on the relativistic mean field theory with the parameter set TM1. We show results for different values for the asymmetry parameter, and (3 equilibrium is considered as a special case. 

Results for the composition of nuclear matter at temperature T = 10 MeV with proton fraction V/"1, = 0.2 are shown in Fig. 1, for symmetric matter Yp0t = 0.5 in Fig. 2. The model of an ideal mixture of free nucleons and clusters applies to the low density limit. At higher baryon density, medium effects are relevant to calculate the composition shown in Figs. 1, 2, which are described in the following sections. 

Figure 1. Composition of nuclear matter with proton fraction 0.2 as function of the baryon density, T = 10 MeV.

The meson fields op, too and po are found by solving a set of equations self-consistently as shown in [11], Also expressions for the energy density, pressure and the entropy density can be found there. The empirical values of the binding energy of nuclear matter and nuclear matter density are reproduced using the above mentioned parameterization. The nuclear matter EOS can be found expressing the chemical potentials as functions of temperature, baryon density... 

For a given temperature T = 10 MeV the composition with respect to the two-particle correlation is shown as a function of the baryon density in Fig.2. 

We conclude that not only the a-particle but also the other fight clusters contribute significantly to the composition. Furthermore they also contribute to the baryon chemical potential and this way the modification of the phase instability region with respect to the temperature, baryon density and asymmetry can be obtained. As an example, for symmetric matter the baryon chemical potential as a function of density for T = 10 MeV is shown in Fig.3... 

Figure 5. The neutron star gravitational mass (in units of solar mass Mq ) is displayed vs. the radius (left panel) and the normalized central baryon density pc (po = 0.17 fm-3) (rightpanel).

Figure 9. Neutron star gravitational mass vs. radius (left panel) and the central baryon density pc (right panel). Calculations involving different nucleonic TBF are compared.

The results obtained with a purely baryonic EOS call for an estimate of the effects due to the hypothetical presence of quark matter in the interior of the neutron star. Unfortunately, the current theoretical description of quark matter is burdened with large uncertainties, seriously limiting the predictive power of any theoretical approach at high baryonic density. For the time being we can therefore only resort to phenomenological models for the quark matter EOS and try to constrain them as well as possible by the few experimental information on high density baryonic matter. 

However, a more realistic model for the phase transition between baryonic and quark phase inside the star is the Glendenning construction [16], which determines the range of baryon density where both phases coexist. The essential point of this procedure is that both the hadron and the quark phase are allowed to be separately charged, still preserving the total charge neutrality. This implies that neutron star matter can be treated as a two-component system, and therefore can be parametrized by two chemical potentials like electron and baryon chemical potentials [if. and iin. The pressure is the same in the two phases to ensure mechanical stability, while the chemical potentials of the different species are related to each other satisfying chemical and beta stability. The Gibbs condition for mechanical and chemical equilibrium at zero temperature between both phases reads... 

From this, the baryon density pM and the energy density cm of the mixed phase can be calculated as... 

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