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We highlight the general scenario of dark matter freeze-out while the energy density of the universe is dominated by a decoupled non-relativistic species. Decoupling during matter domination changes the freeze-out dynamics, since the Hubble rate is parametrically different for matter and radiation domination. Furthermore, for successful Big Bang Nucleosynthesis the state dominating the early universe energy density must decay, this dilutes (or repopulates) the dark matter. As a result, the masses and couplings required to reproduce the observed dark matter relic density can differ significantly from radiation-dominated freeze-out.

Abundances of primordial deuterium, and helium, Y_p, are examined by modifying the early universe expansion rate and hence the time–temperature relation, including a constant vacuum energy motivated by the cyclic scenario of brane cosmology. Enhancement of abundances with respect to standard BBN prediction is found. Rapid expansion leads to early freeze-out of weak interaction and hence to an enhanced neutron fraction at elevated freeze-out temperature, which in turn results in more helium. Nucleosynthesis at a much lower temperature (due to rapid expansion) faces a larger Coulomb barrier and leaves more deuterium behind, which is also implied by a lower baryon-to-photon ratio (η) as we increase the vacuum energy density. The change in the helium fraction agrees within orders of magnitudes with that found by the effect of more neutrino flavors on Y_p. Elevation of the neutron fraction at freeze-out is revealed by decrease in the neutron–proton mass difference (Q) from 1.293 MeV to 1.279 MeV, which is consistent with the study of the influence of extra dimension size on BBN. The lowest Q value corresponds to the highest vacuum energy and also to the largest size of the extra dimension. The upper limit on vacuum energy density is found by estimating the contribution from nonbaryonic dark matter by using X-ray emission from galaxy clusters and taking a flat spatial geometry, which is found to be the cosmological constant (Λ) observed today, so that the abundances do not run beyond the observational upper bounds. The allowed range of Ω_Λ, 0.786 ≤ Ω _Λ ≤ 0.844, makes Y_p and lie within the observational upper bounds, which yields a Big Bang equivalence of the Λ universe. This is expected to further motivate the cyclic scenario, which incorporates a small and constant vacuum energy density tied to spacetime.

On the basis of the proposed algorithm for calculation of the hadron reaction rates, the space-time structure of the relativistic nucleus–nucleus collisions is studied. The reaction zones and the reaction frequencies for various types of reactions are calculated for Alternating Gradient Synchrotron (AGS) and Super Proton Synchrotron (SPS) energies within the microscopic transport model. The relation of the reaction zones to the kinetic and chemical freeze-out processes is discussed. It is shown that the space-time freeze-out layer is most extended in time in the central region, while, especially for higher collision energies, the layer becomes very narrow at the sides. The parametrization of freeze-out hypersurface in the form of specific hyperbola of constant proper time was confirmed. The specific characteristic time moments of the fireball evolution are introduced. It is found that the time of the division of a reaction zone into two separate parts does not depend on the collision energy. Calculations of the hadronic reaction frequency show that the evolution of nucleus–nucleus collision can be divided into two hadronic stages.

In this paper, we consider hadron production in high energy collisions as an Unruh radiation phenomenon. This mechanism describes the production pattern of newly formed hadrons and is directly applicable at vanishing baryon chemical potential, μ ≃ 0. It had already been found to correctly yield the hadronization temperature, in terms of the string tension σ. Here, we show that the Unruh mechanism also predicts hadronic freeze-out conditions, giving in terms of the entropy density s and for the average energy per hadron. These predictions provide a theoretical basis for previous phenomenological results and are also in accord with recent lattice studies.

We study the hadronic yields produced in two small collision systems $d-\mathrm{\text{Au}}$ at $\sqrt{s_{NN}}=0.2$TeV and $p-\mathrm{\text{Pb}}$ at $\sqrt{s_{NN}}=5.02$TeV, and extracted the chemical freeze-out (CFO) parameters. The CFO parameters are obtained using a hadron resonance gas (HRG) model and in this study present the system size dependence of the parameters. We observe that with the strangeness suppression factor ${\gamma }_S$ included in the model, a single freeze-out scenario can describe hadronic yields for all the centralities of $d-\mathrm{\text{Au}}$ collision at $\sqrt{s_{NN}}=0.2$TeV, indicating that the strange hadrons have not reached full equilibrium. On the other hand, for small average charged particle multiplicity ($〈d{N}_{ch}/d\eta 〉$) bins of $p-\mathrm{\text{Pb}}$ collision at $\sqrt{s_{NN}}=5.02$TeV strangeness is not fully equilibrated whereas strangeness equilibration seems to be reached in large $〈d{N}_{ch}/d\eta 〉$. For both the collision systems, no significant system volume dependence of the temperature has been observed. However, in comparable $〈d{N}_{ch}/d\eta 〉$ values, temperatures are 10–20MeV larger for $d-\mathrm{\text{Au}}$ collision compared to $p-\mathrm{\text{Pb}}$ collision. We observe that the volume of the system at the CFO increases with increase of charge multiplicity for both the collisions. The increase is much steeper in $p-\mathrm{\text{Pb}}$ collision at $\sqrt{s_{NN}}=5.02$TeV than $d-\mathrm{\text{Au}}$ collision at $\sqrt{s_{NN}}=0.2$TeV. Further, we analyze the transverse momentum ($p_T$) spectra of different hadrons produced in $d-\mathrm{\text{Au}}$ collision at $\sqrt{s_{NN}}=0.2$TeV in a combined freeze-out scenario. We show the $〈d{N}_{ch}/d\eta 〉$ dependence of freeze-out parameters. It is observed that with ${\gamma }_S$ included in the model, a single freeze-out scheme can describe the $p_T$ spectra. For similar $〈d{N}_{ch}/d\eta 〉$ values, ${\gamma }_S$ in both the collision systems are close to each other and overall values of ${\gamma }_S$ increase with increase of $〈d{N}_{ch}/d\eta 〉$. Unlike CFO scenario using the produced hadron yields only, freeze-out temperature in combined scenario of chemical and kinetic freeze-out, obtained from $p_T$ spectra, increases with increase of $〈d{N}_{ch}/d\eta 〉$. For smaller $〈d{N}_{ch}/d\eta 〉$ values, the temperature in $d-\mathrm{\text{Au}}$ collision at $\sqrt{s_{NN}}=0.2$TeV is similar to that of $p-\mathrm{\text{Pb}}$ collision at $\sqrt{s_{NN}}=5.02$TeV. However, temperatures are larger in $d-\mathrm{\text{Au}}$ collision than $p-\mathrm{\text{Pb}}$ collision at larger $〈d{N}_{ch}/d\eta 〉$ values.