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Register a new userVerification of Maxwell-Boltzmann distribution with Big-Bang Nucleosyntheis theory
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The current Big-Bang Nucleosynthesis (BBN) model has been constructed based on a nuclear reaction network operating with thermal reactivities of Maxwell-Boltzmann (MB) distribution plasma. However, does the classical MB distribution still hold for the extremely high-temperature (in order of 10$^9$ K) plasma involved in the Big-Bang environment? In this work, we have investigated the impact of non-extensive Tsallis statistics (in $q$-Guassian distribution) on the thermonuclear reaction rates. We show for the first time that the reverse rates are extremely sensitive to the non-extensive $q$ parameter. Such sensitivity does not allow a large deviation of non-extensive distribution from the usual MB distribution. With a newly developed BBN code, the impact of primordial light-element abundances on $q$ values has been studied by utilizing the most recent BBN cosmological parameters and the available nuclear cross-section data. For the first time, we have accurately verified the microscopic MB distribution with the macroscopic BBN theory and bservation. By comparing the recent observed primordial abundances with our predictions, only a tiny deviation of $pm$6$times$10$^{-4}$ at most can be allowed for the MB distribution. However, validity of the classical statistics needs to be studied further for the self-gravitating stars and binaries of high-density environment, with the extreme sensitivity of reverse rate on $q$ found here.
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We provide the most stringent constraint to date on possible deviations from the usually-assumed Maxwell-Boltzmann (MB) velocity distribution for nuclei in the Big-Bang plasma. The impact of non-extensive Tsallis statistics on thermonuclear reaction rates involved in standard models of Big-Bang Nucleosynthesis (BBN) has been investigated. We find that the non-extensive parameter $q$ may deviate by, at most, $|delta q|$=6$times$10$^{-4}$ from unity for BBN predictions to be consistent with observed primordial abundances; $q$=1 represents the classical Boltzmann-Gibbs statistics. This constraint arises primarily from the {em super}sensitivity of endothermic rates on the value of $q$, which is found for the first time. As such, the implications of non-extensive statistics in other astrophysical environments should be explored. This may offer new insight into the nucleosynthesis of heavy elements.
Primordial nucleosynthesis is one of the three historical evidences for the big bang model, together with the expansion of the universe and the cosmic microwave background. Now that the number of neutrino families and the baryonic densities have been fixed by laboratory measurements or CMB observations, the model has no free parameter and its predictions are rigid. Departure from its predictions could provide hints or constraints on new physics or astrophysics in the early universe. Precision on primordial abundances deduced from observations have recently been drastically improved and reach the percent level for both deuterium and helium-4. Accordingly, the BBN predictions should reach the same level of precision. For most isotopes, the dominant sources of uncertainty come from those on the laboratory thermonuclear reactions. This article focuses on helium-4 whose predicted primordial abundance depends essentially on weak interactions which control the neutron-proton ratio. The rates of the various weak interaction processes depend on the experimentally measured neutron lifetime, but also includes numerous corrections that we thoroughly investigate here. They are the radiative, zero-temperature, corrections, finite nucleon mass corrections, finite temperature radiative corrections, weak-magnetism, and QED plasma effects, which are for the first time all included and calculated in a self consistent way, allowing to take into account the correlations between them, and verifying that all satisfy detailed balance. The helium-4 predicted mass fraction is $0.24709pm0.00017$. In addition, we provide a Mathematica code (PRIMAT) that incorporates, not only these corrections but also a full network of reactions, using the best available thermonuclear reaction rates, allowing the predictions of primordial abundances up to the CNO region.
Nuclear reactions in stars occur between nuclei in the high-energy tail of the energy distribution and are sensitive to possible deviations from the standard equilibrium thermal-energy distribution, the well-known Maxwell-Boltzmann Distribution (textsf{MBD}). In a previous paper published in Physics Letters 441B(1998)291, DeglInnocenti {it et al}. made strong constrains on such deviations with the detailed helioseismic information of the solar structure. With a small deviation parameterized with a factor exp$[{-delta (E/kT)^2}]$, it was shown $delta$ restricted between -0.005 and +0.002. These constrains have been carefully reexamined in the present work. We find that a normalization factor was missed in the previous modified textsf{MBD}. In this work, the normalization factor $c$ is calculated as a function of $delta$. It shows the factor $c$ is almost unity within the range 0$< delta leq$0.002, which supports the previous conclusion. However, it demonstrates that $delta$ cannot take a negative value from the normalization point of view. As a result, a stronger constraint on $delta$ is defined as 0$leq delta leq$0.002. The astrophysical implication on the solar neutrino fluxes is simply discussed based on a positive $delta$ value of 0.003. The reduction of the $^7$Be and $^8$B neutrino fluxes expected from the modified textsf{MBD} can possibly shed alternative light on the solar neutrino problem. In addition, the resonant reaction rates for the $^{14}$N($p$,$gamma$)$^{15}$O reaction are calculated with a standard textsf{MBD} and a modified textsf{MBD}, respectively. It shows that the rates are quite sensitive even to a very small $delta$. This work demonstrates the importance and necessity of experimental verification or test of the well-known textsf{MBD} at high temperatures.
By carrying out a systematic investigation of linear, test quantum fields $hat{phi}(x)$ in cosmological space-times, we show that $hat{phi}(x)$ remain well-defined across the big bang as operator valued distributions in a large class of Friedmann, Lema^itre, Robertson, Walker space-times, including radiation and dust filled universes. In particular, the expectation values $langle hat{phi}(x),hat{phi}(x)rangle$ are well-defined bi-distributions in the extended space-time in spite of the big bang singularity. Interestingly, correlations between fields evaluated at spatially and temporally separated points exhibit an asymmetry that is reminiscent of the Belinskii, Khalatnikov, Lifshitz behavior. The renormalized products of fields $langle hat{phi}^2(x)rangle_{rm ren}$ and $langle hat{T}_{ab}(x) rangle_{rm ren}$ also remain well-defined as distributions. Conformal coupling is not necessary for these considerations to hold. Thus, when probed with observables associated with quantum fields, the big bang (and the big crunch) singularities are quite harmless.
Big bang of the Friedmann-Robertson-Walker (FRW)-brane universe is studied. In contrast to the spacelike initial singularity of the usual FRW universe, the initial singularity of the FRW-brane universe is point-like from the viewpoint of causality including gravitational waves propagating in the bulk. Existence of null singularities (seam singuralities) is also shown in the flat and open FRW-brane universe models.
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