Big bang nucleosynthesis andΛQCD

Abstract

Big Bang Nucleosynthesis (BBN) has increasingly become the tool of choice for investigating the permitted variation of fundamental constants during the earliest epochs of the Universe. Here we present a BBN calculation that has been modified to permit changes in the QCD scale, ΛQCD. The primary effects of changing the QCD scale upon BBN are through the deuteron binding energy, BD, and the neutron-proton mass difference, δmnp, which both play crucial roles in determining the primordial abundances. In this paper, we show how a simplified BBN calculation allows us to restrict the nuclear data we need to just BD and δmnp yet still gives useful results so that any variation in ΛQCD may be constrained via the corresponding shifts in BD and δmnp by using the current estimates of the primordial deuterium abundance and helium mass fraction. The simplification predicts the helium-4 and deuterium abundances to within 1% and 50% respectively when compared with the results of a standard BBN code. But ΛQCD also affects much of remaining required nuclear input so this method introduces a systematic error into the calculation and we find a degeneracy between BD and δmnp. We show how increased understanding of the relationship of the pion mass and/or BD to other nuclear parameters, such as the binding energy of tritium and the cross section of T + D → 4 He + n, would yield constraints upon any change in BD and δmnp at the 10% level.PACS numbers: 99.99

Big bang nucleosynthesis constraints on universal extra dimensions and varying fundamental constants

“…The departure from NSE leads directly to the result that the back reaction rates become much smaller than the forward ones and are essentially switched off [8]. By T ∼ 0.2 MeV, only the deuteron abundance is still held in NSE and the abundances for all other composite nuclei are many orders of magnitude lower than their NSE values; some complex nuclei have been synthesized but the amounts are yet negligible.…”

“…Note that in [52] the authors, while quoting their results in terms of the pion mass m π , were varying the ratio of the quark mass to Λ QCD , and so they indeed showed a range of B d vs m π which is effectively a function [8] (using Eq. (42)) as…”

“…In Ref. [8] Eq. (43) is used to obtain the relation between B d and m np , both of which depend on the quantity Λ QCD ; here we adopt the same relation to estimate the variation of B d in the present model.…”

“…(32) and (33) are frequently used while considering m np 's fundamental-constantdependences, e.g. [2,4,7,8,17,26].…”

“…For example, in [2,3,4] the authors use BBN to constrain the change of fine structure constant, in [5,6,7] constraints on the change of Higgs vacuum expectation value are considered, and the effects of a varying strong coupling are discussed in e.g. [8,9]; the variation of gravitational constant has also been investigated [10,11,12,13,14] in the context of BBN. Besides, there is another reason for the interests in the interplay between varying fundamental constants and BBN: in contrast to the excellent consistency between BBN theory and observation with η given by WMAP for the deuteron (D) abundance, the predicted 4 He and 7 Li abundances are smaller than the results implied by WMAP [15,16]; it is then suggested that the variations of fundamental constants such as the fine structure constant [4,17] or the * Email address: bli@phy.cuhk.edu.hk † Email address: mcchu@phy.cuhk.edu.hk deuteron binding energy B d [18] (B d itself is certainly not a fundamental constant, but its variation possibly originates from some other fundamental constants as suggested in [7]) etc.…”