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2 mev protons and neutrons interconverted via the weak interaction as the temperature dropped these reactions fell out of equilibrium neutrons primarily decayed to protons and the neutron to proton ratio fell to around 1 7 2 315 this sets the initial conditions for the onset of the formation of light nuclei 13 63 bbn began in earnest when the temperature of standard model particles dropped below roughly 1 mev 12 at this temperature the average energy of photons in the early universe was too low to break apart deuterium as it formed but the universe remained hot and dense enough for fusion reactions to occur at a significant rate 1 this meant that a substantial population of deuterium formed this deuterium then fused to heavier nuclei including tritium helium 3 helium 4 and lithium 7 2 315 helium 4 has a large binding energy which means that once a helium 4 nucleus is formed it is difficult to break apart and incorporate its constituents into heavier nuclei as a result of this matter in the universe after bbn is primarily hydrogen and helium 13 68 standard bbn predicts by the time bbn ends the universe is composed of about 75 of hydrogen and 25 helium 4 by mass roughly 1 nucleus in 100 000 is deuterium or helium 3 and 1 nucleus in 1 000 000 000 is lithium 7 even smaller amounts of heavier elements as heavy as oxygen 20 have been predicted to form 10 bbn coincides or nearly coincides with two other important events in cosmology neutrino decoupling occurred when the weak interaction fell out of equilibrium 14 just before bbn began electron positron annihilation occurred during bbn at around 0 5 mev when photons no longer had enough energy to convert back to electrons and positrons to maintain equilibrium 15 this resulted in the depletion of the abundance of positrons in the universe and heated photons since electron positron annihilation occurred after neutrino decoupling neutrinos did not heat alongside photons when electrons and positrons annihilated and photons developed a separate temperature from neutrinos this has important consequences for the rates of proton neutron interconversion and the prediction of light element abundances 16 determination of light element abundances edit important parameters edit the creation of light elements during bbn was dependent on nuclear reaction rate parameters and two cosmological input parameters neutron proton ratio calculable from standard model physics and the baryon photon ratio the nuclear reaction rates are well known from detailed laboratory studies at similar temperatures to those that appear in bbn 11 baryon to photon ratio edit the evolution of different light element abundances for different values of the baryon to photon ratio η 17 note the final abundances values at the latest times can vary dramatically depending on the value of this parameter light element abundances and in particular deuterium are sensitive to the value of the baryon to photon number ratio η which is the ratio of the number density of baryons to the number density of photons its value is small at roughly 6 10 10 18 this parameter is proportional to the baryon density and controls the entropy of the universe which in turn determines the temperature at which nuclear fusion can begin 12 high entropy prevents light element nuclei from forming which delays the onset of bbn low entropy conversely lets bbn last longer and therefore depletes the abundances of light elements that can fuse into helium 4 deuterium in particular is extremely sensitive to the value of the baryon to photon ratio 19 decreasing η by a factor of 10 leads to a corresponding increase in the abundance of primordial deuterium by a factor of roughly 50 1 expansion rate edit particles and nuclei fall out of equilibrium when their rates of interaction become slower than the rate of the expansion of the universe if the rate keeping a nuclear species in equilibrium drops below the expansion rate the relative abundance of that species stops evolving or decreases if decay is possible 20 340 during bbn the universe is radiation dominated and so the expansion of the universe is primarily determined by the energy density in radiative species like photons and neutrinos light element abundances are therefore sensitive to the energy densities of these species 21 sequence of nucleosynthesis edit main nuclear reaction chains for big bang nucleosynthesis bbn begins shortly after neutrinos decouple from the standard model and processes interconverting protons and neutrons fall out of equilibrium 22 by roughly 20 seconds after the big bang the universe had cooled sufficiently to allow deuterium nuclei to survive disruption by high energy photons at this time there were about six protons for every neutron as the universe expanded and cooled other light elements began to form becoming heavier through nuclear fusion at temperatures below 0 3 mev conditions were right for helium 4 to form and below 0 1 mev the abundance of deuterium climbed high enough for a burst of element formation 12 however very shortly thereafter around twenty minutes after the big bang the temperature and density became too low for any significant fusion to occur at this point the elemental abundances were nearly fixed further changes were the result of the radioactive decay of the two major unstable products of bbn tritium and beryllium 7 23 as well as continued decay of neutrons that did not fuse into any nuclei at the end of nucleosynthesis there were about seven protons to every neutron and almost all the neutrons were in helium 4 nuclei 24 neutron proton interconversion edit at temperatures above roughly 2 mev roughly 1 second to 1 minute after the big bang protons and neutrons interconverted via reactions involving electrons positrons neutrinos and antineutrinos 22 n e ν e p displaystyle ce n e overline nu _ e p n ν e p e displaystyle ce n nu_ e p e at times much earlier than 1 second these reactions were fast and maintained a neutron proton ratio close to 1 neutrons are slightly heavier than protons so even though these rates remained in equilibrium as the temperature began to drop equilibrium shifted in favor of protons and the neutron proton ratio smoothly decreased around a temperature of 2 mev these reactions fell out of equilibrium as neutrinos decoupled from the rest of the standard model after this time interconversion between protons and neutrons became inefficient and the neutron proton ratio was fixed to about 1 6 12 however this fraction continued to evolve during bbn since free neutrons are unstable with a lifetime of about 15 minutes 25 had nucleosynthesis not occurred this ratio would have fallen to 0 but since neutrons are usually stable when bound in nuclei the neutron proton ratio settles to about 1 7 by the end of bbn 12 virtually all of these remaining neutrons are therefore incorporated into nuclei at the end of bbn deuterium edit deuterium is the first nucleus to fuse during bbn its formation is the first step in all reaction chains to synthesize heavier elements it has a small binding energy 26 meaning it is generally easy to break deuterium nuclei apart and incorporate them into heavier nuclei for example to fuse tritium a deuterium nucleus breaks when it encounters another deuterium nucleus and the neutron from the first nucleus is incorporated into the second this process is efficient because the deuterium binding energy is low the deuterium abundance climbs steadily during bbn until temperatures lower than about 0 1 mev 10 after that deuterium fusion becomes inefficient due to the decreasing temperature and density of the universe bbn proceeds for a time as the remaining deuterium is fused into heavier nuclei but eventually those processes become inefficient as well and a tiny abundance of deuterium roughly one out of every 100 000 nuclei remains tritium helium 3 and helium 4 edit tritium and helium 3 form next when the deuterium abundance is large enough that deuterium fuses efficiently helium 4 forms quickly thereafter reaching an appreciable abundance roughly 10 seconds after the big bang and quickly surpassing the deuterium abundance thereafter as deuterium is consumed to make heavier elements 27 helium 4 has a very large binding energy compared to all other nuclei of similar atomic weight 28 unlike deuterium processes that require fusing helium 4 nuclei with other nuclei are therefore inefficient further the absence of a stable nucleus with 5 or 8 nucleons means it is impossible to fuse helium 4 with helium 4 or helium 4 with protons the two most abundant nuclei in the universe the helium 4 abundance closely tracks the neutron abundance neutrons that did not decay during bbn are very likely to be in a helium 4 nucleus since helium 4 must be formed on the way to heavier elements and incorporating additional nucleons requires significant energy the neutron proton ratio alone is sufficient to estimate that about 8 of all atoms should be helium 4 leading to a mass fraction of helium 4 of about 25 this estimate is in accordance with observations 27 heavier elements edit a version of the periodic table indicating the origins including big bang nucleosynthesis of the elements all elements above 103 lawrencium are also man made and are not included trace amounts of elements heavier than helium 4 also form during bbn these abundances are suppressed tightly bound helium 4 must be produced and then broken apart in order to form heavier nuclei elements heavier than helium 4 are instead primarily produced in stars where this bottleneck is overcome via triple collisions of helium 4 nuclei producing carbon the triple alpha process 29 this process is too slow to be relevant during bbn s 20 minute duration precise numerical codes make predictions for the abundances of heavy elements as heavy as oxygen 10 these form sequentially during bbn in reactions involving lighter nuclei that formed prior measurements of primordial abundances edit in order to test the predictions of bbn astrophysicists make precise measurements of light element abundances in the universe these measurements are complicated by the fact that stars change the relative abundances of hydrogen deuterium helium 3 helium 4 and heavier elements as the universe evolves therefore measurements of primordial element abundances are taken in metal poor systems where contamination from stellar nucleosynthesis is expected to be low 22 measurements of primordial deuterium involve measuring absorption spectra from metal poor clouds of gas passing in front of bright distant quasars 30 measurements of primordial helium 4 involve measuring helium 4 recombination lines emitted when an electron and ionized helium 4 combine back into a neutral atom in metal poor dwarf galaxies 31 these two isotopes have each been measured to percent level precision the observed abundance of each of these nuclei is generally consistent with the abundances predicted by bbn 13 69 2 313 there are also measurements of primordial lithium 7 both in stars and in the interstellar medium 32 in the 1980s measurements of population ii dwarf stars appeared to have similar abundances of lithium despite having different metallicities 33 this result called the spite plateau was thought to coincide with the primordial lithium 7 abundance however more recent measurements of lower metallicity stars have found a smaller lithium abundance raising questions about the assumption that the abundance of lithium 7 on the spite plateau is primordial 34 the resulting measurement of primordial lithium 7 is a factor of 2 4 lower than the predicted bbn abundance 35 a discrepancy known as the cosmological lithium problem though there remain open questions about the spite plateau and the reliability of these measurements 36 37 finally there is an observational upper bound on the abundance of primordial helium 3 primordial helium 3 is difficult to measure because systems are easily contaminated by nearby stellar activity and measurements can vary widely with no clear correlation to metallicity or location of the system being measured 27 therefore only an upper bound can be reported from observation as contamination should increase the amount of helium 3 in the system 38 though it is not often used in precision analyses 37 significance edit for standard cosmology edit bbn provides a direct measurement of the baryon to photon ratio one of the six parameters in the lambda cdm model of cosmology 37 deuterium in particular is extraordinarily sensitive to the value of this parameter the baryon to photon ratio is determined by calculating the value of η that produces a prediction of the deuterium abundance that matches the measured abundance recent work uses bbn to determine the baryon to photon ratio with an uncertainty of 1 39 the baryon to photon ratio can also be inferred from the cosmic microwave background cmb 18 bbn and the formation of the cmb are separated by roughly 400 000 years of evolution they are two independent epochs in cosmology and yet the lambda cdm model of cosmology requires they share the same value of the baryon to photon ratio concordance between these epochs is observed and so lambda cdm passes this consistency test 39 fitting the six parameters of lambda cdm to observed data from cmb experiments also requires knowledge of the primordial helium 4 abundance while in some analyses this parameter is inferred from cmb data state of the art inference of the parameters of lambda cdm requires input from bbn 18 the bbn determination of the baryon to photon ratio is also used in analyses of baryon acoustic oscillation bao data bao is sensitive to the baryon to photon ratio and in so in analyses where independence from the cmb is desired the bbn determination of this parameter is used during data analysis 40 for new physics edit bbn is often used to constrain particle physics scenarios beyond the standard model including dark matter scenarios massive neutrinos 41 42 and other particles or phenomena not included in the standard model 43 bbn takes place near temperatures of 1 mev and therefore is sensitive to processes that are characterized by a similar energy scale in standard cosmology this includes neutrino decoupling and electron positron annihilation scenarios that include for example energy injections from exotic particles into the standard model plasma around the same temperature can also be probed with bbn as these new processes change the predictions for primordial element abundances 44 45 other scenarios including time varying fundamental constants or scenarios with new light particles can be probed in much the same way 43 see also edit big bang chronology of the universe nucleosynthesis relic abundance stellar nucleosynthesis cosmological lithium problem references edit 1 2 3 patrignani c et al particle data group 2016 big bang nucleosynthesis pdf chin phys c 40 100001 archived pdf from the original on 2016 12 01 1 2 3 4 schramm david n tur...