Big Bang Nucleosynthesis Alexander Knebe (Universidad Autonoma De Madrid) Big Bang Nucleosynthesis

Home , Big Bang nucleosynthesis, Neutrino decoupling, Reionization

Big Bang Nucleosynthesis Alexander Knebe (Universidad Autonoma de Madrid) Big Bang Nucleosynthesis

! introduction ! particle physics ! cosmology ! big bang nucleosynthesis Big Bang Nucleosynthesis introduction

where do all the elements come from? Big Bang Nucleosynthesis introduction

where do all the elements come from?

stellar fusion reactions!?’s…) (stellar evolution work in 1920/30 Big Bang Nucleosynthesis introduction

! stellar fusion…

• cannot account for observed 4He abundance Big Bang Nucleosynthesis introduction

! stellar fusion…

• cannot account for observed 4He abundance

→ if MW were to “shine” for 1010 years, it would generate* 4% 4He

*(Burbidge, 1958, PASP, 70, 83) Big Bang Nucleosynthesis introduction

! stellar fusion…

• cannot account for observed 4He abundance

→ if MW were to “shine” for 1010 years, it would generate 4% 4He vs. 24% 4He as observed! 0.35 HII regions 0.30

0.25

0.20

0.15

Izotov & Thuan fit & Turner,& arxiv:9903300, Fig.4)

Helium Mass Fraction 0.10 Izotov & Thuan data Other data 0.05 Nollett

0.00 (Burles, 0 100 200 106 times O/H Ratio (“metalicity” = indicator of stellar processing) Big Bang Nucleosynthesis introduction

! stellar fusion…

• cannot account for observed 4He abundance

• cannot create D* but only burn it: fusion reactions in the sun are consuming D faster than generating it

*D=2H=p+n Big Bang Nucleosynthesis introduction

! stellar fusion…

• cannot account for observed 4He abundance

• cannot create D but only burn it: fusion reactions in the sun are consuming D faster than generating it

…but we do observe D Turner,& arxiv:9903300, Fig.2) in the interstellar medium: Nollett (Burles, Big Bang Nucleosynthesis introduction

! stellar fusion…

• cannot account for observed 4He abundance

• cannot create D but only burn it

’s existence… fusion events otherGyrs thanof stellarthe Universe must have happened during the ca. 13.7 Big Bang Nucleosynthesis introduction

! cosmological considerations

• z = 0 (today):

TCMB = 2.73K -31 3 rb = 5 x 10 g/cm Big Bang Nucleosynthesis introduction

! cosmological considerations

• z = 0 (today):

TCMB = 2.73K -31 3 rb = 5 x 10 g/cm

• z ≈ 1010 (t≈1sec.):

10 TCMB ≈ 10 K 3 rb ≈ 80 g/cm Big Bang Nucleosynthesis introduction

! cosmological considerations

• z = 0 (today):

TCMB = 2.73K -31 3 rb = 5 x 10 g/cm

• z ≈ 1010 (t≈1sec.):

10 TCMB ≈ 10 K 3 rb ≈ 80 g/cm

sufficient for nuclear fusion! Big Bang Nucleosynthesis introduction

! cosmological considerations

• z = 0 (today):

TCMB = 2.73K -31 3 rb = 5 x 10 g/cm

• z ≈ 1010 (t≈1sec.):

10 TCMB ≈ 10 K 3 rb ≈ 80 g/cm

sufficient for nuclear fusion " “Big Bang Nucleosynthesis” !? Big Bang Nucleosynthesis introduction

! BBN: Alpher, Bethe & Gamow (1948) “The Origin of Chemical Elements”

PH VSICAL REVIEW VOLUME 73, NUM HER 7 AP RI L 1, 1948

We may remark at first that the building-up process was . : etters to t.ze 'a.itor apparently completed when the temperature of the neutron gas was still rather high, since otherwise the observed

S pointed out by one of us, ' various nuclear species (10'jt')dt =5X 104, (2) A must have originated not as the result of an equilib- J&0 rium corresponding to a certain temperature and density, but rather as a consequence of a continuous building-up which gives us to=20 sec. and p0=2.5)&105 g sec./cm'. This process arrested by a rapid expansion and cooling of the result may have two meanings: (a) for the higher densities primordial matter. According to this picture, we must existing prior to that time the temperature of the neutron imagine the early stage of matter as a highly compressed gas was so high that no aggregation was taking place, (b) neutron gas (overheated neutral nuclear Quid) which the density of the universe never exceeded the value 10' /cm' started decaying into protons and electrons when the gas 2.5 )& g sec. which can possibly be understood if we pressure fell down as the result of universal expansion. The radiative capture of the still remaining neutrons by the newly formed protons must have led first to the formation of deuterium nuclei, and the subsequent neutron captures resulted in the building up of heavier and heavier nuclei. It must be remembered that, due to the comparatively short time allowed for this procgss, ' the building up of heavier nuclei must have proceeded just above the upper fringe of the stable elements (short-lived Fermi elements), and the present frequency distribution of various atomic species was attained only somewhat later as the result of adjust- ment of their electric charges by P-decay. Thus the observed slope of the abundance curve must not be related to the temperature of the original neutron gas, but rather to the time period permitted by the expan- CAt ClMlKO sion process. Also, the individual abundances of various nuclear species must depend not so much on their intrinsic stabilities (mass defects) as on the values of their neutron capture cross sections. The equations governing such a -2 building-up process apparently can be written in the form: lsd — n; —;n;) i=1,2, " 238 =f(t)(;, '0 /50 BO

where n; and a;. are the relative numbers and capture cross Fio. 1. sections for the nuclei of atomic weight i, and where f(t) is a Log of relative abundance factor characterizing the decrease of the density with time. Atomic weight 803 Big Bang Nucleosynthesis introduction

! BBN: Alpher, Bethe & Gamow (1948) “The Origin of Chemical Elements”

PH VSICAL REVIEW VOLUME 73, NUM HER 7 AP RI L 1, 1948

We may remark at first that the building-up process was . : etters to t.ze 'a.itor apparently completed when the temperature of the neutron gas was still rather high, since otherwise the observed

~ ~ ~ UBLICA TION of brief reports of important discoveries abundances would have been strongly affected by the ~ ~ in physics may be secured by addressing them to this resonances in the region of the slow neutrons. According to ~ ~ 2 department. The closing date for this department is five ueeks Hughes, the neutron capture cross sections of various elements (for neutron energies of about 1 Mev) increase prior to the date ofissue. ¹ proof a@ill be sent to the authors. The Board of Editors does not hold itself responsible for the exponentially with atomic number halfway up the periodic opinions expressed by the correspondents. Communications system, remaining approximately constant for heavier should not exceed 600 words in length. elements. Using these cross sections, one finds by integrating Eqs. (1)as shown in Fig. 1 that the relative abundances of various nuclear species decrease rapidly for the lighter elements and remain approximately constant for the ele- The Origin of Chemical Elements ments heavier than silver. In order to fit the calculated R. A. ALPHER+ curve with the observed abundances' it is necessary to Applied Physics Laboratory, The Johns Hopkins Un&rersity, assume thy integral of p„dt during the building-up period is Silver Spring, Maryland equal to 5 X104 sec./cm'. AND g On the other hand, according to the relativistic theory of H. BETHE Cornell University, Ithaca, %em York the expanding universe4 the density dependence on time is given by p —10'/t~. Since the integral of this expression G. GAMow diverges at t =0, it is necessary to assume that the building- The George Washington University, 8'ashington, D. C. up process began at a certain time to, satisfying the February 18, 1948 relation:Big Bang Nucleosynthesis introduction S pointed out by one of us, ' various nuclear species (10'jt')dt =5X 104, (2) A must have originated not as the result of an equilib- J&0 rium corresponding to a certain temperature and density, but rather as a consequence of a continuous building-up which gives us to=20 sec. and p0=2.5)&105 g sec./cm'. This process arrested by a rapid expansion and cooling of the result! BBN:may have two meanings: (a) for the higher densities primordial matter. According to this picture, we must existing prior to that time the temperature of the neutron imagine the early stage of matter as a highly compressed gas was so high that no aggregation was taking place, (b) neutron gas (overheated neutral nuclear Quid) which the density of the universe never exceededAlpherthe value, Bethe & Gamow (1948) 10' /cm' started decaying into protons and electrons when the gas 2.5 )& g sec. which can possibly be understood“The ifOriginwe of Chemical Elements” pressure fell down as the result of universal expansion. The radiative capture of the still remaining neutrons by the PH VSICAL REVIEW VOLUME 73, NUM HER 7 AP RI L 1, 1948

We may remark at first that the building-up process was newly formed protons must have led first to the formation . : etters to t.ze 'a.itor apparently completed when the temperature of the neutron gas was still rather high, since otherwise the observed

~ ~ ~ of deuterium nuclei, and the subsequent neutron captures UBLICA TION of brief reports of important discoveries abundances would have been strongly affected by the ~ ~ in physics may be secured by addressing them to this resonances in the region of the slow neutrons. According to ~ ~ 2 resulted in the building up of heavier and heavier nuclei. It department. The closing date for this department is five ueeks Hughes, the neutron capture cross sections of various elements (for neutron energies of about 1 Mev) increase prior to the date ofissue. ¹ proof a@ill be sent to the authors. The Board of Editors does not hold itself responsible for the exponentially with atomic number halfway up the periodic must be remembered that, due to the comparatively short opinions expressed by the correspondents. Communications system, remaining approximately constant for heavier should not exceed 600 words in length. elements. ' Using these cross sections, one finds by integrating time allowed for this procgss, the building up of heavier Eqs. (1)as shown in Fig. 1 that the relative abundances of various nuclear species decrease rapidly for the lighter nuclei must have proceeded just above the upper fringe of elements and remain approximately constant for the ele- The Origin of Chemical Elements ments heavier than silver. In order to fit the calculated R. A. ALPHER+ curve with the observed abundances' it is necessary to the stable elements (short-lived Fermi and the Applied Physics Laboratory, The Johns Hopkins Un&rersity, assume thy integral of p„dt during the building-up period is elements), Silver Spring, Maryland equal to 5 X104 sec./cm'. AND g On the other hand, according to the relativistic theory of present frequency distribution of various atomic species H. BETHE Cornell University, Ithaca, %em York the expanding universe4 the density dependence on time is given by p —10'/t~. Since the integral of this expression was attained only somewhat later as the result of adjust- G. GAMow diverges at t =0, it is necessary to assume that the building- The George Washington University, 8'ashington, D. C. up process began at a certain time to, satisfying the ment of their electric charges by P-decay. February 18, 1948 relation: S pointed out by one of us, ' various nuclear species (10'jt')dt =5X 104, (2) A must have originated not as the result of an equilib- J&0 Thus the observed slope of the abundance curve must rium corresponding to a certain temperature and density, but rather as a consequence of a continuous building-up which gives us to=20 sec. and p0=2.5)&105 g sec./cm'. This not be related to the temperature of the original neutron process arrested by a rapid expansion and cooling of the result may have two meanings: (a) for the higher densities primordial matter. According to this picture, we must existing prior to that time the temperature of the neutron gas was so high that no aggregation was taking place, (b) CAt ClMlKO imagine the early stage of matter as a highly compressed gas, but rather to the time period permitted by the expan- neutron gas (overheated neutral nuclear Quid) which the density of the universe never exceeded the value 10' /cm' started decaying into protons and electrons when the gas 2.5 )& g sec. which can possibly be understood if we sion process. Also, the individual abundances of various pressure fell down as the result of universal expansion. The radiative capture of the still remaining neutrons by the newly formed protons must have led first to the formation nuclear species must depend not so much on their intrinsic of deuterium nuclei, and the subsequent neutron captures resulted in the building up of heavier and heavier nuclei. It stabilities (mass as on the values must be remembered that, due to the comparatively short defects) of their neutron time allowed for this procgss, ' the building up of heavier -2 nuclei must have proceeded just above the upper fringe of capture cross sections. The equations governing such a the stable elements (short-lived Fermi elements), and the present frequency distribution of various atomic species building-up was attained only somewhat later as the result of adjust- process apparently can be written in the form: ment of their electric charges by P-decay. Thus the observed slope of the abundance curve must not be related to the temperature of the original neutron gas, but rather to the time period permitted by the expan- CAt ClMlKO lsd sion process. Also, the individual abundances of various —=f(t)(;,n; —;n;) i=1,2, " 238 nuclear species must depend not so much on their intrinsic '0 /50 stabilitiesBO (mass defects) as on the values of their neutron capture cross sections. The equations governing such a -2 building-up process apparently can be written in the form: lsd Fio. 1. —=f(t)(;,n; —;n;) i=1,2, " 238 where n; and a;. are the relative numbers and capture cross '0 /50 BO where n; and a;. are the relative numbers and capture cross Fio. 1. of relative abundance of relative abundance sections for the nuclei of atomic weight i, and where f(t) is a Log sections for the nuclei of atomic weight i, and where f(t) is a Log factor characterizing the decrease of the density with time. Atomic weight factor characterizing the decrease of the density with time. Atomic weight 803 803 all elements are produced in BBN !? Big Bang Nucleosynthesis introduction

! BBN: Alpher, Bethe & Gamow (1948) “The Origin of Chemical Elements”

PH VSICAL REVIEW VOLUME 73, NUM HER 7 AP RI L 1, 1948

We may remark at first that the building-up process was . : etters to t.ze 'a.itor apparently completed when the temperature of the neutron gas was still rather high, since otherwise the observed

S pointed out by one of us, ' various nuclear species (10'jt')dt =5X 104, (2) A must have originated not as the result of an equilib- J&0 rium corresponding to a certain temperature and density, but rather as a consequence of a continuous building-up which gives us to=20 sec. and p0=2.5)&105 g sec./cm'. This process arrested by a rapid expansion and cooling of the result may have two meanings: (a) for the higher densities time of the neutron this is the whole publication! primordial matter. According to this picture, we must existing prior to that the temperature imagine the early stage of matter as a highly compressed gas was so high that no aggregation was taking place, (b) neutron gas (overheated neutral nuclear Quid) which the density of the universe never exceeded the value 10' /cm' started decaying into protons and electrons when the gas 2.5 )& g sec. which can possibly be understood if we pressure fell down as the result of universal expansion. The radiative capture of the still remaining neutrons by the newly formed protons must have led first to the formation of deuterium nuclei, and the subsequent neutron captures resulted in the building up of heavier and heavier nuclei. It must be remembered that, due to the comparatively short time allowed for this procgss, ' the building up of heavier nuclei must have proceeded just above the upper fringe of the stable elements (short-lived Fermi elements), and the present frequency distribution of various atomic species was attained only somewhat later as the result of adjust- ment of their electric charges by P-decay. Thus the observed slope of the abundance curve must not be related to the temperature of the original neutron gas, but rather to the time period permitted by the expan- CAt ClMlKO sion process. Also, the individual abundances of various nuclear species must depend not so much on their intrinsic stabilities (mass defects) as on the values of their neutron capture cross sections. The equations governing such a -2 building-up process apparently can be written in the form: lsd — n; —;n;) i=1,2, " 238 =f(t)(;, '0 /50 BO

! BBN:

VOLUME 16, NUMBERPeebles10 (1966)PHYSICAL RKVIKW LKTTKRS 7 MPRcH 1966 “Primeval Helium abundance and the primeval Fireball” will be difficult to explain on the basis of con- TEMPERATURE K ventiona 1 general relativity. lo+ I LI 5x K Ixlo K 5x 0 K ' ' 5 I I I It is a pleasure to acknow lede gee fruitfulr dis- J f this problem with R. H.. Dicke, Z D. T. Wilkinson, P. G. Roll, an I lo NEUTRONS I-le4

Ll ' 0 IO~ I l *This research wasas supportepp d in ppart by the National Z NUCLEAR Science Foundation annd thee Office of Nava ese 0 BURNING +- lo P. G.. Ro1]., and D. T. Wilkinson,on Physys. Rev. Letters 5 16, 405 (1966). A A. Penzias and R. W.. Wilson, Astrophys.s ro 142, ~ IO- J. TER IUM P G Rll dD T ~ IO'- ' lJ I I K J. H. Oort, Onziem'erne Conseil e ns 10 IO2 Io5 IO aal de Physique Solvay,lva, Laa Structure et l'E voolutionu de TIME (SECONDS) ' { 'o oop,oo s Brussels, FIG. 2. Abundances of the elements versus time. S. van den Bergb,r b Z. Astrophys. 53, 2 dn 2 2 + 3Hn = − σ v n − neq : detailed calculationhere of thatthe temporaltbe present evolutionprimor ofordial elementia fireballi abundances… J. Gaustad, Astrop h ys.. J. 139, 4 dt ( ) i "io p ature is 3.5'K an e p le and R. J. Tayler, Nature 2 ' ' ' mass densitye in the unive rse is 7x g C. Hayashi, in Origin of the Solar System: Proceed- ings of a Conferencerence held at the Go ar Space Studies,es New York, 1963, editedi e by R. Jastrow ' y tion and neutrinos.nos. Assumings that the nucleoncleon and A. G. Cameron (Academic ress, ' mass density now is at least 7X1 g York, 1963). ' dition of an amount of raradiation con- J. W Truran, C. J. Hansen,sen anand A. G. W. Cameron, p sistent wiith the limits implied by th 1 ' 9 d ie, Paris Symposium on a tion arameter the first effectef ec is morem impor- p edited by R. Bracewell (Stan or tant, and the primeva e iu ia 1958), p. 352. increased. For a reasonableble value of the mean mass C. Hayas b,i, Progr. Theoret. Phys. (Kyoto it in the universe we haveve concluconcludede that (1950). e uires a large prim R. A. Alpher, J. W. Follin,ollin, anand R. C. Herman, Phys. abundance, anand if this agrees wi'th oob t'o 1953). Elementary artie e y be considered a remarrkablya stringent ' ' WesleyWes ey Publishing Company,m an, Inc. , Rea ing, test of general rela y. 0 d if the primevameval heliume i abundance is oun E. Ferm nd A. Turkurkevich, in wor kd bdb be low, and ththe presence of thee 3'K primordial R. A. Alpher and R. C.. Herman,e Rev. Mo . fireball confirmed, we believe th at the result 193 {1950).

413 Big Bang Nucleosynthesis introduction

! BBN vs. stellar fusion:

• no stable elements with A=5 or A=8 Big Bang Nucleosynthesis introduction

! BBN vs. stellar fusion:

• no stable elements with A=5 or A=8

3 • BBN: rb ≈ 80 g/cm

3 • sun: rb ≈ 150 g/cm Big Bang Nucleosynthesis introduction

! BBN vs. stellar fusion:

• no stable elements with A=5 or A=8

3 • BBN: rb ≈ 80 g/cm

3 • sun: rb ≈ 150 g/cm

similar conditions!? Big Bang Nucleosynthesis introduction

! BBN vs. stellar fusion:

• no stable elements with A=5 or A=8

3 • BBN: rb ≈ 80 g/cm → unable to process anything heavier than 7Li, 7Be due to very short timescale for fusion

3 • sun: rb ≈ 150 g/cm → able to process heavy elements* due to extended timescale for fusion

*via unstable 8Be (“triple-a process”) Big Bang Nucleosynthesis introduction

! BBN vs. stellar fusion:

• no stable elements with A=5 or A=8

3 • BBN: rb ≈ 80 g/cm → unable to process anything heavier than 7Li, 7Be due to very short timescale for fusion

• sun: r ≈ 150 g/cm3 b BBN → able to process heavy elements* due to extended timescale for fusion

*via unstable 8Be (“triple-a process”) Big Bang Nucleosynthesis introduction

! BBN summary:

• production of H, 2H, 3H, 3He, 4He, 7Be, 7Li 2H: deuterium D 3H: trillium T

! all other elements are in fact produced in stars…

anything heavier than 56Fe produced in SN explosions… Big Bang Nucleosynthesis introduction

! BBN summary:

• production of H, 2H, 3H, 3He, 4He, 7Be, 7Li 2H: deuterium D 3H: trillium T

• prediction for mass fractions:

YHe ≈ 0.24

YH ≈ 0.73

! all other elements are in fact produced in stars…

anything heavier than 56Fe produced in SN explosions… Big Bang Nucleosynthesis introduction

where do all the elements come from?

(APOD 24/10/2017) Big Bang Nucleosynthesis

! introduction ! particle physics ! cosmology ! big bang nucleosynthesis Big Bang Nucleosynthesis particle physics Big Bang Nucleosynthesis particle physics

when did they form? Big Bang Nucleosynthesis particle physics Big Bang Nucleosynthesis particle physics Big Bang Nucleosynthesis particle physics Big Bang Nucleosynthesis particle physics

!? Big Bang Nucleosynthesis particle physics

n, p, … BBNS Big Bang Nucleosynthesis particle physics

e-, n, µ

n, p, … BBNS

− νe + n ⇔ p + e + e + n ⇔ p +νe ✗ p and n held in equilibrium via weak interaction ✗ − n ⇔ p + e +νe Big Bang Nucleosynthesis particle physics

e-, n, µ

n, p, … BBNS

n and p: BBNS requires free -out of weak interaction! only available after freeze

− νe + n ⇔ p + e + e + n ⇔ p +νe ✗ p and n held in equilibrium via weak interaction ✗ − n ⇔ p + e +νe Big Bang Nucleosynthesis particle physics

e-, n, µ

recombination

CMB lecture(s)… 46 3. ThermalBig Bang History Nucleosynthesis particle physics

Event time t redshift z temperature T

34 Inﬂation 10 s(?) – –

Baryogenesis ? ? ?

EW phase transition 20 ps 1015 100 GeV

QCD phase transition 20 µs 1012 150 MeV

Dark matter freeze-out ? ? ?

Neutrino decoupling 1 s 6 109 1 MeV ⇥ Electron-positron annihilation 6 s 2 109 500 keV ⇥ Big Bang nucleosynthesis 3 min 4 108 100 keV ⇥ Matter-radiation equality 60 kyr 3400 0.75 eV

Recombination 260–380 kyr 1100–1400 0.26–0.33 eV

Photon decoupling 380 kyr 1000–1200 0.23–0.28 eV

Reionization 100–400 Myr 11–30 2.6–7.0 meV

Dark energy-matter equality 9 Gyr 0.4 0.33 meV

Present 13.8 Gyr 0 0.24 meV

Table 3.1: Key events in the thermal history of the universe.

show that choosing natural values for the mass of the dark matter particles and their interaction cross section with ordinary matter reproduces the observed relic dark matter density surprisingly well.

Neutrino decoupling. Neutrinos only interact with the rest of the primordial plasma • through the weak interaction. The estimate in (3.1.10) therefore applies and neutrinos decouple at 0.8 MeV.

Electron-positron annihilation. Electrons and positrons annihilate shortly after neu- • trino decoupling. The energies of the electrons and positrons gets transferred to the photons, but not the neutrinos. In 3.2.4, we will explain that this is the reason why the § photon temperature today is greater than the neutrino temperature.

Big Bang nucleosynthesis. Around 3 minutes after the Big Bang, the light elements • were formed. In 3.3.4, we will study this process of Big Bang nucleosynthesis (BBN). § Recombination. Neutral hydrogen forms through the reaction e +p+ H+ when the • ! temperature has become low enough that the reverse reaction is energetically disfavoured. We will study recombination in 3.3.3. § Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: p + e- → H + g Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: p + e- → H + g

this requires free electrons, but they are still coupled to the photons… Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g )

this requires free electrons, but they are still coupled to the photons…

Note: in BBNS we are forming nuclei and not atoms! Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

requires free protons and neutrons!*

*available after decoupling of neutrinos…(cf. Thermal History lecture) Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

two-body processes only, as probability for others too low (‘bottom-up’ fusion of He4) Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

! all A>2 nuclei require D and n for synthesis Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

(T @ neutrino decoupling) E b ≈ 2MeV ; kTν ≈ 0.8MeV

! all A>2 nuclei require D and n for synthesis € * but: D easily photo-dissociated by g until kTD ≅ 0.086MeV (ca. t » 100s )

* 1/2 T −1/4 #1s & ≅1.5g*S % ( 1MeV $ t ' Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

(T @ neutrino decoupling) E b ≈ 2MeV ; kTν ≈ 0.8MeV ! all A>2 nuclei require D and n for synthesis ? € * but: D easily photo-dissociated by g until kTD ≅ 0.086MeV (ca. t » 100s )

* 1/2 T −1/4 #1s & ≅1.5g*S % ( 1MeV $ t ' Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

(T @ neutrino decoupling) E b ≈ 2MeV ; kTν ≈ 0.8MeV

! all A>2 nuclei require D and n for synthesis € but: D easily photo-dissociated by g until kTD ≅ 0.086MeV (ca. t » 100s)

kTD < Eb as for temperatures even lower than Eb there will still be lots of higher energy photons in the Planck distribution

2eV 8eV Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

(T @ neutrino decoupling) E b ≈ 2MeV ; kTν ≈ 0.8MeV

! all A>2 nuclei require D and n for synthesis € but: D easily photo-dissociated by g until kTD ≅ 0.086MeV (ca. t » 100s)

kTD < Eb as for temperatures even lower than Eb there will still be lots of higher energy photons in the Planck distribution

" deuterium production (and all successive nuclei) sensitively depends on baryon-to-photon ratio!

2eV 8eV Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

(T @ neutrino decoupling) E b ≈ 2MeV ; kTν ≈ 0.8MeV

! all A>2 nuclei require D and n for synthesis € but: D easily photo-dissociated by g until kTD ≅ 0.086MeV (ca. t » 100s)

→ ‘Deuterium bottleneck’: • too few D → important fusion agent is missing • too much D → locks up neutrons for further synthesis

" deuterium production (and all successive nuclei) sensitively depends on baryon-to-photon ratio! Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g

(T @ neutrino decoupling) E b ≈ 2MeV ; kTν ≈ 0.8MeV

! all A>2 nuclei require D and n for synthesis € but: D easily photo-dissociated by g until kTD ≅ 0.086MeV (ca. t » 100s)

→ ‘Deuterium bottleneck’: • too few D → important fusion agent is missing • too much D → locks up neutrons for further synthesis

" deuterium production (and all successive nuclei) sensitively depends on baryon-to-photon ratio! ! photon-to-baryon ratio* (frozen in at BBNS):

nb −10 −10 2 η = =10 η10 =10 ⋅ 274Ωbh nγ *see Baryogenesis lecture Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g ! lighter elements: D + n → 3H + g D + D → 3H + p D + p → 3He + g D + D → 3He + n 3He + n → 3H + p Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g ! lighter elements: D + n → 3H + g D + D → 3H + p D + p → 3He + g D + D → 3He + n 3He + n → 3H + p ! 4He: D + D → 4He + g D + 3He → 4He + p D + 3H → 4He + n 3He + 3He → 4He + 2p 3He + n → 4He + g 3H + p → 4He + g Big Bang Nucleosynthesis synthesis of elements

E 4 He ≈ 28.3MeV Þ highest binding energy (safe from photo-dissociation) Big Bang Nucleosynthesis synthesis of elements

! 7Be, 7Li: 3He + 4He → 7Be + g 7 7 + Be → Li + e + ne 3 4 7 + H + He → Li + e + ne Big Bang Nucleosynthesis synthesis of elements

! 7Be, 7Li: 3He + 4He → 7Be + g 7 7 + Be → Li + e + ne gap at A=8 prohibits3 4 production7 of+ heavier isotopes! H + He → Li + e + ne Big Bang Nucleosynthesis synthesis of elements

H, 2H, 3H, 3He, 4He, 7Be, 7Li ! Hydrogen: ( p + e - → H + g ) ! Deuterium: p + n → D + g ! lighter elements: → 3 we require D + n H + g freeD +protonsD → and3H neutrons…+ p D + p → 3He + g D + D → 3He + n 3He + n → 3H + p ! 4He: D + D → 4He + g D + 3He → 4He + p D + 3H → 4He + n 3He + 3He → 4He + 2p 3He + n → 4He + g 3H + p → 4He + g

! 7Be, 7Li: 3He + 4He → 7Be + g 7 7 + Be → Li + e + ne gap at A=8 prohibits3 4 production7 of+ heavier isotopes! H + He → Li + e + ne Big Bang Nucleosynthesis

! introduction ! particle physics ! cosmology ! big bang nucleosynthesis Big Bang Nucleosynthesis cosmology

! thermal equilibrium of radiation & matter: γ +γ ⇔ P + P

! interaction rate of particles: Γc ∝ n σ v

! expansion rate of Universe: Γe ∝ H

*see ‘Thermal History’ lecture Big Bang Nucleosynthesis cosmology

! thermal equilibrium of radiation & matter: γ +γ ⇔ P + P

! interaction rate of particles: Γc ∝ n σ v Γ c <1 => “freeze-out” ! expansion rate of Universe: Γe ∝ H H Big Bang Nucleosynthesis cosmology

! thermal equilibrium of radiation & matter: γ +γ ⇔ P + P

! interaction rate of particles: Γc ∝ n σ v Γ c <1 => “freeze-out” ! expansion rate of Universe: Γe ∝ H H

• freeze-out depends on “temperature window” Big Bang Nucleosynthesis cosmology

! thermal equilibrium of radiation & matter: γ +γ ⇔ P + P

! interaction rate of particles: Γc ∝ n σ v Γ c <1 => “freeze-out” ! expansion rate of Universe: Γe ∝ H H

• freeze-out depends on “temperature window”

• temperature window depends on H:

−1 # T ∝ R % 2 radiation domination: $H ∝T −2 H ∝ R &% Big Bang Nucleosynthesis cosmology

! thermal equilibrium of radiation & matter: γ +γ ⇔ P + P

! interaction rate of particles: Γc ∝ n σ v Γ c <1 => “freeze-out” ! expansion rate of Universe: Γe ∝ H H

• freeze-out depends on “temperature window”

• temperature window depends on H:

−1 # T ∝ R % 2 radiation domination: $H ∝T −2 H ∝ R &%

⇒ BBN is sensitive to cosmology and Thermal History of the Universe, respectively! Big Bang Nucleosynthesis cosmology

! thermal equilibrium of radiation & matter: γ +γ ⇔ P + P

! interaction rate of particles: Γc ∝ n σ v Γ c <1 => “freeze-out” ! expansion rate of Universe: Γe ∝ H H

• freeze-out depends on “temperature window”

• temperature window depends on H:

−1 # T ∝ R % 2 radiation domination: $H ∝T −2 H ∝ R &%

⇒ BBN is sensitive to cosmology and Thermal History of the Universe, respectively!

...for neutrons and protons => Big Bang Nucleosynthesis cosmology

! thermal equilibrium of neutrons & protons:

− νe + n ⇔ p + e + e + n ⇔ p +νe weak interaction* − n ⇔ p + e +νe

p ν + γ e e νe γ p + e νe γ νe p n − e− e γ γ − n γ e νe *only ne contributes to weak interaction Big Bang Nucleosynthesis cosmology

! thermal equilibrium of neutrons & protons:

− νe + n ⇔ p + e + e + n ⇔ p +νe weak interaction − n ⇔ p + e +νe

! weak interaction freezes out at T ≈ 0.8 MeV

n n γ n γ n

γ − − e γ e γ n p pp e− n p γ n p Big Bang Nucleosynthesis cosmology

! inventory (T < 0.8MeV): • relativistic particles in equilibrium: e-, e+ • decoupled relativistic particles: n • decoupled non-relativistic particles: n, p

thermal bath decoupled species

nn n γ n γ relativistic

γ − − e γ e γ n p pp e− n p γ n p non-relativistic Big Bang Nucleosynthesis cosmology

! inventory (T < 0.8MeV): • relativistic particles in equilibrium: e-, e+ • decoupled relativistic particles: n

• decoupled non-relativistic particles: n, p building blocks for nuclei!

thermal bath decoupled species

nn n γ n γ relativistic

γ − − e γ e γ n p pp e− n p γ n p non-relativistic Big Bang Nucleosynthesis cosmology

! inventory (T < 0.8MeV): • relativistic particles in equilibrium: e-, e+ • decoupled relativistic particles: n

• decoupled non-relativistic particles: n, p building blocks for nuclei!

thermal bath decoupled species

nn n γ n γ relativistic Note: we do not care about the (still coupled) e- γ − − e γ e γ n p pp e− n p γ n p non-relativistic Big Bang Nucleosynthesis cosmology

! inventory (T < 0.8MeV): • relativistic particles in equilibrium: e-, e+ • decoupled relativistic particles: n

• decoupled non-relativistic particles: n, p building blocks for nuclei!

let’s calculate the number densities of n and p...

thermal bath decoupled species

nn n γ n γ relativistic Note: we do not care about the (still coupled) e- γ − − e γ e γ n p pp e− n p γ n p non-relativistic Big Bang Nucleosynthesis

! introduction ! particle physics ! cosmology ! big bang nucleosynthesis Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio:*

the abundance of neutrons determines how many nuclei beyond (A=1) can be formed…

*we will measure neutron abundance relative to protons… Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio:

p + νe e − γ νe + n ⇔ p + e ν γ + e e + n ⇔ p +νe + − p n ⇔ p + e +νe e νe νe γ p e− +γ ↔ e− +γ n − e− e γ γ − n γ e νe

thermal bath Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio: 3/2 2 ! mAkT $ −(mA −µA )c /kT nA = g?A # 2 & e " 2π! %

p + νe e − γ νe + n ⇔ p + e ν γ + e e + n ⇔ p +νe + − p n ⇔ p + e +νe e νe νe γ p e− +γ ↔ e− +γ n − e− e γ γ − n γ e νe

thermal bath Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio: 3/2 2 ! mAkT $ −(mA −µA )c /kT nA = gA # & e (non-relativistic particles) " 2π!2 % 3/2 n ! m $ − m −m c2 /kT µ −µ /kT n n ( n pp ) ( n p ) = # & e +e # & νe np mp e − " γ% νe + n ⇔ p + e ν γ + e e + n ⇔ p +νe + − p n ⇔ p + e +νe e νe νe γ p e− +γ ↔ e− +γ n − e− e γ γ − n γ e νe

thermal bath Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio: 3/2 2 ! mAkT $ −(mA −µA )c /kT nA = gA # & e (non-relativistic particles) " 2π!2 % 3/2 ! $ µ −µ /kT nn mn −Q/kT ( n p ) (Q=1.293 MeV) = # & e e np " mp % Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio: 3/2 2 ! mAkT $ −(mA −µA )c /kT nA = gA # & e (non-relativistic particles) " 2π!2 % 3/2 ! $ µ −µ /kT nn mn −Q/kT ( n p ) (Q=1.293 MeV) = # & e e np " mp %

what about µn and µp? Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio: 3/2 2 ! mAkT $ −(mA −µA )c /kT nA = gA # & e (non-relativistic particles) " 2π!2 % 3/2 ! $ µ −µ /kT nn mn −Q/kT ( n p ) (Q=1.293 MeV) = # & e e np " mp %

what about µn and µp?

! chemical potential: • energy absorbed or released during chemical reaction • chemical equilibrium*: chemical equilibrium A + B ↔ C + D """"""→ µA + µB = µC + µD

*nuclear reactions are faster than cosmic expansion… Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio: 3/2 2 ! mAkT $ −(mA −µA )c /kT nA = gA # & e (non-relativistic particles) " 2π!2 % 3/2 ! $ µ −µ /kT nn mn −Q/kT ( n p ) (Q=1.293 MeV) = # & e e np " mp %

what about µn and µp?

! chemical potential: • energy absorbed or released during chemical reaction • chemical equilibrium: chemical equilibrium A + B ↔ C + D """"""→ µA + µB = µC + µD

what reaction is going on? Big Bang Nucleosynthesis neutron-to-proton ratio

! neutron-to-proton ratio: 3/2 2 ! mAkT $ −(mA −µA )c /kT nA = gA # & e (non-relativistic particles) " 2π!2 % 3/2 ! $ µ −µ /kT nn mn −Q/kT ( n p ) (Q=1.293 MeV) = # & e e np " mp %

what about µn and µp?

! b-decay: − νe + n ↔ p + e ⟶ �!! + �" = �# + �$ Big Bang Nucleosynthesis neutron-to-proton ratio