Nucleosynthesis Lecture 3: Big-bang nucleosynthesis

Overview

• Lecture 1: Introduction & overview April 18• Lecture 2: Thermonuclear reactions April 25• Lecture 3: Big-bang nucleosynthesis May 2• Lecture 4: Thermonuclear reactions inside stars — I (H-burning) May 7• Lecture 5: Thermonuclear reactions inside stars — II (advanced burning) May 16• Lecture 6: Neutron-capture and supernovae — I May 23• Lecture 7: Neutron-capture and supernovae — II June 6• Lecture 8: Thermonuclear supernovae June 13• Lecture 9: Li, Be and B July 4• Lecture 10: Galactic chemical evolution and relation to astrobiology July 11

Paper presentations I June 21 Paper presentations II June 27

Overview of previous lecture

Energetics of nuclear reactions

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Exothermic reactionEndothermic reaction

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Blackboard

Nuclear reaction rate

with

Z�(v)dv = 1

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r↵X = N↵NX

Z 1

0v�(v)�(v)dv = N↵NXh�vi

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Ways to evaluate <σv>

• lab measurements (usually high energies, strong and E/M reactions)• nuclear theory (approximate) + simplifications (e.g., away from resonances:constant astrophysical

factor, dependence only on Gamow penetration and thermal energy distribution)

Overview of previous lecture

Three salient properties of <σv>

1. Depends on nature of interaction2. Significant only for narrow range of

energies (Gamow peak for constant T)3. Strongly varying function of temperature

https://github.com/jantoniadis/nucleosynthesis/blob/master/demos/Nuc_Lecture_2_Interactive_Rates.ipynbBlackboard

At sufficiently high temperatures, forward and reverse reactions balance. When this happens, abundances are determined by statistical physics, N(A,Z) / exp[Q(A,Z)/kT ]

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When this happens for all possible reactions, nuclear statistical equilibrium is achieved

Once rates and conditions (in T.E.: composition, temperature and density) are known, we can start cooking up the elements

Overview of previous lecture

Blackboard

dXi

dt= Ai

mu

⇢

⇣�X

rreactions that destroy i +X

rreactions that create i

⌘

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✏↵X =Q↵X

m2u

X↵XX

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Energy generation rate:

The origin of light elements (isotopes of H, He and Li)

H and He isotopes account for ~98% of the baryonic mass in the Universe. Can they be made in stars?

No. • Only ~10% of a star is converted to He via fusion• Most of the He is subsequently destroyed in reactions or retained in stellar remnants• Observationally, He abundance does not vary significantly with metallicity • Deuterium is destroyed during the pre-ms via which has a large cross sectionD(p, �)3He

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Figure from Izotov & Thuan (2004a) ApJ, 602, 230

The origin of light elements (isotopes of H, He and Li)

The Alpher, Bethe & Gamow (1948) paper (aka αβγ paper)

Hypothesis: Light elements (particularly H and He isotopes) were created shortly after the Big Bang under very special conditions

The origin of light elements (isotopes of H, He and Li)

Spoiler: this paper is wrong

Big Bang Nucleosynthesis

Ingredients needed to construct a quantitative theory

We need to know:

Nuclear fusion is only possible if the Universe was hot (~MeV) enough for a sufficiently long period of time. The Universe is expanding (and cooling) which means that nucleosynthesis could only occur at very early epochs, when the scale factor was of order 1e-10. Only at such early times, the rates of some reactions could be much faster than the expansion rate (thermal equilibrium)

1. Temperature (and density) as a function of time

2. Primordial composition of elementary particles

3. Reaction rates between all components

Cosmology

Observables

Assumptions• Cosmological principle (the Universe is isotropic and homogeneous) • General relativity describes gravity at all scales• Standard model of particle physics

Blackboard

vexpansion = D ⇥H0;H0 = (67.4± 0.5) km s�1<latexit sha1_base64="l738QN3boNXR5haBcU4Uaud9uE4=">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</latexit><latexit sha1_base64="l738QN3boNXR5haBcU4Uaud9uE4=">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</latexit><latexit sha1_base64="l738QN3boNXR5haBcU4Uaud9uE4=">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</latexit><latexit sha1_base64="l738QN3boNXR5haBcU4Uaud9uE4=">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</latexit>

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Adiabatic expansion

so the Universe was indeed hot very early onz ⌘ �� �0

�0, T = TCMB

⇣a0a

⌘= 2.73K ⇥ (1 + z)

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General relativity

H2 =

✓a

a

◆=

8⇡

3G⇢+

⇤

3� kc

2

a2=

8⇡

3G

⇣%baryon

a3+

%rad

a4

⌘+

⇤

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Big Bang Nucleosynthesis

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E / 1/� / 1/a<latexit sha1_base64="VXXp/NrtYpxVKKmWobAM3FdbcJI=">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</latexit><latexit sha1_base64="VXXp/NrtYpxVKKmWobAM3FdbcJI=">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</latexit><latexit sha1_base64="VXXp/NrtYpxVKKmWobAM3FdbcJI=">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</latexit><latexit sha1_base64="VXXp/NrtYpxVKKmWobAM3FdbcJI=">AAAE1XicxVRbTxNBFF5oVVxvoI++TCRN2lDLbotAYkhQMDZRCZgCjZ12c7qdtpPuzdnZhrKZB43x1f/mm7/BP+HZ3RYE+uSLk0zmzHcu33fOXrqBw0NpGL8WFnP5W7fvLN3V791/8PDR8srjk9CPhM2Obd/xRbMLIXO4x44llw5rBoKB23XYaXe0l/hPx0yE3PcachKwtgsDj/e5DRIha2Xxd6HeqZIdQh3Wl0XaF2DHtOfLGJTCTQUfDGUpCUhd2zTgKq4p8vZKwhiEGPpWTIVLuiAmvpdkd2pqjcyJENBL3RuKzOpfxL1H7T1IKPR/VoZE8wqS51NsZHeqCX9V/Y++5sjQC8KKm4SCEwwhEXVgNXFndxwAeAOHERrygQtkjMVTQC8cFF+VP5VoIPxA+oSys6AVH6XY+qih2nohlbWviukZqDIdgOtCqVNLgTpD5nGmHXPBS16ThH6fSu6ykNSt2FAvswPh4uZWZYMGLjEqL0q0nOaNXFoOO/FzU2Gtc9TwOeLjWdNO2nTScGZZhoovzTJpYNFGxr/34bXKRj9NToMvHvNOtbJVo+V3mbCiuXZe0t/MGjfXZ0yXCBAcz8UdUGFNWcurRsVIF7lpmFNjVZuuQ2v5J75wduQyT9oOhGHLNALZjkFIbjs4PBqFLAB7BAPWQtMD1NaO069SkQIiPdL3BW5PkhT9OyMGNwwnbhcjXZDD8LovAef5WpHsb7dj7gWRZJ6dEfUjh2CfySdOelwwWzoTNMAWHLUSewg4U4k/Ah2HYF5v+aZxUq2YRsU82ljd3ZyOY0l7qj3TipqpbWm7Wl071I41O/cxd5b7kvuaP82r/Lf89yx0cWGa80S7svI//gCP65M+</latexit>

See WS 2009/10 lecture notes by Peter Schneider for details

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XXXa ! 0

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so at very early epochs, radiation completely dominates; no need to worry about dark matter/energy

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This scaling of temperature with cosmic time is very important for nucleosynthesis. It means that the early Universe was a “defect” reactor; reaction rates compete with the expansion rateA more exact relation will be derived later

Blackboard

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Thermal history of the Universe (backwards)

The energy of relativistic particles (photons, neutrinos, electrons, positrons, etc increased as we move back in cosmic time

scal

e fa

ctor

cosmic time

Tem

pera

ture

Today, T~3K

T~3000 K (eV)

All atoms ionisedCMB origin

First stars/galaxies

kT >MeV

photon energycomparable to nuclear binding energy10 MeV

All reactions in equilibrium

baryon to photon ratio, η

The primordial composition influences nucleosynthesis, so it’s important to know the number of (anti)baryons and the number of relativistic particles (photons, neutrinos). How many of each are present?

All particles+anti-particles are in equilibrium. Some examples:T > 1013 K<latexit sha1_base64="A75VbvA0tbRLK2zx007swvTfR9I=">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</latexit><latexit sha1_base64="A75VbvA0tbRLK2zx007swvTfR9I=">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</latexit><latexit sha1_base64="A75VbvA0tbRLK2zx007swvTfR9I=">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</latexit><latexit sha1_base64="A75VbvA0tbRLK2zx007swvTfR9I=">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</latexit>

e�e+ $ 2�;xx $ 2�; ⌫⌫ $ 2�;n+ ⌫ $ p+ e�; p+ ⌫ $ n+ e+<latexit sha1_base64="vohAVZd9ZeYxp6MaifpgrNKqURw=">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</latexit><latexit sha1_base64="vohAVZd9ZeYxp6MaifpgrNKqURw=">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</latexit><latexit sha1_base64="vohAVZd9ZeYxp6MaifpgrNKqURw=">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</latexit><latexit sha1_base64="vohAVZd9ZeYxp6MaifpgrNKqURw=">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</latexit>

Roughly equal number of baryons and photons: ⌘ ⌘ nb

np' 1

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At lower temperatures photons are no longer energetic enough to create (anti)baryons. For equal number of particles and anti-particles, this would soon lead to η=0. Obviously, this is not the case, which means that the number of particles was slightly larger (at least in this part of the Universe). Still η << 1

neutrinos no longer in equilibrium with e-e+

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transferred to photons

Conclusion: shortly after the big bang (and before the onset of nucleosynthesis η became very small. Since this quantity is conserved it remains small (of order 1e-10) to the present day.η can be measured directly (exercise 3.3), but for now we shall treat it as a free parameter

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proton to neutron ratio

Initially, neutrons and protons are in statistical equilibrium

Figure from Bertulani et al. (2016) Prog. Part. Nucl. Phys., 89, 56-100

n / e(�938.2MeV/kT ); p / e(�939.5MeV/kT ) ! p / e(�938.2MeV/kT ) ⇥ e(�1.3MeV/kT )<latexit sha1_base64="a4Wqz3YbAmhfRXEnJzYVCXsH3Ro=">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</latexit><latexit sha1_base64="a4Wqz3YbAmhfRXEnJzYVCXsH3Ro=">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</latexit><latexit sha1_base64="a4Wqz3YbAmhfRXEnJzYVCXsH3Ro=">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</latexit><latexit sha1_base64="a4Wqz3YbAmhfRXEnJzYVCXsH3Ro=">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</latexit>

The first reaction that happens is which is only possible due to the high abundance of neutrons. Even though the binding energy of D is ~2.2 MeV the reaction starts around 1MeV, due to the high number of energetic photons at the tail of the thermal distribution

nucleosynthesis beginsNow we know the initial conditions (temperature vs time, η, n/p) for this very special environment. Together with a nuclear reaction network we can thus calculate the evolution of nuclear abundances

Figure from Pitrou et al. (2018), Physical Reports, 04, 005

D b

indi

ng e

nerg

yn+ p ! D + �

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Eventually almost all neutrons end up in Helium nuclei

Out of 100 nuclei:

88 protons and 12 neutrons76 protons and 12 Deuterium

76 protons and 6 Helium

or by mass: 24% Helium

Y = 2Xn = 2n/p

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so even without detailed calculations one sees that BBN can reproduce the observed He abundance, which mostly depends on n/p at the onset of D burning

detailed BBN predictionsDetailed nuclear reaction network + plasma properties coupled in a numerical code

Figures from Pitrou et al. (2018), Physical Reports, 04, 005

detailed BBN predictions

Final abundances determined by competition between the expansion rate H and the rates of the nuclear reactions involved

Figures from Pitrou et al. (2018), Physical Reports, 04, 005

Most relevant reactions involve a strong interaction. The cross-sections of weak and EM reactions are too small, i.e. the timescales are large (especially for weak interactions which are completely negligible in BBN

D+ p ! 3He + �

D+D ! 3He + n

D+D ! 3H+ p

3He + n ! 3

H+ p3He +D ! 4

He + p3H+D ! 4

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Helium

3He +

4He !7

Be + �3H+

4He !7

Li + �7Be + n !7

Li + p7Li + p ! 2

4He

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Lithium

There are no stable isotopes with mass number 5 (rates of proton and neutron captures on 4He are far too slow), which halts the production of heavier nuclei. At the same time, temperature drops and all nuclear reactions stop

Variations of standard BBNη as a free parameter

4He

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3He

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D<latexit sha1_base64="5W/ek27IP/0xR6F+WDhtG4xO3+w=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKeyKoHgK6MFjBBMDyRJmJ7PJkHmsM7NCWPITXjwo4tXf8ebfOJvsQRMLGoqqbrq7ooQzY33/2yutrK6tb5Q3K1vbO7t71f2DtlGpJrRFFFe6E2FDOZO0ZZnltJNoikXE6UM0vs79hyeqDVPy3k4SGgo8lCxmBFsndbKeFuhmWulXa37dnwEtk6AgNSjQ7Fe/egNFUkGlJRwb0w38xIYZ1pYRTqeVXmpogskYD2nXUYkFNWE2u3eKTpwyQLHSrqRFM/X3RIaFMRMRuU6B7cgsern4n9dNbXwZZkwmqaWSzBfFKUdWofx5NGCaEssnjmCimbsVkRHWmFgXUR5CsPjyMmmf1QO/Htyd1xpXRRxlOIJjOIUALqABt9CEFhDg8Ayv8OY9ei/eu/cxby15xcwh/IH3+QM3fo9j</latexit><latexit sha1_base64="5W/ek27IP/0xR6F+WDhtG4xO3+w=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKeyKoHgK6MFjBBMDyRJmJ7PJkHmsM7NCWPITXjwo4tXf8ebfOJvsQRMLGoqqbrq7ooQzY33/2yutrK6tb5Q3K1vbO7t71f2DtlGpJrRFFFe6E2FDOZO0ZZnltJNoikXE6UM0vs79hyeqDVPy3k4SGgo8lCxmBFsndbKeFuhmWulXa37dnwEtk6AgNSjQ7Fe/egNFUkGlJRwb0w38xIYZ1pYRTqeVXmpogskYD2nXUYkFNWE2u3eKTpwyQLHSrqRFM/X3RIaFMRMRuU6B7cgsern4n9dNbXwZZkwmqaWSzBfFKUdWofx5NGCaEssnjmCimbsVkRHWmFgXUR5CsPjyMmmf1QO/Htyd1xpXRRxlOIJjOIUALqABt9CEFhDg8Ayv8OY9ei/eu/cxby15xcwh/IH3+QM3fo9j</latexit><latexit sha1_base64="5W/ek27IP/0xR6F+WDhtG4xO3+w=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKeyKoHgK6MFjBBMDyRJmJ7PJkHmsM7NCWPITXjwo4tXf8ebfOJvsQRMLGoqqbrq7ooQzY33/2yutrK6tb5Q3K1vbO7t71f2DtlGpJrRFFFe6E2FDOZO0ZZnltJNoikXE6UM0vs79hyeqDVPy3k4SGgo8lCxmBFsndbKeFuhmWulXa37dnwEtk6AgNSjQ7Fe/egNFUkGlJRwb0w38xIYZ1pYRTqeVXmpogskYD2nXUYkFNWE2u3eKTpwyQLHSrqRFM/X3RIaFMRMRuU6B7cgsern4n9dNbXwZZkwmqaWSzBfFKUdWofx5NGCaEssnjmCimbsVkRHWmFgXUR5CsPjyMmmf1QO/Htyd1xpXRRxlOIJjOIUALqABt9CEFhDg8Ayv8OY9ei/eu/cxby15xcwh/IH3+QM3fo9j</latexit><latexit sha1_base64="5W/ek27IP/0xR6F+WDhtG4xO3+w=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKeyKoHgK6MFjBBMDyRJmJ7PJkHmsM7NCWPITXjwo4tXf8ebfOJvsQRMLGoqqbrq7ooQzY33/2yutrK6tb5Q3K1vbO7t71f2DtlGpJrRFFFe6E2FDOZO0ZZnltJNoikXE6UM0vs79hyeqDVPy3k4SGgo8lCxmBFsndbKeFuhmWulXa37dnwEtk6AgNSjQ7Fe/egNFUkGlJRwb0w38xIYZ1pYRTqeVXmpogskYD2nXUYkFNWE2u3eKTpwyQLHSrqRFM/X3RIaFMRMRuU6B7cgsern4n9dNbXwZZkwmqaWSzBfFKUdWofx5NGCaEssnjmCimbsVkRHWmFgXUR5CsPjyMmmf1QO/Htyd1xpXRRxlOIJjOIUALqABt9CEFhDg8Ayv8OY9ei/eu/cxby15xcwh/IH3+QM3fo9j</latexit>

7Li<latexit sha1_base64="HAnzl25x75eeAY9yVP/yMyxtmYs=">AAAB8nicbVBNS8NAEN3Ur1q/qh69LBbBU0lEqHgqePHgoYL9gDSWzXbTLt3dhN2JUEJ/hhcPinj113jz37hpc9DWBwOP92aYmRcmghtw3W+ntLa+sblV3q7s7O7tH1QPjzomTjVlbRqLWPdCYpjgirWBg2C9RDMiQ8G64eQm97tPTBseqweYJiyQZKR4xCkBK/mPjayvJb7js8qgWnPr7hx4lXgFqaECrUH1qz+MaSqZAiqIMb7nJhBkRAOngs0q/dSwhNAJGTHfUkUkM0E2P3mGz6wyxFGsbSnAc/X3REakMVMZ2k5JYGyWvVz8z/NTiK6CjKskBaboYlGUCgwxzv/HQ64ZBTG1hFDN7a2YjokmFGxKeQje8surpHNR99y6d39Za14XcZTRCTpF58hDDdREt6iF2oiiGD2jV/TmgPPivDsfi9aSU8wcoz9wPn8APC+Qhw==</latexit><latexit sha1_base64="HAnzl25x75eeAY9yVP/yMyxtmYs=">AAAB8nicbVBNS8NAEN3Ur1q/qh69LBbBU0lEqHgqePHgoYL9gDSWzXbTLt3dhN2JUEJ/hhcPinj113jz37hpc9DWBwOP92aYmRcmghtw3W+ntLa+sblV3q7s7O7tH1QPjzomTjVlbRqLWPdCYpjgirWBg2C9RDMiQ8G64eQm97tPTBseqweYJiyQZKR4xCkBK/mPjayvJb7js8qgWnPr7hx4lXgFqaECrUH1qz+MaSqZAiqIMb7nJhBkRAOngs0q/dSwhNAJGTHfUkUkM0E2P3mGz6wyxFGsbSnAc/X3REakMVMZ2k5JYGyWvVz8z/NTiK6CjKskBaboYlGUCgwxzv/HQ64ZBTG1hFDN7a2YjokmFGxKeQje8surpHNR99y6d39Za14XcZTRCTpF58hDDdREt6iF2oiiGD2jV/TmgPPivDsfi9aSU8wcoz9wPn8APC+Qhw==</latexit><latexit sha1_base64="HAnzl25x75eeAY9yVP/yMyxtmYs=">AAAB8nicbVBNS8NAEN3Ur1q/qh69LBbBU0lEqHgqePHgoYL9gDSWzXbTLt3dhN2JUEJ/hhcPinj113jz37hpc9DWBwOP92aYmRcmghtw3W+ntLa+sblV3q7s7O7tH1QPjzomTjVlbRqLWPdCYpjgirWBg2C9RDMiQ8G64eQm97tPTBseqweYJiyQZKR4xCkBK/mPjayvJb7js8qgWnPr7hx4lXgFqaECrUH1qz+MaSqZAiqIMb7nJhBkRAOngs0q/dSwhNAJGTHfUkUkM0E2P3mGz6wyxFGsbSnAc/X3REakMVMZ2k5JYGyWvVz8z/NTiK6CjKskBaboYlGUCgwxzv/HQ64ZBTG1hFDN7a2YjokmFGxKeQje8surpHNR99y6d39Za14XcZTRCTpF58hDDdREt6iF2oiiGD2jV/TmgPPivDsfi9aSU8wcoz9wPn8APC+Qhw==</latexit><latexit sha1_base64="HAnzl25x75eeAY9yVP/yMyxtmYs=">AAAB8nicbVBNS8NAEN3Ur1q/qh69LBbBU0lEqHgqePHgoYL9gDSWzXbTLt3dhN2JUEJ/hhcPinj113jz37hpc9DWBwOP92aYmRcmghtw3W+ntLa+sblV3q7s7O7tH1QPjzomTjVlbRqLWPdCYpjgirWBg2C9RDMiQ8G64eQm97tPTBseqweYJiyQZKR4xCkBK/mPjayvJb7js8qgWnPr7hx4lXgFqaECrUH1qz+MaSqZAiqIMb7nJhBkRAOngs0q/dSwhNAJGTHfUkUkM0E2P3mGz6wyxFGsbSnAc/X3REakMVMZ2k5JYGyWvVz8z/NTiK6CjKskBaboYlGUCgwxzv/HQ64ZBTG1hFDN7a2YjokmFGxKeQje8surpHNR99y6d39Za14XcZTRCTpF58hDDdREt6iF2oiiGD2jV/TmgPPivDsfi9aSU8wcoz9wPn8APC+Qhw==</latexit>

Figure from Pitrou et al. (2018), Physical Reports, 04, 005

Helium abundances not very sensitive to η (almost all neutrons end up in helium nuclei anyways…)Excellent agreement with observations

Yp = 0.2449± 0.0040<latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit><latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit><latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit><latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit>

numbers from Cyburt et al. 2015

(D/H)p = (2.53± 0.04)⇥ 10�5<latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">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</latexit><latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">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</latexit><latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">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</latexit><latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">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</latexit>

With increasing η, deuterium can more easily be converted to helium, so its residual abundance decreases. This sensitivity and the fact that D is not produced in stars, makes it an excellent “baryometer”. Again, there is perfect agreement with observations for the value of η derived by Planck

Helium 3 is far more difficult to measure since its abundance is low and it is also created in stars

Lithium increases at low η (less protons around to destroy it), but also at high η (more beryllium produced which later decays to lithium)

The Universe has a lithium problem! 2-4 times less lithium than predicted

Observational constraints on BBNTo understand why there is a problem for Li while predictions for other elements seem to be OK, it is important to get precise observational constraints

HeliumMost stars (except at very high T) have no helium absorption lines in optical wavelengths (why?)

Sun abundance constrained by chromospheric emission

Pierre Janssen (1868)

Constraints mostly from emission lines in low-metallicity nebulae and galaxies.Indirect constraints also come from its influence on stellar structure (e.g. asteroseismology, GC populations, etc)

Figure from Izotov & Thuan (2004a) ApJ, 602, 230

Yp = 0.2449± 0.0040<latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit><latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit><latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit><latexit sha1_base64="AptOuH6aVYp+J0p1tjclBi33h44=">AAACEnicbZDLSsNAFIYnXmu8RV26GSwF3ZSkBKsLoeDGhYsK9iJNLJPppB06k4SZiVBCn8GNr+LGhSJuXbnzbZy0XWjrDwMf/zmHM+cPEkalsu1vY2l5ZXVtvbBhbm5t7+xae/tNGacCkwaOWSzaAZKE0Yg0FFWMtBNBEA8YaQXDy7zeeiBC0ji6VaOE+Bz1IxpSjJS2utZJ6b6aeYLDazo277oTTMbwAtrliuueQy/hGm3btbtWMYdccBGcGRTBTPWu9eX1YpxyEinMkJQdx06UnyGhKGZkbHqpJAnCQ9QnHY0R4kT62eSkMSxppwfDWOgXKThxf09kiEs54oHu5EgN5HwtN/+rdVIVnvkZjZJUkQhPF4UpgyqGeT6wRwXBio00ICyo/ivEAyQQVjpFU4fgzJ+8CM1K2bHLzo1brJ3O4iiAQ3AEjoEDqqAGrkAdNAAGj+AZvII348l4Md6Nj2nrkjGbOQB/ZHz+APbOmck=</latexit>

Observational constraints on BBNDeuteriumAll deuterium must have originated during BBN since it is only destroyed in stars and it is vastly more abundant than lithium which can also result from spallation

Tytler, O’Meara, Suzuki and Lubin (2000)

D/H on earth is greatly enhanced by fractionation,hence, not representative of primordial abundance

Early constraints from solar wind, Moon, planets, gas-rich meteorites and C1 chondrites

(D/H)p = (2.53± 0.04)⇥ 10�5<latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">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</latexit><latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">AAACPXicbZA7T8MwFIUdniW8CowsFlWlMlCcEigMSEgwMDAUifJQUyLHdcHCTiLbQaqi/DEW/gMbGwsDCLGy4rRF4nUlS5/OuVfX9wQxZ0oj9GiNjI6NT0wWpuzpmdm5+eLC4qmKEklok0Q8kucBVpSzkDY105yex5JiEXB6Ftzs5/7ZLZWKReGJ7sW0LfBVyLqMYG0kv3hSvqynnhTwiGV2+cLvc5zBXYiqNdfdgV4sDCLkIrtysH646qd9t1Krbm58me6qp5mgCjroMl3bzPxiKR/JC/4FZwglMKyGX3zwOhFJBA014ViploNi3U6x1IxwmtleomiMyQ2+oi2DITbL2mn/+gyWjdKB3UiaF2rYV79PpFgo1ROB6RRYX6vfXi7+57US3d1upyyME01DMljUTTjUEcyjhB0mKdG8ZwATycxfIbnGEhNtArdNCM7vk//Caa3qoKpz7Jb2toZxFMAyWAEV4IA62AOHoAGagIA78ARewKt1bz1bb9b7oHXEGs4sgR9lfXwCju2nAQ==</latexit><latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">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</latexit><latexit sha1_base64="+itKQ2NYWR9byl7HVovR2G0BgJY=">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</latexit>

UV

At radio wavelengths: Transitions in DCN, DCH+, DI hyperfine structure

HD and DI transitions in the ISM

With the advent of 10-m class mirrors, more directconstraints using the isotopic blue shift (87 km/s!) relative to H

both in the ISM and in stars

Observational constraints on BBNHelium-3Extremely difficult to constrain primordial abundance for several reasons

Figures from Rood et al (1993), Baina et al. (2002), Nature, 415, 54-57

Abundance lower than D, no absorption lines (similar to 4), atomic lines almost identical to Helium-4, also created and destroyed in stars

At radio wavelengths: 3He+ hyperfine transition at 3.46cm in “unevolved” objects (i.e. H II regions) but challenging due to background noise and competing emission mechanisms which require careful modelling

Observational constraints on BBNLithium-7

Measurement of lithium in stars of different metallicities; extrapolated to Z = 0

Figures from Rood et al (1993), Baina et al. (2002), Nature, 415, 54-57

In meteorites, most is in the form of Lithium-7 (92.5%)

In low-mass stars (including the Sun) with convective envelopes, lithium is depleted from the surface and destroyed. Abundance on the Sun is ~150 lower than “standard” theory predictsNevertheless, at low metallicities, all stars seem to have the same abundance, with very small scatter

Spite plateau

The observed abundances are 2-4 times lower than standard BBN predictions

What is causing the lithium problem? Unknown

Could be either due to observations, astrophysical variables (e.g. meridi), or new physics (unknown resonances). Exotic BBN is unlikely, as it is hard to change the Lithium abundance only

Some recent results

SMC constraints on 7Li are closer to BBN predictionsHowk et al. (2012), Nature, 489, 7414

Cross section of 7Be(n,α)4He, even lower than expected!

Barbagallo et al. (2016) PRL, 117, 15

BBN as a probe of cosmology and fundamental physics

Q: Why do we care about ultra-precise abundance measurements in the first place? A: Because they can probe the conditions of the Universe well before the CMB era

We already discussed treating η as a free parameter

Then, constraints on primordial D/H yield an (independent) constraint on η, and through that, on the baryon density Ωm (exercise 3.3)

BBN predicts an extremely small baryon density (the very reason it was dismissed in the 50s…), which is consistent with the CMB constraints

What else?

⌘D = 2.73⇥ 10�8⌦bh2 ) ⌦bh

2 = 0.0222± 0.0003<latexit sha1_base64="SfDBJwe3YEq0wYeG+3xrxybrxpM=">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</latexit><latexit sha1_base64="SfDBJwe3YEq0wYeG+3xrxybrxpM=">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</latexit><latexit sha1_base64="SfDBJwe3YEq0wYeG+3xrxybrxpM=">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</latexit><latexit sha1_base64="SfDBJwe3YEq0wYeG+3xrxybrxpM=">AAACy3icbVFdb9MwFHXC1wgfK/DIyxVVpe6B4GTZOh6QJrGHPoAYiG5DdRs5rttai5NgO4wS8sgf5I1XfglO26HRcSVLR+fce3zsmxSp0AbjX4574+at23e27nr37j94uN169PhE56VifMDyNFdnCdU8FRkfGGFSflYoTmWS8tPk/HWjn37hSos8+2gWBR9JOsvEVDBqLBW3fnfGvYooCW9E7XU+xUtc1PAKsB9G0UsghbQQ4wh7ne7Ri/5OXC3lbujv7V6q0Q4xQnINAR5Xz/esE+GGxlWAayDaKp9h3w+AKDGbG6pUfgHkneQzeqlaD281ctSYh37Pel+xPKhX/XEC83EI5MOmUVwldaM0uXEYhn9z49241V4CW3AdBGvQRus6jls/ySRnpeSZYSnVehjgwowqqoxgKa89UmpeUHZOZ3xoYUZtzFG13EUNHctMYJorezIDS/bqREWl1guZ2E5JzVxvag35P21YmunBqBJZURqesdVF0zIFk0OzWJgIxZlJFxZQpoTNCmxOFWXGrt+znxBsPvk6OAn9APvB+6h9uL/+ji30FD1DXRSgHjpEfXSMBog5fSdzLpyv7ltXu9/c76tW11nPPEH/lPvjD+5t0Gs=</latexit>

We can also treat the number of neutrino families as a free parameter

%rad = %� + %e± +N⌫%⌫ := (g?/2)%� ) T =

✓3c2

16⇡g?aG

◆t�1/2

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This affects the energy density vs T and therefore the expansion rate vs time, the freeze out value of n/p and the temperature Tp at which it occurs —> Helium abundance affected

BBN as a probe of cosmology and fundamental physics

Cyburt et al. 2015

Joint constraints on η, Nv

The physics describing the Universe at MeV scales are consistent with the physics at eV scales

The expansion rate varies with , while for n-p reactions equilibrium is

broken at ~0.8 MeV,

⇢1/2 /✓11

4+

7

8N⌫

◆1/2

T 2

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e�1.29MeV/0.8MeV ' 0.2<latexit sha1_base64="yvaYG4m24RTmsChKIXKeT+Giuw8=">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</latexit><latexit sha1_base64="yvaYG4m24RTmsChKIXKeT+Giuw8=">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</latexit><latexit sha1_base64="yvaYG4m24RTmsChKIXKeT+Giuw8=">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</latexit><latexit sha1_base64="yvaYG4m24RTmsChKIXKeT+Giuw8=">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</latexit>

The precise value of the critical temperature Td for decoupling, scales as T 2d / ⌧1/2

✓11

4+

7

8N⌫

◆1/2

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Other possibilities

Deviations from GR affecting the expansion rate, weak interaction physics (affecting initial abundances), neutron lifetime, alternative reaction rates….

BBN as a probe of cosmology and fundamental physics

Neutron decay

Thus far, the measured mean lifetime of neutrons seems to depend on the measurement method. Could be due to new physics! What is the effect on BBN?

Can we the Universe before the onset BBN?

An interesting recent result

First (indirect) detection of the cosmic neutrino background!

Summary

Take Home Message

1. Big bang nucleosynthesis predicts the abundances of light isotopes extremely accurately, over 9 orders of magnitude

2. Lithium abundance remains challenging3. Inference of primordial abundances from observations is challenging4. BBN probes the very early Universe, well before the CMB was emitted 5. As precision in measurements increases, we will be able to constrain physics

beyond the standard model and GR with increasing precision

Coming up

Hydrogen burning in (and on) stars (spoiler: quite different than BBN)