Lecture - The Early Universe

The Early Universe In the first 3 minutes of the universe, it was full of energetic gamma rays. When the temperature of the radiation field is high enough, the gamma-rays will annihilate and produce particles and antiparticles Proton-antiproton pairs can be produced when the energy of the background radiation field is high enough:   

kT > mpc2 or T >> 1013 K This is the case during the first 10-4 seconds! After that the universe cooled, and most of the protons and antiprotons annihilated to produce a pair of gamma rays

But wait, we’re here! For some (unknown) reason, there were slightly more protons than antiprotons in the early universe. 109 + 1 protons for every 109 antiprotons. This means there was matter left over to create galaxies (and stars, and planets, and us!) The photons from this annihilation are what we see in the cosmic microwave background.

The Early Universe Note that the early universe is radiation dominated. The energy density of photons decreases as R-4 while the energy density of matter decreases as R-3 where R is the scale factor. This is because the photon’s energy is decreasing due to the redshifting by an extra factor of 1/R (alternatively the temperature is dropping.) This means the expansion rate of the early universe is different, R ~ t1/2 As the expansion proceeds the matter density drops more slowly than the radiation density, eventually the universe becomes matter dominated. This happens when the universe cools to 4000K at about 10,000 years. When the universe is radiation dominated, any density perturbations didn’t grow. Between matter-radiation equality and recombination (T=380,000 years), only perturbations in non-baryonic dark matter grow. Baryonic matter interacts with photons and is supported against collapse. After recombination, baryonic matter can also fall into the dark matter potential wells. This extra growth in density perturbations for non-baryonic dark matter means a lower initial density perturbation is needed to produce the structure we see today.

Time

Temperature

What’s Happening?

t<10-10s

T>1015K

???

10-10
1015>T>1012K

Free electrons, quarks, photons, neutrinos, strong interactions

10-4
1012>T>1010K

Free electrons, protons, neutrons, photons, neutrinos, strong interactions

1
1010>T>10000K Nucleosynthesis begins --

1012
10000K>T>300 0K 3000K>T>3K

1013s
atomic nuclei, free electrons, photons, neutrinos

Universe becomes matter dominated Atoms formed from nuclei and free electrons, CMB

Timeline (in temperature units) of symmetry breaking in the early universe

Density versus Time

17,000 years old 100,000 Kelvin

13 billion years old 3 Kelvin

Time [Gyr]

Density [logarithmic]

Temperature [Kelvin]

Temperature versus Time

17,000 years old 10 trillion atoms per m3

13 billion years old 0.1 atoms per m3

Time [Gyr]

The Early Universe Electrons are 2000 times less massive than protons, with restenergies of 0.5 MeV. So the radiation still produces pairs of electrons and positrons (antielectrons), they can annihilate to produce electron neutrinos (νe and antineutrinos νe). Similarly neutrons and protons were being created and destroyed. Pair production also occurs.    

e- + e+ ←→ νe + νe e- + p ←→ n + νe , νe + p ←→ n + e+ n ←→ p + e- + νe e- + e+ ←→ γ + γ

This occurs until the temperature drops to T~1010 K, t ~ 1 sec In equilibrium there will slightly more protons than neutrons since the neutron mass is slightly (1.293 MeV) larger

The Early Universe We can calculate the equilibrium ratio of neutrons to protons via the Boltzmann equation,  

n/p = exp{-(mp – mn)c2/kT} At T~ 1012 K, n/p = 0.985

Neutrinos are only weakly interacting particles, we need a high density of neutrinos for them to interact with neutrons and protons and keep them in equilibrium. By the time the universe has cooled to T~1010 K, the density is low enough that neutrinos are highly unlikely to interact with protons or neutrons. At the same time, the energy level drops below the electron-positron pair production energy level, so no new neutrinos are produced. Thus the n/p ratio is “frozen” at the value it had at T= 1010 K , n/p = 0.223. For every 1000 protons, there are 223 neutrons.

The Early Universe Neutrons by themselves (not in atomic nuclei) are unstable to beta decay   

n → p + e- + νe The exponential decay time for this is 886 seconds. This decay destroys about 25% of the neutrons, before we can the neutrons can combine with the protons.

When the temperature has dropped to 109 K (t=230s), neutrons can combine with protons to form deuterium. (Recall that deuterium is “heavy hydrogen” with a nucleus containing both a neutron and a proton.)  

n+p →D+γ At this point n/p has dropped to ~0.14, so there are 140 neutrons for every 1000 protons. The excess protons (which are converted become the nuclei of hydrogen atoms) account for about 75% of the total mass.

Big Bang Nucleosynthesis Once we have deuterium, and the universe has cooled a bit (T<109 K), we are ready to create some slightly heavier elements (helium)     

D + D → 3H + 1H 3H + D → 4He + n D + D → 3He + n 3He + D → 4He + 1H These are not the same reactions as in stars (the pp chain)!

All of the neutrons are converted into helium. This means that the we will end up with 140/2 = 70 He nuclei for every 1000 protons. 140 of those protons will end up in He, the rest (860) are left to form the nuclei of Hydrogen atoms. So the mass fraction of helium (Y) in the early universe is:  

Y = 4(70)/[860+4(70)] =25% This is very close to observed primordial helium abundance of 2224% which is one of confirmations of the Big Bang model!

Big Bang Nucleosynthesis Because all the neutrons are tied up in helium, the abundance of helium is insensitive to the matter density of the universe. In contrast, the other elements produces in the early universe, D, 3He, and 7Li are dependent on the amount of baryonic matter in the universe. (We also see some beryllium.)  



 

4He

+ 3H ←→ 7Li + γ These elements are much less abundant than helium. The universe expanded to rapidly to build up heavier elements. Note that there are no stable mass-5 nuclides, and combining helium and tritium to get lithium requires overcoming coulomb repulsion. So almost all of the neutrons end up in helium instead. There is another gap at mass-8, so BBN ends with lithium! At t~1000s (20 minutes), BBN ends when the temperature drops below 3 x 108 K and the density becomes too low for fusion. There is another “freeze-out”, as no new nuclei are created and none are destroyed. From then until recombination (T=3000K, t=380,000 years) nothing much happens (yawn!).

Stable mass gaps in the periodic table

9Be

7Li 6Li

4He 3He 2H

No stable nuclei

1H

The lack of stable elements with masses 5 and 8 make it more difficult for cosmic nucleosynthesis to progress beyond Lithium and even Helium.

1%

Mass fraction of nuclei vs time (and temperature)

Big Bang Nucleosynthesis The BBN model makes detailed predictions of the abundances of light elements These are generally given as a function of η which is baryon to photon ratio, nn/nγ. This number is pretty small, so we usually define it in units of 1010. Also it is directly related to Ωb, the baryon density relative to the critical density of the universe. Thus, η10 = 1010(nn/nγ) = 274 Ωbh2 As the universe evolves this ratio is preserved, so that what we observe today should reflect the conditions in the early universe. If we can observe PRIMORDIAL abundances of these elements we can:  

Test the big bang model! Measure the baryon density of the universe!

SBBN predicted primordial abundances of D, 3He, 7Li, and the helium mass fraction Y as a function of nucleon abundance

Deuterium Any deuterium that is incorporated into stars is quickly fused into helium and destroyed. But there is also no astrophysical locations where deuterium will be created in large amounts after BBN. Thus, we need to measure deuterium in an area that has undergone very little stellar processing This can be done by measuring deuterium absorption in QSO absorption line systems. The intervening systems are high redshift (and low metallicity). This has been done for ~6 QSO absorption line systems. (Requires high resolution spectra from 10m-class telescopes, this is hard!) One also has to separate out H absorption from D absorption and account for any velocity effects. There is a lot of dispersion in the results, D/H = (2.6 +/- 0.4) x 10-5

Measuring D/H in QSO absorption lines

Tytler & Burles

Deuterium abundance (D/H) vs metallicity (X where X is generally Si) from QSO absorption line systems

Helium-3 Interstellar 3He that is incorporated into stars is burned to 4He in the hot stellar interiors, but preserved in cooler, outer stellar layers. 3He is also created in hydrogen fusion in low-mass stars. Unclear how much of this is returned into the interstellar medium versus being consumed in post-main sequence evolution. Thus any determination of primordial 3He abundance is model dependent. Can be used to provide a consistency check on other measurements. Singly ionized 3He has been observed in emission in a handful of Galactic HII regions, 3He/H = (1.1 +/- 0.2) x 10-5

Helium-4 4He

is the second most abundant element in the universe. It is created in main sequence stars raising its abundance over its primordial value. We need to observe 4He from recombination lines in extremely low-metallicity regions. These conditions can be found in extragalactic HII regions in low-metallicity galaxies. Expect a plateau in helium abundance. We have measured Y (helium mass fraction) in galaxies ranging from ~1/2 to 1/40 solar. We can either measure the bound from the lowest metallicity measurement OR extrapolate the trend to zero metallicity. Note there are statistical uncertainties in these measurements related to corrections for collisional excitation of neutral helium, assumed temperature and ionization, temperature fluctuations, etc. Find Y = 0.234 +/- 0.003, 0.244 +/- 0.002, OR the compromise mean with the larger error bar: 0.238 +/- 0.005.

Helium mass fraction Y vs O/H for low-metallicity extragalactic HII regions

Helium mass fraction Y vs O/H for low-metallicity extragalactic HII regions. Same data, different interpretation!

Lithium-7 7Li

is fragile, it burns in stars at a relatively low temperature. Thus the majority of any interstellar 7Li is cycled through stars and destroyed. However it is also difficult for stars to create new 7Li or to return any newly synthesized 7Li to the ISM before it is destroyed by nuclear burning. We expect a plateau in 7Li in low metallicity environments. 7Li is observed in absorption in the atmospheres of cool, metalpoor, Population II halo stars. There are uncertainties due to not only observational uncertainties, but model dependencies in stellar atmospheres. Find [Li] = 12 + log(Li/H) = 2.2 +/- 0.1, but values have been quoted from 2.1 to 2.4…

1012 (Li/H)

Compilation of Lithium abundance data vs. [Fe/H] from stellar observations.

What does it mean? We can use the observed deuterium abundance to fix the photon/baryon ratio. This gives η10 = 6.1 +/- 0.7 which corresponds to Ωbh2 = 0.022 +/- 0.003. This is in AMAZING agreement with the WMAP estimate of Ωbh2 = 0.0223 +/- 0.0009. Big bang nucleosynthesis works!! To first order, this baryon density is consistent with the observed abundances of 3He, 4He, and 7Li. But there are some discrepancies with 4He and 7Li. BBN prediction for 3He fraction is (1.0 +/- 0.1) x 10-5, measurement is (1.1 +/- 0.1) x 10-5. This is good. BBN prediction for Y (4He mass fraction) is 0.248 +/- 0.001. It is tightly constrained. But the measurement is 0.238 +/- 0.005. This is bad … BBN prediction for 7Li is [Li] = 2.65 +/- 0.11. The observation is [Li] = 2.2 +/- 0.1. This is also bad …

SBBN predicted primordial abundances of D, 3He, 7Li, and the helium mass fraction Y vs. baryon density

SBBN predicted primordial mass fraction of 4He (Y) vs. D/H. Point is measurement of primoridal abundances

SBBN predicted primordial Li/H vs. D/H. Points are measurements of primoridal abundances

What does it mean? Can we save BBN? Maybe this is a sign of new physics – 

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 

Y is dependent on the expansion rate. If the universe expands slower, the predicted Y will go down. WMAP data also are sensitive to early universe expansion rate and agree with BBN, but data are still consistent with standard BBN. What would cause this is a mystery … Another possibility is neutrino asymmetry, (number of electron neutrinos to electron antineutrinos) which regulates the pre-BBN neutron/proton ratio. Again data are not inconsistent with symmetry but skew towards slightly more neutrinos than antineutrinos. This would be due to a non-zero chemical potential for neutrino-antineutrino annihilation.

Note that neither of these solves the lithium discrepancy! This may be due a poor understanding of the evolution of very old, metal-poor halo stars. Perhaps lithium is being depleted in the surfaces of these stars.

SBBN predicted primordial mass fraction of 4He (Y) vs. D/H plus predictions of faster and slower early universe expansion rates. Point is measurement of primordial abundances.