Physical Cosmology 27/4/2017

Physical Cosmology 27/4/2017

Alessandro Melchiorri

alessandro.melchiorri@roma1.infn.it slides can be found here:

oberon.roma1.infn.it/alessandro/cosmo2016

T. Padmanabhan, structure formation in the universe Most of the discussion on BBN in current lectures

can be found here:

T>0.1 MeV Protons and

Neutrons are unbounded

T <0.1 MeV Protons and neutrons

are bounded to form light elements nuclei 4He, 3He, D, Li7

BBN at equilibrium

The photon/baryon appears here, to

the power of A-1 !

It is not enough to have B^A>T

to have X^A of order one !

We need to go to much lower temperatures ! This term is VERY

small !

BBN at equilibrium

We have X^A of order one at a temperature:

this number is 3 for Helium 4

This number is about 22 This number is of order 10 Element

Binding

Energy T^A at which X^A is of order 1

Much much lower !!!!

BBN at equilibrium

Why we have this ?

We have many more CMB photons than baryons !

Photons are distributed as a blackbody at temperature T.

Even at temperatures much lower than the binding energy, we have in the tail of the distribution many photons at energies able to destroy that element !

BBN at equilibrium

This discussion however, while it gives a physical idea of what is going on is NOT correct because BBN happens out of equilibrium !

In particular we have assumed neutrons and protons in equilibrium at the same temperature T.

This is possible thanks to the weak interaction processes:

But neutrinos decouple at T=1 MeV !! these reactions are not working a T =0.1 MeV !

Helium abundance

A rough but uselful aestimate of the final Helium 4 abundance can be obtained also in this case.

Neutrons and protons are in equilibrium thanks to the following reactions:

At equilibrium we have that:

We have then that until equilibrium holds the neutron to proton numer density decreases as:

Helium abundance

The equilibrium will end when the rate of reactions is smaller than the Hubble parameter H(T).

Computing the quantity reaction rate times neutron lifetime this a function just of the temperature.

Reaction rate n to p (it flattens because of beta decay)

Reaction rate p to n

Twice Hubble rate. To be

compared to the sum of the two reaction rates.

T=0.8 MeV

Helium abundance

Assuming for the neutron lifetime a value of 915.4 s, we have a decoupling temperature of T^D=0.8 MeV.

The neutron to proton ratio freezes at T^D=0.7 MeV :

However the beta decay still works and we have a small decrease to n/p also for later times.

From the previous calculation we had that Helium could be produced only for T< 0.28 MeV. However Helium can be produced only if D is available thanks to the reactions:

and D starts to be present only for T < 0.1 MeV…

Helium abundance

Let us assume then that BBN start at T=0.1 MeV.

At this temperature the n/p ratio is reduced thanks to the beta decay (from 1 MeV to 0.1 MeV) by a factor 0.8, to:

BBN

Assuming that at end of BBN all neutrons go to form Helium 4 (this is quite correct) we have for the

Helium mass fraction:

in agreement with the observations of primordial Helium in the Universe ! Stellar nucleosynthesis is unable to

produce such large abundance of Helium !!

Nice and very pedagogical review

BBN: accurate calculations

In order to properly compute the several abundances we need to integrate a system of Boltzmann equations.

There are several numerical codes available to do this.

In Figure we see that Helium abundance starts to be there just after D reaches enough mass fraction.

BBN: numerical calculations

BBN starts only after D is formed.

Mostly of the

neutrons goes to Helium.

Standard BBN

If we assume 3 neutrinos then BBN has just one

free parameter,

the baryon to photon ratio:

i.e. the baryon (atoms) energy density.

Predictions for the elements are in the figure in function of the baryon density.

The width of the lines are due to uncertainties in the rates.

Why we have mostly He4 ?

Helium “peak”.

If we plot nucleon binding energy versus A

we see that Helium has a

“peak”.

i.e. nuclei with larger A (6-7) are less stable.

The nuclei density is small, we don’t have any triple alpha:

Universe is expanding. BBN ends after few minutes.

Standard BBN

As we will see, observations can restrict the range in the baryon density to:

In this range we have the following approximated formulas:

What enters in the computations are several reaction rates.

Some of them are really well measured others are not.

In the estimate of D the largest error

comes from this reaction (6%)

BBN: systematics

BBN: systematics

Taken from Nollett and Holder

http://arxiv.org/pdf 1112.2683.pdf.

Few datapoint and in tension with theoretical expectations.

The LUNA400 experiment under Gran Sasso could measure the reaction rate with the better

accuracy.

BBN: Systematics

The largest systematic we have for the final Helium abundance comes from the measurement of the neutron lifetime !

Particle data group

http://pdg.lbl.gov/2014/listings/rpp2014-list-n.pdf

quotes 1.1 s error, but it comes from measurements that are scattered….

BBN:neutron lifetime

Measuring the neutron lifetime is fundamental in measuring the Fermi constant:

that enters in the weak interactions rate:

that fixes the neutron freeze-out that happens when:

BBN neutron lifetime

Lower neutron lifetime

Higher reaction rate

Freeze out happens later (smaller T) Lower density of neutrons at BBN start

Lower final Helium abundance predicted

Non-standard BBN

There is the possibility of having extra relativistic particles at BBN.

This can be parametrized by

increasing the effective neutrino number.

This increases the radiation content:

We then have larger H at BBN.

The freeze-out happens earlier (larger T).

We have more neutrons at BBN, more helium !

Non-standard BBN

We also have approximate formulas in this case if:

If we define:

We have:

http://parthenope.na.infn.it

http://superiso.in2p3.fr/relic/alterbbn/

Observations of primordial abundance of light elements

BBN theory predicts with high precision the amount of primordial Helium, Deuterium and Lithium.

These predictions depend on the baryon density and on the neutrino effective number.

If we could have a precise measurement of primordial abundances we could infer constraints on these

parameters of the theory.

Stellar nucleosynthesis can produce/destroy primordial abundances, how we can derive the primordial values ?

Observations of primordial Helium

Observations are made by looking at Helium lines in extragalactic HII regions (ionized hydrogen).

Stellar activity is tracked by metallicity, (O/H) for example.

The value of Yp (primordial Helium 4) can be recovered by extrapolating at “low metallicities”.

In practice one expects that going to O/H=0 the

Yp abundance should flattens to the primordial value.

Expectations vs Reality

We don’t see much (any) flattening going

to zero O/H (zero metallicity)

From this dataset (2007) we can derive the constraint:

Systematics in the recovery of Yp

Constraints during the years have improved in

precision but not in accuracy.

There is a large scatter in the measurements.

Systematics are important.

Value obtained from SBBN assuming baryon density

consistent with cosmic microwave background anisotropies.

Recent developments

Constraints on Yp have been improved by observations of the He I λ10830 line that strongly traces the electron

density of the HI region and helps in breaking degeneracies with temperature of the HI region.

Strongest dependence on ne compared

to other lines

Lower dependence on Temperature

Analysis by Izotov, Thuan and Guzeva, 2014

Following this method, observations made by Izotov and Thuan found an higher Helium abundance.

http://arxiv.org/pdf/1408.6953v1.pdf

Analysis by Izotov, Thuan, Guzeva 2014

Assuming BBN e combining with observations

of primordial D (see next slides) IT found a best

fit value for a larger than 3.046

neutrino number !

Aver et al, 2015

http://arxiv.org/pdf/1503.08146v1.pdf extrapolated value

at zero metallicity Flattening is still not really clear…

However, a more recent analysis by Aver at al., has found a lower value, consistent with Neff=3.046

Primordial Deuterium

Deuterium is destroyed by stellar nucleosynthesis.

Best measurements are again, in low metallicity regions.

The best way to probe it is in damped lyman alpha systems.

Primordial Deuterium

At rest, the Lyman-alpha line (transition from level n=1 to n=2 in neutral H)

is at wavelength of 1216 Å.

Along the line of sight we

have many clouds, each of them absorbing the Lyman-alpha at wavelenght (1+z)1216 Å

Quasars light is absorbed by neutral H clouds between us and the quasar.

Primordial Deuterium

At rest, the Lyman-alpha line (transition from level n=1 to n=2 in neutral H)

is at wavelength of 1216 Å.

Along the line of sight we

have many clouds, each of them absorbing the Lyman-alpha at wavelenght (1+z)1216 Å

Primordial Deuterium

Cloud is at z=3.572.

Lyman-alpha absorption is at (1+z)Lya = 5557 Å

It falls in the visible (4000-7000)Å !

We can measure it from earth !

1216Å is on the UV.

It would be absorbed by the atmosphere.

Primordial Deuterium

Cloud is at z=3.572.

Lyman-alpha absorption is at (1+z)Lya = 5557 Å

It falls in the visible (4000-7000)Å !

We can measure it from earth !

1216Å is on the UV.

It would be absorbed by the atmosphere.

Primordial Deuterium

We see here a “damped"

lyman-alpha system large column density N > 2*10^20 /cmˆ2

In these systems is "easier" to isolate the D line from H lines

from other systems and clouds.

In reality this was possible just in about 10 cases.

Primordial Deuterium

We see here a “damped"

lyman-alpha system large column density N > 2*10^20 /cmˆ2

In these systems is "easier" to isolate the D line from H lines

from other systems and clouds.

In reality this was possible just in about 10 cases.

ISM In the Interstellar Medium we measure low values.

Chengalur, Braun e Burton(1997) looking in a

direction opposite to the galactic center :

(^{3.9 ±1.0})^⋅10−5

H = D

Libowich (2000),

Looking towards the galactic center:

(^{1.7 ± 0.3})^⋅10−6

H =

>> D

ISM In the Interstellar Medium we measure low values.

Chengalur, Braun e Burton(1997) looking in a

direction opposite to the galactic center :

Solar System

(^{3.9 ±1.0})^⋅10−5

H = D

Libowich (2000),

Looking towards the galactic center:

(^{1.7 ± 0.3})^⋅10−6

H =

>> D

Jupiter atmosphere (Mahaffy et al. 1998) :

(^{2.6 ± 0.7})^⋅10−5

H = D

Solar wind (Gloecker, 1999) :

(^{1.94 ± 0.36})^⋅10−5

H = D

Primordial Deuterium

Measurements @2007 based on Lyman-alpha.

We see a large scatter.

No clear plateau at small metallicities but values

are higher respect to

“local" measurements.

Measurements in our solar system and

interstella medium.

We can consider them just as lower limit since we had stellar activity.

Primordial Deuterium

The best measurement comes from DLA of Pettini & Cooke

http://arxiv.org/pdf/1205.3785.pdf that gives:

Combined with other measurements we have:

Primordial Deuterium

Once we have a D

measurement we can trace a line on this

plane and considering the intersection with the BBN predictions we

can bound eta and the baryon density.

We get:

Consistency D and He4

When comparing with Helium data

we found consistency with the measurements of Aver et al, 2015

but not with

Izotov et al, 2014 but this assumes standard BBN !

Izotov et al, 2014 Aver et et al, 2015

Consistency D and He4

You can increase

Helium by increasing Neff ! You keep same Yp by

increasing eta and lowering Neff

Deuterium depends also by Neff

You have same D increasing eta and increasing Neff

Consistency D and He4

Using both Helium and D measurements we can constrain both Neff and the baryon density.

Using Cooke and Pettini and Izotov et al., we get:

Constraint from D Pettini and Cooke

Constraint from He4 Izotov 2014

Neff>3.046 ? Systematics

may be present…

Lithium 7

Primordial Lithium is measured on very old

stars with low metallicity in our galaxy or globular clusters.

When we go to lower metallicities we see a plateau….

… but the value is in

complete disagreement with the expectations from standard BBN.

Observed:

Spite Plateau

Again, we plot the Lithium abundance in

function of the metallicity.

At lower metallicities we see a plateau: «Spite

Plateau»

That should indicate The primordial

abundance.

Lithium 7

The values of the baryon

density inferred from D and Li7 are very different if we

assume SBBN !!

The problem of Lithium 7

- In old stars we see a plateau as expected but the Lithium abundance is far lower than expected !

- We don’t see old stars with higher Lithium abundance ! (Lithium desert).

- We see higher Lithium abundance in the small Magellan cloud. But this system has an high metallicity. If we have

depletion of Lithium 7 by stars, why we have more Lithium in stars with higher metallicity ?

- We may have new physics in BBN, but this would alter D abundance. It is difficult to avoid this.

Big Bang Nucleosynthesis

The consequences of BBN are (from D measurements):

Assuming h=0.67 we get:

Since SN-Ia, assuming a flat universe, gives:

About 80% of the matter in the universe should be Non Baryonic !!!