PRODUCTION OF INOS IN THE BIG BANG

Fermi National Accelerator

Laboratory FERMILAB-Conf-85119-A January 1985

PRODUCTION OF INOS IN THE BIG BANG Edward W. Kolb Theoretical Astrophysics National Accelerator Laboratory Batavia, IL 60510 U.S.A.

Fermi

Astronomy and Astrophysics The University of Chicago Chicago, IL 60637 U.S.A.

ABSTRACT The

production

("ino")

is

numbers

to contribute

of

production

I.

produced

dark

in the

in

the

possibility

that

big

bang and is

present

mass density

is

illustrated

with

axions

big

bang

some elementary

overall

matter

the

today

in

particle sufficient

of the Universe several

is

in the The

examples.

and baryons

are covered

of galaxies

reveals

in detail.

INTRODUCTION

component

of

of the the

structure

total not

the

of the

local

larger

vicinity

systems,

clusters

of galaxies,

by Universities

Research

galaxy

in galactic

Only

such as

of the

mass

seems to be present

Operated

particles

to the

of neutrinos,

The study

s

elementary

In particular,

discussed.

form

of

solar

system.

binary

Association

in the

that

halos,

small Universe

Inc. under contract

presence

but

also

in the disk

is also

groups

of

a

Dark matter

is dark.

Dark matter

galaxies,

and perhaps

the

of

as a whole.

present

in in

galaxies, 1.1

with the United States Department

01 Energy

2 It

is not

solution.

It

the

dark

clear

in

baryons,

clusters

be

interest

in the

the

of the

In this in

the

given

paper

big

for

pyrgons

the particles mass the and

if

is

been remarkably In this Universe. of the

big

candidates since will ino

it then

in

in Table

neutrinos

I

and

range

same than

the

dark

clear

whether

jupiters,

etc.

cosmological

of

dark

particle,

matter

or ino,

iS

which

review

I.

I will

that

baryons

neutrinos,

since

in Table of about fact

iS

the

are

examples

I will of

of fact

of the from

masses

ino

physicists

inos

from

have

the

of

then "hot"

early

standard

model

several

to do with baryons,

the

in

the production

have something than

to

One striking

of

production

other

axions

inos.

results

review

are

fraction

particle

production

first

matter

abundances

33 in possible

is that

the

for

The relic

I. 10

particles

ino dark

10 -5eV

candidate

we know exists.

axions

for

from

some general discuss

of elementary

a significant

in providing

will

Table

I that

component

candidates

given

striking

reviewing

discuss

not

holes,

monopoles.

is a range

I will

is obvious

is also

the production

masses

are also

generous

bang,

than

Of particular

of some elementary

discuss

Another

After

matter.

the

is different

different

It

some

have

disk

black

are to contribute

there

paper

dark

or Kaluza-Klein

they

abundances.

is

etc.

that

Possible

that

in the

in turn

Some proposed

of the Universe table

problems

bang.

bang."* I.

matter

of primordial

of the

I will

in Table

1028eV

form

form

big

dark

matter

galaxies,

all)

in the

dark

which

possibility

non-baryonic, a remnant

the

of

some (or is

the

in the halo,

either

could

all

may be that

matter

matter

if

they

discuss and tqcold"

of

the

of baryons, galaxies. are

I

the only

axiOnS. dark

The matter

respectively. TABLE I SOME IN0 CANDIDATES FOR DARK MATTER Candidate

Present Abundance

Mass

Axion Neutrinos Gravitino/Photino

10m5eV

10gcm -3

1OeV

lO*cm -3

1 03eV

1 cme3

1O'eV

10+cme3

Sneutrino/Photino

1OlleV

10~'cm -3

GUT Monopoles

1 Oz5eV

1 0-22cm-3

1028eV

10-25cm-3

Baryons

Pyrgons/K.-K.

II.

Monopoles

THE BIG BANG MODEL Although

structure

is

the

structure

seems

scales,

background. they

are correlated.

two-point excess F,(r)

Galaxies

correlation probability galaxies

>> 1,

distributed

as spread

r.

If

that

P,(r)

E(r)

MN, where MN is

the

if

it

the Universe

the

falls

of the Universe

3.2 0'

Universe

the baryon

nucleon number,

from matter

this

Furthermore,

when the

temperature If

mass. nN = ni,

we

number density

is

of would

when T me, the cross

a(e+e-

++

V.“. 1-1)

where G is Fermi’s F electrons

iS

the

neutrino

section

for

family,

e,~,

neutrino

or T (or

production

possibly

more).

is

= G;E2

(4.1)

constant.

given

When

by ne - T3,

E

>

so the

me,

the

production

number rate

density

of

of neutrinos

is

(EST)

r

This T2/m

P

= no = T3G2E2 = GgT* F

rate

is

to be compared

.

(4.2)

with

the

expansion

rate

of the Universe

TE =

Pl

- rP rE

= G2T3m F Pl (4.3) = O(1)

When

the

[T/1MeV13

temperature

iz much greater

than

they

are destroyed.

rest

of the matter

Universe

iz

neutrinos

“freeze

equilibrate

less

with

.

of the Universe

is greater

than

about

one and neutrinos

interact;

they

are

The neutrinos in

the

than out.” the rest

would

Universe.

about After

1 MeV,

freeze-out

of the Universe.

then

1 MeV, fP/rE created

be in equilibrium

When

the

they

no

with

the

of

the

temperature

!YP/rE is much less longer

A more detailed

and

than

one and

interact calculation

and

18 can be done by solving neutrino

annihilation

If at

Eq. crosz

we azsume that

freeze

at freeze

out

(T=T~)

number density

(3/4)

The

at freeze

because

T; = (3/4)

neutrinos density

entropy

in e+e-

(since

neutrino

haz

a fraction

Rvi = 0.01

If

h = l/2,

fivi

5 1, then

the present

relativistic

(plus

antineutrinos)

(4.4)

and n y is the number

pairs

nvo,

is

a

mazz

of the

is

mvi,

closure

density

by a factor

decoupled). (per

The

into

of

photons

but the

Therefore

not

number

family)

.

then

(4.5)

the

relic

neutrinos

would

density

(4.6)

The limit

bounds

e+e-

(11/4)“3

.

mvi as low as 25eV could mvi ( 100h2eV.

annihilation.

converted

nYo = 110cmm3

(mvi/eV)hm2

experimental

e+etemperature

have

today,

(4/11)

contribute

total

ny

before

neutrinos

“0 = (314)

the

be

will

of neutrinos

neutrinos

the neutrino

of neutrinos

n

If

decouple

increases the

the

out.

neutrinos

annihilation

oA[vl

be

where we have assumed 2-component of photons

with

neutrinos 4.1

section.

would

n v = (s(3)/n2)

for

mu tu)

important

physics

usual

the

theory

of strong

interactions,

QCD, it

is possible

to add to

Lagrangian

Lo = -(l/4)

G,:

Gap”

,

(5.1)

20 where G a = a Aa - a Aa ilv

Le = (e/32~~~)

pu

where express can

L

is e

the

be discarded

odd

under

contribution

(W32r2)

There

L e has the

coup1 ing

form

it

can have physical

- eE’*8’, it

neutron

electric

dipole

dipole

e

a contribution

the

than

of

the

due to

P and T, hence L8 term would

be a

moment.

The fact

of order

10 -19 e cm requires

to 8. The quarks

a vacuum expectation the

quarks

to have the

that

the

iz

value

neither

mass

real

matrix

receive