VERY Early Universe

Tuesday, January 29Tuesday, January 29 (planetarium show tonight: 7 pm, 5(planetarium show tonight: 7 pm, 5thth floor floor

Smith Lab)Smith Lab)

It’s about time!

Different calendars have different starting times (birth of Christ,

hijra to Medina, etc.)

The Big Bang (start of expansion) provides an absolute zeroabsolute zero for time.

Universe started expanding at a time t = 0t = 0.

What is the currentcurrent time t = tt = t00? (That is, how much time has elapsed since the Big Bang?)

We’ve already answered that question (approximately).

1/H0, called the “HubbleHubble timetime”, is the approximate age of the

universe in the Big Bang Model.

At a finite time in the past (t ≈ 1/H0), the universe began in a very dense state.

Flashback slide!

The Hubble time, 1/H0, is approximately equal to t0 (time elapsed since Big Bang).

If expansion has been slowing downslowing down, the universe is younger younger than 1/H0.

If expansion has been speeding upspeeding up, the universe is olderolder.

Redshift (z) of a distant object: measure of how much the universe has

expanded since light was emitted.

Since universe has been expanding continuously, each zz corresponds to a

unique time tt.

Looking at the Cosmic Microwave Background:

z ≈ 1000, t ≈ 350,000 years

As time (t) increases, density and temperature decreasedecrease.

What the *&@% do I mean by “thethe temperature of the early universe”?

Today, the universe is full of things with many different temperatures.

The earlyearly universe was dense: particles frequently collided, and came to the same same equilibrium temperature.

The very early universe was a nearly homogeneous “soup” of

elementary particles.

Particle Physics for Dummies

Electron: low mass, negative charge

Proton: higher mass, positive charge

Neutron: ≈ proton mass, no charge

Neutrino: VERY low mass, no charge

Neutrinos, they are very small. They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them,

through which they simply pass, Like dustmaids down a drafty hall Or

photons through a pane of glass.

Cosmic Gall (John Updike)

What’s a photon?What’s a photon?

A photonphoton is a particleparticle of light.

On very small scales, the laws of quantum mechanicsquantum mechanics apply.

One of these laws states that a particle can have the properties of

a wave, and vice versa.

This concept of “wave-particle duality” is mind-bending but useful.

Light of a given color can be treated as: 1) waves of a given wavelengthwavelength

2) photons of a given energyenergy

EnergyEnergy can be measured in BTUs, kilowatt-hours, calories, ergs, etc…

The energy of individual particles is usually measured in electron-voltselectron-volts.

1 electron-volt (eV) is the energy gained by an electron when its

electrical potential increases by 1 volt.

An electron-volt is a tinytiny amount of energy, appropriate for dealing with

single particles and atoms.

photon of red light: energy = 1.8 eV

photon of violetviolet light: energy = 3.1 eV

The temperature TT of the early universe determines the average

particle energy EE.

K 10,000

TeV 3 E

t T E

30,000 yr 10,000 K 3 eV

12 days 10 million K 3 keV

1 second 10 billion K 3 MeV

10-6 sec 10 trillion K 3 GeV

1 GeV = 1 billion electron-volts = energy of a gamma ray photon

How far back in How far back in time dare we go?time dare we go?

Looking againagain at the CMB:

z ≈ 1000, t ≈ 350,000 years, T ≈ 3000 K

Universe became transparent because hydrogen went from ionized to neutral.

It takes 13.6 eV of energy to ionize a hydrogen atom.

Any photon with E > 13.6 eV (ultraviolet, X-ray, gamma-ray)

can ionize hydrogen.

Hydrogen atom:Hydrogen atom: a proton and electron

held together by electrostatic attraction.

At T = 3000 K, some photons are energetic enough

to ionize hydrogen.

At T < 3000 K, hydrogen forms

neutral atoms: too few ionizing photons! 13.6 eV 13.6 eV

photonsphotons

It takes 2,200,000 eV of energy to dissociate a deuterium nucleus.

Any photon with E > 2.2 MeV (gamma-ray) can dissociate deuterium.

Deuterium nucleus:Deuterium nucleus: a proton and

neutronneutron held together by strong nuclear strong nuclear

forceforce.

nucleus

If hydrogen atoms are safe from ionization when T < 3000 K, then deuterium nuclei will be safe from dissociation when

T < ???160,000K 3000

eV6.13

eV000,200,2K 3000

K10 4.8 8

The temperature of the universe fell below 480 million K when

its age was t ≈ 7 minutes.

Photons were no longer energetic enough to blast apart deuterium nuclei.

Deuterium nuclei could form and be safe from destruction.

p + n → D + γ

Primordial nucleosynthesis:

proton neutron deuterium nucleus

gamma ray (energetic photon)

The very early universe was a nuclear fusion reactor.

There’s not a lot of deuterium in the universe today. Why not?

Because fusion continued:

D + n → T + γ

tritium nucleus

There’s not a lot of tritiumtritium in the universe today. Why not?

For one thing, tritium is unstable. For another, fusion continued:

T + p → He + γ

helium nucleus

Before primordial nucleosynthesis, there were 2 neutrons for every 14 protons. (Neutrons tend to decay into protons.)

2 neutrons combine with 2 protons to form 1 stable helium nucleus, with 12 lonely

protons (hydrogen nuclei) left over.

25% of the initial protons & neutrons (and hence 25% of their mass) should be in

helium: the rest will be hydrogen.

When we look at the spectra of the first stars that formed, they consist of 25% helium by mass, and 75% hydrogen.

TRIUMPH FOR PRIMORDIAL TRIUMPH FOR PRIMORDIAL NUCLEOSYNTHESIS!NUCLEOSYNTHESIS!

There’s just the amount of H & He that was predicted.

nucleo-nucleo-synthesissynthesis

trans- trans- parencyparency

galaxy galaxy formationformation

7 min7 min 350,000 yr350,000 yr 1 billion yr1 billion yr

Gosh! We understand what the universe was like when it was a

few minutes old!

1) At t < 1 minute, things get more speculative.

2) Cosmologists love to speculate.

Thursday’s Lecture:

Reading:

Chapter 5

Gravity and the Expanding Universe