Our Our Place Place in in the the Cosmos Cosmos the Universe - - PDF document

Our Our Place Place in in the the Cosmos Cosmos

Lecture 18 The Big Bang

The Big Bang

• We saw in the last lecture that the Universe

is expanding

• Following that expansion backward in time,

the Universe must have been much smaller in the past

• We believe the Universe was created in an

event called the Big Bang about 13.6 billion years ago

• This is an empirical model - does it make any

testable predictions?

Predictions of The Big Bang

• When a gas is compressed it gets hotter
• It thus seems reasonable to assume that the

young Universe contained an extremely hot, dense gas, filled with high energy radiation with a Planck spectrum

• In the 1940s, Ralph Alpher and Robert

Herman reasoned that as the Universe expanded, this cosmic background radiation (CBR) would have have been redshifted to longer and longer wavelengths, corresponding to a much cooler blackbody [recall Wien’s law: T = (2,900 µm)/peak] Planck radiation in the hot, dense, young Universe is stretched by Hubble expansion to longer-wavelength radiation at a lower temperature

Prediction of CBR

• The first theoretical prediction of the residual

radiation from the Big Bang was published in 1948 by Alpher and Herman

• They asserted that the radiation should be

visible today with a temperature in the range 5-10 K, corresponding to radiation in the microwave part of the spectrum

• Telescope technology at the time was not far

enough advanced to detect this radiation and their landmark paper languished largely unnoticed until the 1960s

Discovery of CBR

• In the early 1960s Arno

Penzias and Robert Wilson were puzzled by a faint microwave signal detected by the Bell Telephone Labs radio telescope in Holmdel, New Jersey

• No matter where they

pointed the telescope, the signal persisted

Discovery of CBR

• Meanwhile, Robert Dicke in nearby Princeton

University independently arrived at Alpher and Herman’s prediction of CMB radiation

• When Dicke heard of the signal that Penzias

and Wilson had found, it was realised that the cosmic background radiation had been discovered [an achievement for which Penzias and Wilson shared the 1979 Nobel Prize]

• The temperature of their signal was around

3K, close to the predicted temperature and corresponding to radiation in the microwave part of the spectrum

Origin of the CBR

• The cosmic background radiation originates in the hot,

young Universe when most hydrogen was ionized

• Photons of radiation interact strongly with free

electrons and thus cannot travel far and acquire a Planck spectrum

• As the Universe expanded and cooled to a

temperature of a few thousand degrees (corresponding to redshift z 1100 around 105 years after the Big Bang) the protons and electrons of hydrogen were able to recombine, resulting in a Universe transparent to radiation

• The CBR photons were then able to stream freely,

being redshifted as the Universe expanded

COBE Satellite

• Although Penizas and Wilson had detected the

CBR at the predicted temperature, they were unable to confirm that it had a Planck spectrum as predicted

• The COsmic Background Explorer (COBE)

launched in 1989 made an accurate measurement of the spectrum of the CBR

• The CBR spectrum corresponded perfectly to a

Planck spectrum with corresponding temperature of 2.728 K

• Very strong support for Big Bang model

CBR Spectrum Earth’s Motion

• The COBE satellite also discovered that the

temperature of the CBR is not the same everywhere

• The temperature differs by about 0.003 K in opposite

directions on the sky

• This is due to Earth’s motion with respect to the CBR
• the CBR provides a frame of reference that is at

rest with respect to the expansion of the Universe

• The CBR is blueshifted (slightly hotter) in the

direction of our motion and redshifted (slightly cooler) in the opposite direction

• v 368 km/s

CBR Temperature Anisotropy

• If we subtract from the COBE map the effects of our

motion and microwave emission from the Milky Way, very small fluctuations in temperature of about 1 part in 105 remain

• These temperature anisotropies result from equally

small density perturbations in the post-recombination Universe

• These density perturbations also give rise to the

large-scale structures in the galaxy distribution that we see today

• 2006 Nobel Prize

awarded to COBE team for this discovery

Nucleosynthesis

• Temperatures and densities when the Universe was

less than a few minutes old were similar to those in the cores of stars today

• Nuclear fusion reactions could thus fuse hydrogen into

heavier nuclei

• Only the lightest nuclei were synthesised during Big

Bang nucleosynthesis: deuterium (heavy hydrogen), helium, lithium, beryllium and boron

• The amounts of each isotope formed depend

sensitively on the temperature and density of matter in the early Universe, and hence on the present-day density of baryonic (“normal”) matter

Agreement of predicted abundances with observations requires that the present-day baryon density lies within the vertical yellow band - the vertical black line shows the observed baryon density

Nucleosynthesis

• About 24% of the mass of baryonic matter formed in

the early Universe is in the form of 4He regardless of the baryon density

• The predicted abundances of other isotopes are

sensitive to the baryon density

• In order to agree with observed abundances, the

present-day baryon density must be around 3 x 10-28 kg/m3 - again in good prediction with observations

• Big Bang nucleosynthesis is inconsistent with dark

matter being in the form of baryons such as protons and neutrons

• Dark matter must thus be in non-baryonic form

Successes of the Big Bang Model

• The Big Bang model is supported by three

main pieces of observational evidence

1. The observed expansion of the Universe

• 2. The blackbody form and expected temperature of

the cosmic background radiation

• 3. The observed abundances of the light elements
• No other theory, such as the steady state

model, or plasma Universe, can explain these

• bservations so naturally

Fate of the Universe

• We know the Universe is expanding today - will this

expansion continue forever?

• This depends in part on the mass of the Universe
• Recall our discussion of escape velocity - the fate of

a projectile fired straight up from the surface of the Moon depends upon its speed

• If the speed is less than the escape velocity then gravity

will eventually pull the projectile back to the Moon’s surface

• If the speed is greater than the escape velocity the

projectile can escape from the Moon

• The gravity of the mass in the Universe acts in a

similar way, slowing down the expansion

Fate of the Universe

• If there is enough mass in the Universe then gravity

will eventually stop the expansion

• The Universe will slow, stop and eventually collapse
• n itself in a Big Crunch
• If there is not enough mass the expansion may slow,

but will never stop

• Escape velocity from a planet is determined by its

mass and radius

• The escape velocity of the Universe is determined by

its average density

• The critical density is the limiting density that

determines the future fate of the Universe

Critical Density

• The faster the Universe is expanding, the more mass

is required to turn that expansion around

• The critical density c thus depends on the Hubble

constant H0

• H0 = 72 km/s/Mpc c = 8 x 10-27 kg/m3
• We write the ratio of the actual density 0 of the

Universe to the critical density as m (omega-matter)

• Recall that nucleosynthesis 0 3 x 10-28 kg/m3

and so baryons alone fall far short of providing critical density

• The above argument supposes that gravity is the only

important force in determining the fate of the Universe - an assumption which has recently been

• verturned

An Accelerating Universe!

• Whatever the actual value of m one would

expect the expansion rate of the Universe to be slowing down

• This can be checked by measuring the

brightness of standard candles such as Type I supernovae at high redshift [brightness distance integrated expansion rate]

• To astronomers’ great surprise, such
• bservations carried out in the late 1990s

showed that the expansion of the Universe is in fact speeding up!

Most supernovae at high redshift are fainter than we would expect in the case of unaccelerated Hubble expansion Those

• bservations

below the curve suggest expansion is speeding up

Einstein’s “Greatest Blunder”

• Einstein formulated his general theory of relativity in

1915, before Hubble had discovered the expansion of the Universe

• In order to produce a static solution to his equations

describing the Universe, Einstein introduced a term he called the cosmological constant , a repulsive term which balanced the attractive force of gravity

• Once it was realised 14 years later that the Universe

was expanding, the term was no longer necessary

• Einstein apparently regarded his inclusion of the

term (and his failure to predict an expanding Universe) as “my greatest blunder”

The Cosmological Constant

• With the recent discovery of an accelerating

Universe, Einstein’s cosmological constant has made a comeback

• The cosmological constant opposes gravity

and makes a contribution to the density of the Universe, written

• With a cosmological constant term the fate of

the Universe is no longer controlled exclusively by gravity and hence m

• The fate of the Universe depends on the

values of both m and A cosmological constant can cause the Universe to expand faster and faster It can even prevent the collapse of a m > 1 Universe Supernova

• bservations are

compatible with a Universe that is 30% matter and 70% cosmological constant Observational constraints from Type I supernovae and CBR anisotropies are consistent with our Universe having m 0.3, 0.7 m + 1 Universe has a “flat” geometry

Summary

• Overwhelming observational evidence in

favour of the Big Bang model:

• 1. The observed expansion of the Universe
• 2. The blackbody form and expected

temperature of the cosmic background radiation

• 3. The observed abundances of the light

elements

• The Universe is currently undergoing

accelerated expansion due to a cosmological constant or dark energy