Lecture 34: The Big Bang
Readings: Sections 28-3 and
28-6
Key Ideas:
Big Bang Model of the
Universe
Universe starts in a
hot, dense state in the past
Universe expands
& cools with time
Cosmological Redshift &
Lookback Time
Critical Density
Determines the
geometry of the Universe and its expansion history
Hubble Time
Estimate of the Age
of the Universe
Expansion of the Universe
Universe is observed to be
expanding today
Evidence: HubbleÕs
Law
As the Universe expands, it cools
In the past, it must have
been:
Smaller
Denser
Hotter
than it is todayÉ.
The Big Bang
If we run the clock back far
enough, eventually the Universe would be
Very small and very
high density
Very, very hot and
opaque.
This initial state must have
existed at some finite time in the
past.
We call this very hot, very
dense initial state and subsequent expansion
THE BIG BANG
Foundations of the Big Bang
An infinitely dense & hot
Universe in the past follows naturally from three basic physical assumptions:
1. General Relativity
is valid on cosmic scales
2. The Universe is homogenous and isotropic on cosmic scales.
3.
The energy of the vacuum is either zero or very small (the Cosmological
Constant: L)
All of these assumptions are
testable.
The Big Bang is Testable
These basic assumptions are
plausible:
Supported by
empirical data for the most part
Have a reasonably
sound physical basis
But, they are not required to be true
Real Test:
Does the Big Bang Model
explain the properties of the observed Universe?
Expansion & HubbleÕs Law
As the Universe expands:
Space gets stretched
in all directions
Matter is carried
along with expanding space.
The distances
between galaxies get larger with time
The Big Bang predicts
HubbleÕs Law exactly.
Cosmological Redshift
Expansion of space stretches
light:
Wavelengths get
stretched into redder wavelengths
The greater the
distance, the greater the stretching
Result:
The redshift of an
object gets larger with distance
The Big Bang naturally
explains the observed Cosmological redshifts.
Cosmic Lookback Time
Light moves at a finite
speed:
Takes time for light
to reach you from a distant source.
Example,
we see the Sun as it was ~8.5 minutes ago due to the light-travel time.
At cosmic distances:
The
deeper we look into the Universe, the further we look-back in time to when the Universe was younger & smaller.
Very Distant=High
Redshift=Very Young Galaxies
Credit: Hubble Space Telescope
The Shape of the Universe
All forms of matter attract each other via their mutual gravity.
Relativity tells us:
Energy & matter
are equivalent (E=mc2)
Matter & energy
tells spacetime how to curve
The combined matter and
energy density of the Universe determines its global geometry.
The Density Parameter: W0
The geometry of the Universe
depends on the total density of matter & energy
See Figure 28-15
High Density:
Positively curved
(spherical) geometry
Low Density:
Negatively curved
(hyperbolic) geometry
Dividing Line:
Critical Density
Universe is Flat: no
curvature
critical density=density
needed for a flat Universe
Geometry of the Universe
If W0 >1: Positive curvature
Finite &
unbounded
Spherical Universe
Parallel light rays
converge
If W0 < 1: Negative curvature
Infinite, hyperbolic
Universe
Parallel light rays
diverge
If W0=1: Critical, flat Universe
Infinite, flat
Universe
Parallel light rays
stay parallel
See Figure 28-15
General Relativity
Matter and energy
cause spacetime to curve
Curved spacetime
tells matter and light how to move
Bottom Line
Light
follows different paths depending on the curvature of the Universe. This much
be taken into account when viewing light coming from large distances.
Back to the Beginning
The Universe is expanding
now.
In the past:
Universe was smaller
Galaxies were closer
together in space
If we go back far enough in
time:
All galaxies
(matter) in one place.
How far back=ÓAge of the
UniverseÓ
Road Trip Analogy
You leave Columbus by car for
Florida, but leave your watch behind.
How long have you been on the
road?
Your average
speed=100 km/h
Your odometer reads:
distance=230 km
Time since you left:
time=distance / speed
T=230 km / 100 km/h
= 2.30 hours
The Hubble Time: T0
HubbleÕs Law says
A galaxy at distance
d away has a recession speed, v=H0
d
If locally, v is its average speed, then
T0 = d/v
But since v=H0d,
T0=d/H0d=1/H0
HUBBLE TIME: T0
=1/H0
Estimate of the Age of the
Universe
ButÉ
Cosmic expansion is not
expected to be constant over all times:
If faster in the past
Expansion slowed by
gravity of massive objects
T0 would overestimate
the age of the Universe
If slower in the past:
Accelerated by a
non-zero cosmological constant L
T0 would underestimate
the age of the Universe
So, How Old is it Really?
Need two hard-to-measure
numbers:
Hubble Parameter, H0
How fast the
universe is expanding now
Density Parameter, W0:
How
the matter & energy density affected the expansion rate in the past
Can
include an WL
term that enhances the expansion rate
Needed to determine the expansion
history
What is our Universe like?
Flat: W=1 (Wm=0.3, WL=0.7)
Accelerating: WL=0.7
Current expansion rate: H0=70+/-7
km/sec/Mpc
Best Estimate of the Age: