### The Big Bang

```The Big Bang
The Big Bang
Key Concepts
1) The Hubble law (v = H0d) is expected in a
uniformly expanding universe.
2) If the speed of galaxies has been constant,
expansion began a Hubble time ago.
3) The Hubble law is consistent with the Big Bang
theory (expansion from an initial dense state).
There is nothing special about our galaxy.
In a uniformly expanding universe, every
galaxy moves away from every other galaxy.
Hubble law: other galaxies are moving away from
our own, with a velocity proportional to their
distance.
The universe considered as an
1
Why it’s useful to know the Hubble
constant, H0:
With modern telescopes and spectrographs,
astronomers have measured millions of spectra.
Measure redshift of galaxy: z = (λ-λ0)/λ0
Compute radial velocity: v = c z
Compute distance: d = v / H0
Cheap, fast way to find distance!
A “redshift map”
of a slice through
the universe.
Each tiny dot
represents a
galaxy.
Why it’s intriguing to know H0:
d
Two galaxies are separated by a
distance d.
They are moving apart from each other with a
speed v = H0 d.
The Big Bang
• If we run the clock back far enough,
eventually the Universe would be:
– Zero size and therefore infinite density
– Infinitely hot
• This initial state must have existed at
some finite time in the past.
• We call this dense initial state the
• “Big Bang”
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.
2
Back to the Beginning
How long has it been since
the galaxies were touching?
• The Universe is expanding now.
• In the past:
– Universe was smaller.
– Galaxies were closer together in space.
travel time 
• If we go back far enough in time:
– All galaxies (matter) in one place.
• How far back = “Age of the Universe”
Kilometers per second per megaparsec??
What bizarre units!
1 megaparsec = 3.09 × 1019 kilometers
H0 
71 km/sec/Mpc
 2.30  10 18 / sec
3.09  1019 km/Mpc
H0 
t
distance
speed
d
1

 4.35  1017 sec
H 0d H 0
PLEASE NOTE: This length of time (t = 1/H0)
is independent of the distance between
galaxies!!
If galaxies’ speed has been constant, then at a
time 1/H0 in the past, they were all scrunched
together.
1
4.35  1017 sec
Heart of the “Big Bang” concept:
At a finite time in the past (t ≈ 1/H0), the universe
began in a very dense state.
1/H0, called the “Hubble time”,
is the approximate age of the
universe in the Big Bang Model.
t
1
 4.35  1017 sec
H0
Since there are 3.16 × 107 seconds per year,
the Hubble time is
1/H0 = 13.8 billion years
3
But…
• 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:
If age of universe ≈ 1/H0, light from
stars farther than a distance ≈ c/H0
has not had time to reach us.
– accelerated by some “dark energy”
– T0 would underestimate the age of the Universe.
Hubble time:
Is the universe infinitely old?
1/H0 = 13.8 billion years.
Hubble distance:
About 14 billion years have passed since the
universe started expanding from its initial
dense state.
c/H0 = 13.8 billion light-years
= 4200 megaparsecs.
The Observable Universe has a finite age.
Is the universe infinitely big?
We don’t know: we can see only a region