Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30
Lecture 36: The Big Bang
Readings: Ch 28, sections 28-2, 28-3 and 28-6
- Big Bang Model of the Universe
- The Universe started in a hot, dense state
- Universe expands and cools with time
- Cosmological Redshift & Lookback Time
- Critical Density
- Determines the Geometry of the Universe
- Influences the expansion history of the Universe
- Hubble Time
- Estimate of the Age of the Universe
Expansion of the Universe
The Universe is observed to be expanding today.
As the Universe expands, it cools.
In the past, it must therefore have been:
than it is today.
The Big Bang
If we run the clock backwards far enough, eventually the Universe
This initial state must have existed at some finite time
in the past.
- very small & very high density
- Very very hot & opaque
We call this very hot, very dense initial state "The Big Bang"
Foundations of the Big Bang
An infinitely dense and hot Universe in the past follows
naturatlly from three basic physical assumptions:
All of these assumptions are testable observationally.
- General Relativity is valid on cosmic scales.
- The Universe is homogeneous and isotropic on cosmic scales.
- The energy of the vacuum is either zero or very small (the
Cosmological Constant: L)
The Big Bang is a Testable Model
These basic assumptions are plausible:
But, they are not required to be true.
- Supported by empirical data for the most part
- Have Reasonably sound physical basis
The Real Test:
- Does the Big Bang Model explain the properties of the observed
It is important to emphasize that this is why we think this is an
important idea. The Big Bang is not just a conjecture: it makes
powerful predictions that can be tested against observations. If it
could not be tested, it would have no use to us as a model for the
evolution of the Universe.
Expansion & Hubble's Law
As the Universe expands:
- Space gets stretched in all directions.
- Matter is carried along with the expanding space.
- The distances between galaxies get larger with time.
The Big Bang predicts Hubble's Law exactly for recession speeds
that are small compared to the speed of light.
Note that a more detailed description is required at large cosmological
distances that takes into account the detailed geometry of the Universe.
The expansion of space also stretches light waves:
- Wavelengths get stretched into longer
and hence redder wavelengths.
- The greater the distance, the greater the stretching.
- The redshift of an object gets larger with increasing
The Big Bang naturally explains the observed Cosmological
Redshift, distinguishing it from a normal Doppler Shift due to objects
moving through space rather than expanding with space.
Cosmic Lookback Time
We observe the Universe using light, but light moves at a finite speed:
At cosmic distances, the effect is even more pronounced:
- It 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 time
it takes light to travel 1AU.
- The deeper we look into the Universe, the further we are
actually looking back in cosmic time to when the Universe
was younger and smaller.
This fact allows us to reconstruct the past expansion history of the
Universe, provided, as always, that we can measure distances accurately.
This is a startling fact: cosmic lookback time means that we can
actually observe the Big Bang unfolding from the past to the present!
The Shape of the Universe
All forms of matter attract each other via their mutual
Relativity tells us that:
- Energy is equivalent to mass (E=mc2), so all forms of energy
in the Universe gravitate as well.
- Matter & energy combined tell spacetime how to curve.
The combined matter and energy density of the Universe determines its
The Density Parameter, W0
The geometry of the Universe depends on the total density of matter
- Positively curved (spherical) geometry
Dividing Line: Critical Density
- Negatively curved (hyperbolic) geometry
We express this in terms of a Density Parameter,
- Universe is Flat: no curvature
The Density Parameter is the ratio of the current density of matter and
energy in the Universe to the "Critical Density" needed for
a spatially-flat Universe.
The Geometry of the Universe
The important values of W0 are
- W0 > 1:
- Finite yet unbounded spherical Universe
- Parallel light rays converge
- W0 < 1:
- Infinite, hyperbolic Universe
- Parallel light rays diverge
- W0 = 1:
Critical (Flat) Universe
- Infinite, flat Universe
- Parallel light rays stay parallel
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 = "Age of the Universe"
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: T = distance / speed
- T = 230 km / 100 km/h = 2.30 hours
The Hubble Time, T0
Hubble's Law says
- A galaxy at distance d away has a recession speed, v,
given by the Hubble Law:
If locally, v is about its average speed, then:
- T = d / v
- but since, v = H0 d, and T = d/H0 d = 1 / H0
This defines the Hubble Time:
T0 = 1 / H0
This provides an estimate of how long the Universe has been expanding,
and hence its age.
The rate of cosmic expansion is not expected to be constant over all
If the expansion were faster in the past:
- Expansion would be slowed down by the gravity of all the matter and energy
in the Universe.
- T0 would overestimate the age of the Universe.
If the expansion were slower in the past:
- Expansion might be accelerated by a non-zero cosmological constant
- T0 would underestimate the age of the Universe.
So, How old is it really?
We need to know the values of two hard-to-measure numbers:
Hubble Parameter, H0:
- Tells us how fast the universe is expanding now.
Density Parameter, W0:
These are needed to be able to determine the expansion history of
- Tells us how the matter & energy density of the Universe
affects the expansion rate.
- Can include an WL term
(aka a "Cosmological Constant") that enhances the expansion rate.
Our best current estimate of the Age of the Universe is:
T0 = 14.0 +/- 1.4 Gyr
This value is found by using the current "Benchmark" (or "Concordance")
The value W0 consists of a 30%
contribution from all forms of matter (Wm=0.3), and a 70% contribution from the
energy density (WL=0.7).
- H0 = 70 +/- 7 km/sec/Mpc
- W0 = Wm + WL=1.0
This value of W0=1 implies that
we live in an infinite, spatially flat Universe.
This age is consistent with the ages of the oldest stars seen in
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Updated: 2006 February 25
Copyright © Richard W. Pogge, All Rights Reserved.