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Galaxy NGC4414 from HST Astronomy 162:
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

Key Ideas

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 would be

This initial state must have existed at some finite time in the past.

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.

The Big Bang is a Testable Model

These basic assumptions are plausible: But, they are not required to be true.

The Real Test:

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:

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.


Cosmological Redshift

The expansion of space also stretches light waves:

Result:

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:

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 gravity.

Relativity tells us that:

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 and energy:

High Density

Low Density Dividing Line: Critical Density We express this in terms of a Density Parameter, W0:
Density Parameter: Omega_0

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 as follows:
W0 > 1: positive curvature

W0 < 1: negative curvature

W0 = 1: Critical (Flat) Universe

Back to the Beginning

The Universe is expanding now.

In the past:

If we go back far enough in time:

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?

Time since you left: T = distance / speed


The Hubble Time, T0

Hubble's Law says

If locally, v is about its average speed, then:

This defines the Hubble Time:

T0 = 1 / H0
This provides an estimate of how long the Universe has been expanding, and hence its age.

But...

The rate of cosmic expansion is not expected to be constant over all times:

If the expansion were faster in the past:

If the expansion were slower in the past:


So, How old is it really?

We need to know the values of two hard-to-measure numbers:

Hubble Parameter, H0:

Density Parameter, W0:

These are needed to be able to determine the expansion history of the Universe.

The Age of the Universe:

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") Cosmology: 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).

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 globular clusters.


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Updated: 2006 February 25
Copyright Richard W. Pogge, All Rights Reserved.