Lecture 37: The Big Bang

Key Ideas:

Big Bang Model of the Universe

• Initial hot, dense state
• Universe expands and cools

Expansion and Redshift

Critical Density

• Geometry of the Universe

Hubble Time = Age of the Universe

Expansion of the Universe

Universe is expanding today.

• Evidence: Hubble's Law

As the Universe expands, it cools.

In the past, it must have been:

• smaller
• denser
• hotter

The Big Bang

The Universe has expanded to its present observed state from an initially very hot, very dense state.

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

We call this hot, dense state the "Big Bang"

Foundations

The Big Bang Model for the Universe follows from three basic assumptions:

• General Relativity is correct on cosmic scales.
• The Universe is homogeneous and isotropic on large scales.
• The energy of the vacuum is either zero or very small.

Testable Model

These basic assumptions are plausible:

• Empirical support for the most part.
• 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 & Hubble's Law

As the Universe expands:

• Space gets stretched in all directions.
• Matter is carried along with space.
• Distance between galaxies gets larger.

Big Bang predicts Hubble's Law exactly, provided that the speeds are small compared to the speed of light.

Expansion and Redshifts

Expansion of space also stretches photons:

• Wavelengths get stretched = longer = redder.
• More distant the object, the greater the stretch.
• Result: redshift gets larger with distance.

Light moves at a finite speed:

• More distant objects seen in the past.
• "look-back" to when the universe was smaller.

Critical Density

All galaxies attract each other via gravity.

• Gravitational attraction slows the expansion.

How it behaves depends on the density:

• High Density: Expansion slows, stops, & reverses.
• Low Density: Keeps expanding forever.

Dividing Line = "Critical Density"

Density Parameter:

Cosmological Density Parameter:

>1: High Density Universe

<1: Low Density Universe

=1: Critical Density Universe

Geometry of the Universe

If >1:

• positive curvature ("spherical")
• finite yet unbounded Universe

If <1:

• negative curvature ("hyperbolic")
• infinite Universe

If =1: Universe is Flat and infinite.

Fate of the Universe

If >1: "Closed" Universe

• Expansion slows to a maximum size & stops
• Collapses into a Big Crunch

If <1: "Open" Universe

• Expands forever at a near-constant rate.

If =1: "Flat" Universe

• Expands forever at an ever slowing rate.

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
• odometer reads: distance = 230 km

Time since you left: t = distance/speed

• t = 230 km / 100 km/h = 2.30 hours

The Hubble Time

Hubble's Law says

• a galaxy a distance "d" away has a recession speed, v = Hd

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

• t = d / v
• but since, v = Hd,
• t = d/Hd = 1/H

Hubble Time = 1/H

The Age of the Universe

Example:

• For H=70 km/sec/Mpc
• t = 1/H = 14 Billion Years

But,

• Universe does not expand at a constant rate.
• Have to account for faster expansion in past.

Hubble Time is an Upper limit on the age of the Universe.

How old is it really?

Need two numbers we know poorly:

Hubble Constant, H:

• Tells us how fast the universe is expanding now

Density Parameter, :

• Tells us how the expansion has slowed down.

Best Estimate: 12-17 Gyr

• Uncomfortably close to age of oldest stars...