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: