Astronomy 162:
Introduction to Stars, Galaxies, & the Universe Prof. Richard Pogge, MTWThF 9:30 |

- 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

- Evidence: Hubble's Law

As the Universe **expands**, it **cools**.

In the past, it must therefore have been:

- smaller
- denser
- hotter

If we run the clock backwards far enough, eventually the Universe would be

- very small & very high density
- Very very hot & opaque

We call this very hot, very dense initial state "**The Big Bang**"

- 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)

- 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**Universe?

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.

- 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.

- Wavelengths get
**stretched**into**longer**and hence**redder**wavelengths. - The greater the distance, the greater the stretching.

Result:

- The
**redshift**of an object gets**larger**with increasing distance.

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.

- 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!

Relativity tells us that:

- Energy is equivalent to mass (E=mc
^{2}), 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
**global geometry**.

High Density

- Positively curved (spherical) geometry

- Negatively curved (hyperbolic) geometry

- 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.

- W
_{0}> 1: positive curvature**Finite yet unbounded**spherical Universe- Parallel light rays
**converge**

- W
_{0}< 1: negative curvature**Infinite**, hyperbolic Universe- Parallel light rays
**diverge**

- W
_{0}= 1: Critical (Flat) Universe**Infinite, flat**Universe- Parallel light rays
**stay parallel**

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"

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**

- 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 = H
_{0}d, and T = d/H_{0}d = 1 / H_{0}

This defines the **Hubble Time**:

This provides an estimate of how long the Universe has been expanding, and hence its age.T_{0}= 1 / H_{0}

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.
- T
_{0}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 (L).
- T
_{0}would**underestimate**the age of the Universe.

Hubble Parameter, H_{0}:

- Tells us how fast the universe is expanding
**now**.

Density Parameter, W_{0}:

- Tells us how the matter & energy density of the Universe affects the expansion rate.
- Can include an W
_{L}term (aka a "Cosmological Constant") that enhances the expansion rate.

- H
_{0}= 70 +/- 7 km/sec/Mpc - W
_{0}= W_{m}+ W_{L}=1.0

This value of W_{0}=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.