Curvature measures
Topics
The Runaway Universe
Review of models
Just what were they measuring?
What did they expect?
What did they find?
Motivation
Discover the first incontrovertible evidence of the
Universe’s accelerating expansion.
1
Review of the three models
Remember from last class that there were, in the conventional model of
the inflationary Big Bang, three possibilities for the outcome of the cosmic
expansion….
1. Recollapsing Universe
– The matter density exceeds the critical density;
– The Universe is closed and will recollapse.
2. Critical Universe
– The matter density equals the critical density;
– The Universe is flat and only stops expanding at infinite time.
3. Coasting Universe
– The matter density less than the critical density;
– The Universe is open and, while continuously slowing, never stops.
For years, astronomers argued these three cases. Which was it?
Inflation pushed the density to just about the critical density, but how fast
exactly, was our Universe expanding, and what was its fate?
2
What were they measuring?
At the Cerro Tololo Inter-American Observatory (Chile)…
Schmidt et al. conducted a survey of galaxies looking for
transient objects that appeared to be Type Ia supernovae.
These observations were primarily to find candidate objects for
further study.
At the Keck (Hawai’i) and MMT (Arizona)…
Colleagues followed up with high resolution spectra to confirm
the identities of the Type Ia supernovae candidates, and to
determine their redshifts.
Via the Hubble…
The supernovae were observed to obtain extremely high accuracy
magnitudes.
3
Why did they measure these?
At the Keck and MMT…
Once the cosmological redshifts were measured, they could be used to
determine how much space has expanded since the photons first left the
supernovae.
The distances to each galaxy can be thought of as a measure of the
changing size scale of the Universe.
Via the Hubble…
The extremely accurate brightness measurements could be compared to the
power outputs expected for Type Ia supernovae.
Since Type Ia supernovae are extremely reliable standard candles, the
measurements were used to determine how long the light has been
traveling through space, getting dimmer as it traveled ever further from the
source, via the inverse square law. This is called the lookback time.
4
What we might expect: a coasting Universe
Spacing between
galaxies
(from redshifts)
Today
In the coasting Universe, space has always expanded at a constant rate.
Two points in the Universe, separated by a distance D, would recede from each
other at a constant rate (ΔD/Δt).
The further we look back in time, the smaller the distances between the galaxies
should be. In the future, these distances should increase linearly in time.
-15
-10
-5
0
5
10
Lookback time, billions of years ago
(determined from SN brightnesses)
5
What we might expect: a recollapsing Universe
Spacing between
galaxies
(from redshifts)
Today
In the recollapsing Universe, space expanded much faster in the past; it will stop
expanding in the future; it will eventually reverse its expansion in the future.
Two points in the Universe, separated by a distance D, separated very rapidly in the
early universe; in the future they will stop moving apart; after that they will fall
back towards each other.
In the past, the galaxies should have been much closer together (since they used to
be moving apart much faster); in the future, they will return towards each other.
-15
-10
-5
0
5
10
Lookback time, billions of years ago
(determined from SN brightnesses)
6
What we might expect: a critical Universe
In the critical Universe, space has always been expanding, but at a decelerating
rate.
Two points in the Universe, separated by a distance D, would be getting further
from each other at an ever-slowing rate.
Spacing between
galaxies
(from redshifts)
Today
In the past, the galaxies should have been closer together than they would have
been, had they been moving apart at the same speed the whole time.
-15
-10
-5
0
5
10
Lookback time, billions of years ago
(determined from SN brightnesses)
7
What we might expect: all three possibilities
Spacing between galaxies
(from redshifts)
Today
This is what Schmidt et al. investigated. They were hoping to discover which of
the three fit our Universe—the expectation was to find a critical-to-coasting case.
-15
-10
-5
0
5
10
Lookback time, billions of years ago (from brightnesses)
8
So what are the consequences of this discovery?
The expansion of the Universe is accelerating—there is some kind of
anti-gravity effect in operation.
An old idea—Einstein’s cosmological constant, must be revived, and
“Dark Energy” was born.
Things in cosmology suddenly got a whole lot weirder.