1. 1 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.

2. 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? Review of the three models 2

3. 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. What were they measuring? 3

4. 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. Why did they measure these? 4

5. 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). What we might expect: a coasting Universe 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. 5 Today Spacing between galaxies (from redshifts) Coasting Lookback time, billions of years ago (determined from SN brightnesses) -15-10-50510

6. 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. What we might expect: a recollapsing Universe 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. 66 Today Spacing between galaxies (from redshifts) Lookback time, billions of years ago (determined from SN brightnesses) -15-10-50510 Recollapsing

7. 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. What we might expect: a critical Universe 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. 77 Today Spacing between galaxies (from redshifts) Lookback time, billions of years ago (determined from SN brightnesses) -15-10-50510 Critical

8. What we might expect: all three possibilities -15-10-50510 Lookback time, billions of years ago (from brightnesses) Today Spacing between galaxies (from redshifts) 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. Recollapsing Coasting Critical Uh…an accelerating Universe! 8

9. 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. So what are the consequences of this discovery?