Lesson 4 of 6 · Accelerated expansion
Accelerated expansion
10 minute lesson · 3 checks along the way
Your goal for this lessonDistinguish expansion from acceleration and explain how calibrated distance observations test cosmic expansion history.
Words with a dotted underline open a short definition right here in the lesson.
Compare expansion at different times
An expanding universe has increasing large-scale separations between freely following, sufficiently separated regions. Cosmologists describe this with a , a(t). For a fixed , physical distance is proportional to a. Acceleration means that the rate of increase of this scale factor grows with time. Expansion and acceleration are therefore different claims: a universe can expand while its expansion slows.
This description applies to the large-scale cosmological model. It does not say that atoms, people, or a gravitationally bound solar system grow with the scale factor. Local binding and local motions require their own treatment. Even the needs care: H is the scale factor’s rate of change divided by a. H can decrease while a still has positive acceleration, because its denominator is increasing too.
Use a distance–redshift comparison
In 1998, two research teams used Type Ia supernova observations to infer accelerating expansion. Such explosions are useful distance indicators after empirical standardization, including relationships between brightness and light-curve behavior. They are not perfectly identical light bulbs. Observed brightness, spectra, dust, calibration, and sample selection all enter the analysis. Researchers compare standardized brightnesses and redshifts with predictions from cosmological models.
Relative to the comparison models tested, distant supernovae appeared fainter, indicating larger inferred luminosity distances than expected without acceleration. This was a population-level inference about expansion history, not a movie showing one galaxy speeding up. is defined through the relationship between source luminosity and received flux. In an expanding universe, it is not interchangeable with present separation or with light-travel time multiplied by light speed.
Check 1 of 3
10 pointsUse the reading above. You can try again without losing points.
Work through a decision
Read a deliberately simplified expansion record
An invented model gives scale factors 1.00, 1.10, and 1.30 at three equally spaced times. The first interval adds 0.10 and the second adds 0.20. Therefore the second interval’s average rate of scale-factor increase is twice the first. These three values do not by themselves establish that the instantaneous acceleration remained positive at every intervening moment. They support a comparison of interval averages only.
Now consider two regions with a fixed comoving separation chosen so their physical separation is 100 model units when a = 1.00. Their separations become 110 and 130 units at the other two times. The corresponding increases are 10 and 20 units. These numbers are an instructional model, not a fit to supernova data. They make explicit which distance definition, equal time intervals, and fixed-comoving-coordinate assumption support the calculation.
Compare rates over equal intervals
These fictional samples compare interval averages. No curve between the points is specified, so they do not prove positive instantaneous acceleration at every moment. For fixed comoving coordinates, physical separation is proportional to a.
Open full-size diagram in a new tab: Compare rates over equal intervalsCheck 2 of 3
10 pointsUse the reading above. You can try again without losing points.
Name the unknown without pretending to solve it
Within general relativity, a component with sufficiently negative pressure can drive accelerated expansion when its contribution is large enough. A is one possibility; evolving fields are others. “” is a name for the explanatory component in such models, not a detected fuel pouring between galaxies. Alternative descriptions can instead modify gravity, but they must also pass other precise gravitational tests.
A robust assessment compares several observables. Supernova distances, characteristic clustering scales, the cosmic microwave background, and structure growth constrain overlapping pieces of the history. Agreement matters, but shared calibrations and model assumptions must still be tracked. The acceleration evidence motivates a deep physical question; it does not justify assigning the same cause to galaxy rotation, nor does it make and dark energy interchangeable substances.
Check 3 of 3
10 pointsUse the reading above. You can try again without losing points.
Put it together
Your lesson progress
Each check connects to a part of the story. Complete all 3 to earn your 25-point lesson bonus.
Go to the source
Explore the evidence behind this lesson. These optional readings and videos open in a new tab.
- Read: Riess and colleagues: supernova evidenceOriginal 1998 research abstract and analysis.
- Read: Perlmutter and colleagues: the supernova comparisonIndependent research using 42 high-redshift supernovae.
- Read: Particle Data Group: dark energyTechnical definitions of acceleration, pressure, and expansion-history tests.