Lesson 6 of 6 · Cosmic clocks, model comparison & horizons
Build a history that can be revised
10 minute lesson · 3 checks along the way
Your goal for this lessonSeparate cosmic age from lookback time and compare uncertain expansion estimates without turning a discrepancy into a unique discovery.
Words with a dotted underline open a short definition right here in the lesson.
Put observations on a model-dependent clock
is the interval between emission of the light we observe and its arrival now. at emission is the time elapsed since the beginning of the adopted hot-universe chronology. If a model gives a present age of 13.8 billion years and a lookback time of 12.9 billion years for a source, its emission belongs to a cosmic age of 0.9 billion years. These two time labels describe the same observation.
Neither time is automatically the source’s distance today divided by light speed. Distances between unbound regions changed while the photons traveled, and cosmology uses several distance conventions. , luminosity, and angular size constrain different combinations of geometry and expansion history. A reported age or distance should therefore identify the model and uncertainty connecting those observables to the quoted result.
Check 1 of 3
10 pointsUse the reading above. You can try again without losing points.
Use several ways to trace expansion
A links nearby geometric measurements to calibrated stars and more distant supernovae. A uses an independently modeled physical scale to relate apparent size or separation to distance. The CMB constrains an early state; evolving a specified cosmological model forward predicts present quantities. These approaches share the goal of reconstructing history but do not all measure the same observable with the same assumptions.
The concerns disagreement between some locally inferred present expansion rates and values inferred from early-universe data within the standard model. NASA’s April 2026 report described a combined local-distance analysis that continued to show this discrepancy. A tension is a reason to scrutinize calibration, shared systematics, and physical assumptions. It does not identify a particular new component or mechanism merely by existing.
Work through a decision
Quantify a discrepancy before naming its cause
Compare two invented estimates of the same expansion parameter: 67±2 and 73±2 kilometers per second per megaparsec. Assume Gaussian errors, one-standard-deviation uncertainties, and no correlation. Their difference is 6, while the uncertainty of the difference is √(2²+2²)=√8≈2.83 in the same units. The standardized difference is about 2.12. These teaching values are not a current measurement of the Hubble tension.
A two-estimate comparison does not choose between an overlooked error and a new physical model. Nor can the independent-error formula be used unchanged when measurements share calibration information. Write down what a candidate explanation predicts for another observable, then seek an appropriately independent test. Shrinking an error bar without checking how it was obtained can make a graph look more decisive without making the inference more reliable.
Compare the difference with its uncertainty
Original invented example, not a plot of current Hubble-tension measurements. Whiskers show one standard deviation; combining them as square root of summed variances assumes independent Gaussian errors.
Open full-size diagram in a new tab: Compare the difference with its uncertaintyCheck 2 of 3
10 pointsUse the reading above. You can try again without losing points.
An evolving inference is not an observed edge
In July 2026, DESI reported a analysis using absorption and more information from the clustering pattern. Its central result shifted toward the standard ΛCDM model compared with an earlier analysis using the acoustic-scale information alone. This illustrates why hints of changing dark energy are not an established discovery: the method, data combination, and uncertainties matter. The detailed dark-energy question belongs to a separate investigation.
The is limited by which signals can have reached us, not by a photographed wall enclosing all existence. Earlier opacity also limits direct light-based views beyond . Those boundaries leave room for inference from other relics, but not for treating every unobservable proposal as established. A coherent history connects independent evidence, states where the connection depends on a model, and remains open to measurements that discriminate among competing explanations.
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
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