Explain the big bang model of the origin and history of the universe and evaluate the evidence that the universe had a beginning and is expanding

Learning goal: Describe the big bang model: a hot, dense beginning roughly 14 billion years ago, expansion and cooling, the formation of atoms, then of gas clouds, stars and galaxies; explain why the universe is not infinitely old; give evidence that the universe is expanding, including the distance-redshift relationship and the cosmic microwave background; use the raisin-cake and balloon models and state what they cannot show; and explain how technology extends what we can observe.

The model in outline. The big bang model is the broadly accepted scientific account of the origin and history of the universe. According to it, the part of the universe we can observe today was once extremely hot and dense, and about 13.8 billion years ago, by current measurements, it began expanding rapidly. Older sources, including some curriculum documents, quote "12 to 14 billion years" or "13.7 billion years"; those are earlier estimates of the same quantity, which better measurements have since narrowed. This lesson rounds the age to 14 billion years where a round number is convenient, as in the cosmic calendar. As the universe expanded it cooled. Once it was cool enough, atoms could form, mostly hydrogen with some helium. Gravity then pulled the gas into clouds, the clouds collapsed into stars, and stars gathered into young galaxies. Expansion has continued ever since. The model does not describe an explosion of material into empty space that already existed; it describes space itself stretching, carrying galaxies apart.

A beginning, not an infinite past. A universe that is expanding today was smaller in the past. Run the expansion backward and everything crowds together, which points to a beginning a finite time ago. Other measurements agree: the oldest stars we can date are younger than 14 billion years, and no object has been found that is older than the universe the model describes. The universe is not infinitely old. What came "before" is not a question the model answers, and honest teaching says so.

Evidence 1: the distance-redshift relationship. When astronomers spread the light of a distant galaxy into a spectrum, the dark lines produced by its elements appear shifted toward the red end compared with the same lines in a laboratory. In this course the redshift is explained as a Doppler effect: the galaxy and the observer are moving apart, so the arriving waves are stretched. (For very distant galaxies astronomers describe the same stretching as expanding space lengthening the light's wavelength on its way to us; either description gives the same pattern, a larger redshift for faster recession.) In the 1920s Edwin Hubble compared redshifts with distances and found a pattern now called Hubble's law: the farther away a galaxy is, the larger its redshift, so its speed of recession is proportional to its distance. Consider an invented but proportional data set: galaxies at 50, 100, 150 and 200 million light-years receding at 1100, 2200, 3300 and 4400 km/s. Every doubling of distance doubles the speed; the graph of speed against distance is a straight line through the origin. That is exactly what uniform expansion predicts, and it is the single most direct evidence that the universe is expanding. The numbers here are illustrative; real surveys scatter around a line and measuring distances is difficult work.

Evidence 2: the cosmic microwave background. If the universe was once hot and dense, the glow of that early period should still be arriving from every direction, stretched by expansion to long wavelengths. Radio instruments detect exactly that: a faint, nearly uniform microwave glow from every part of the sky, with the spectrum of an object at a temperature of about 2.7 K, a few degrees above absolute zero. It was found in the 1960s, and its uniformity and tiny ripples match the model's predictions in detail. No competing explanation proposed so far accounts for a whole-sky glow with this spectrum.

Evidence 3: the mix of light elements. The model predicts that, in the first minutes, nuclear reactions in the hot early universe made hydrogen, helium and a small amount of lithium, and no heavier elements, before any star existed; far more helium was made in those first minutes than all the stars have made since. Stars have since made heavier elements, but the starting mix is a fingerprint of the hot beginning.

A worked model: the raisin cake and the balloon. Picture a loaf of raisin bread rising in the oven. Each raisin sits still in the dough, yet as the dough expands every raisin moves away from every other one. A raisin 2 cm from you moves to 4 cm as the loaf doubles in size, a gain of 2 cm; a raisin 6 cm away moves to 12 cm, a gain of 6 cm, three times as much in the same time. From any raisin, farther raisins recede faster, in proportion to distance, which is Hubble's law. And no raisin is special: every raisin sees the same pattern, so the observation that everything recedes from us does not mean we are at the center. A balloon with dots drawn on it shows the same thing as it inflates. Both models have limits. The loaf has an edge and a center and the balloon has an inside and outside, while the model of the universe has neither; the raisins do not expand, which is the right feature, since galaxies bound by gravity do not stretch with space; and neither model shows time running backward to a hot dense start.

A cosmic calendar. To grasp the time scale, squeeze the roughly 14 billion years since the beginning into a single 12-month calendar. One day then represents about 38 million years and one hour about 1.6 million years. The beginning is midnight on 1 January. The first stars and small galaxies, forming within the first few hundred million years, appear in the first two weeks of January. The Sun and Earth, formed about 4.6 billion years ago, arrive around 3 September. The earliest single-celled organisms in the fossil record, about 3.8 billion years ago (a figure with real uncertainty), arrive about 24 September. The extinction that ended the age of the large dinosaurs, about 66 million years ago, is on 30 December. Modern humans appeared only a few hundred thousand years ago; estimates vary, and taking 300,000 years as a model value puts them about 11 minutes before midnight on 31 December. All recorded history fits into the last minute. Every date depends on the approximate values chosen; the point is proportion, not precision.

How we know: instruments that reach where we cannot go. No one can observe the early universe directly, and almost nothing in astronomy can be handled or measured in a straightforward way. Technology fills the gap. Telescopes on the ground and in orbit collect light across the whole electromagnetic spectrum: visible, radio, infrared, ultraviolet and x-ray, each revealing different objects and events. Because looking far away means looking back in time, deep images show galaxies as they were billions of years ago. Computers manage enormous data sets and the calculations behind models. Space probes return data and even samples from the solar system, allowing the relative ages of planetary surfaces to be estimated: craters accumulate with time, so on one solid body with no thick atmosphere, such as the Moon, a heavily cratered region has generally been exposed longer than a smooth one, whose earlier craters were erased by lava flows or other resurfacing. The comparison works only between comparable surfaces: erosion, an atmosphere and the rate of resurfacing differ from one body to another, so crater counts on unlike bodies cannot be compared directly. Particle accelerators reproduce, for a fraction of a second, the energies of the early universe before stars formed, letting the model be tested in the laboratory.

Investigation: a stretching-band model of Hubble's law. Materials: a wide rubber band or strip of elastic, a meter stick, a marker, paper clips. Steps: with the band relaxed, mark points at 2, 4, 6 and 8 cm from a chosen "home" mark; stretch the band steadily to double its length while a partner counts 5 s; measure each mark's new distance from home and compute the change in distance and the average recession speed in cm/s for each mark. Record a table and plot speed against original distance. A straight line through the origin, with the 8 cm mark receding four times as fast as the 2 cm mark, supports the claim that uniform expansion produces speed proportional to distance. Then repeat using the 4 cm mark as home to show that any point sees the same law. What the model cannot show: the three-dimensional stretching of space, the cooling of the universe, or redshift itself; it models only the distance-speed pattern.

Worked example 1 — reading a distance-speed table. Invented data: galaxy A at 50 million light-years recedes at 1100 km/s; B at 100 million light-years at 2200 km/s; C at 150 million light-years at 3300 km/s; D at 200 million light-years at 4400 km/s. Speed divided by distance is 22 km/s per million light-years for every galaxy, so the four points lie on one straight line through the origin: recession speed is proportional to distance. A galaxy at 300 million light-years would be predicted to recede at 300 × 22 = 6600 km/s. This proportionality is what uniform expansion produces, and it is the pattern Hubble found. Real measurements scatter around such a line.

Worked example 2 — the raisin-cake arithmetic. A loaf doubles in size in 30 minutes. From one raisin, a neighbor 3 cm away ends up 6 cm away, moving 3 cm in 30 minutes, 0.1 cm per minute. A raisin 9 cm away ends up 18 cm away, moving 9 cm in 30 minutes, 0.3 cm per minute, three times faster because it was three times farther. Now stand on the second raisin instead (all three raisins start in a line, at 0, 3 and 9 cm): the first raisin moved 3 cm away from it, from 3 cm to 6 cm, and the far raisin, which started 6 cm from it, moved 6 cm, from 6 cm to 12 cm. Every raisin gets the same rule, speed proportional to distance, so none can claim to be the center of the expansion.

Worked example 3 — placing an event on the cosmic calendar. Map 14 billion years onto 365 days, so one day is 14,000 million years ÷ 365 ≈ 38.4 million years. The Sun formed about 4600 million years ago: 4600 ÷ 38.4 ≈ 120 days before the end of the year, so about 365 − 120 = 245 days have passed since midnight on 1 January. Counting 245 whole days from 1 January brings the calendar to the start of 3 September (1 January plus 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 = 243 days is 1 September). Modern humans, taking the model value of 0.3 million years ago: 0.3 ÷ 38.4 ≈ 0.0078 day, and 0.0078 × 24 × 60 ≈ 11 minutes before midnight on 31 December. Using the measured 13.8 billion years instead of the rounded 14 shifts the September dates by a day or two (the Sun moves to about 1 September); the proportions barely change.

Worked example 4 — why the microwave background counts as evidence. A student asks why a faint radio glow proves anything. The reasoning: the model predicts that the early universe was hot enough to glow, that expansion since then stretched that glow to microwave wavelengths, and that it should arrive with almost the same brightness from every direction because the early universe was nearly uniform. Observation: a whole-sky microwave glow with the spectrum of a 2.7 K object, uniform to a very high degree with tiny ripples. Prediction and observation match, and the rival ideas put forward so far do not predict it. A prediction made before the observation, then confirmed, is strong evidence in any science.

Representation task: a graph and a calendar. Part 1: plot the invented distance-speed data (50, 100, 150, 200 million light-years against 1100, 2200, 3300, 4400 km/s) on labeled axes, draw the line of best fit, state its slope with units and write two sentences on what the straight line through the origin shows about expansion. Part 2: build a cosmic calendar for 14 billion years on 12 months. Show the arithmetic for one day's worth of time and place at least six events: the beginning, the first galaxies, the Sun's formation, the earliest evidence of life, the end of the large dinosaurs and modern humans, each with the approximate age you used and a note that the ages are rounded.

Independent performance: an evidence brief on the expanding universe. Write a two-page brief that answers "How do we know the universe is expanding and had a beginning?" Success criteria: the big bang model is stated in your own words, including the age as an approximate figure and the sequence expansion, cooling, atoms, gas clouds, stars, galaxies; at least three lines of evidence are described (distance-redshift relationship, cosmic microwave background, light-element abundances), each with what was predicted, what was observed and why they match; the raisin-cake or balloon model is explained together with two things it cannot show; the argument that the universe is not infinitely old is made from the evidence, not asserted; and one technology (a telescope operating outside visible light, a space probe or an accelerator) is explained as a way of collecting data we cannot obtain directly.