The Madau Plot (2014): When the Universe Made Most of Its Stars

The cosmic star-formation history, summarized by Piero Madau and Mark Dickinson in a 2014 review, shows that the universe made stars fastest about 3.5 billion years after the Big Bang. Since then the rate has fallen steadily. Their “Madau plot” is the standard reference for when the stars we see today were born.

The question

Every galaxy has its own history, but astronomers wanted a single number that changes with time: how many solar masses of new stars the whole universe forms per year, in a given volume of space. Measuring it means counting star formation in galaxies at many distances, and so at many cosmic ages, and correcting for dust that hides young stars from optical telescopes. By the 2010s enough surveys existed, from ultraviolet to infrared, to put the pieces together.

What the paper found

• The cosmic star-formation rate density peaked about 3.5 billion years after the Big Bang, at a redshift of about 1.9. Redshift measures how much light has been stretched by cosmic expansion; higher redshift means farther away and earlier in time.
• Since that peak, star formation has declined exponentially, falling by a factor of e (about 2.7) every 3.9 billion years.
• Half of the stellar mass observed today formed before redshift 1.3. About 25% formed before the peak, and another 25% after redshift 0.7.
• Less than about 1% of today’s stars formed during the epoch of reionization, when the first galaxies ionized the gas between them.
• Star formation and the growth of central black holes rise and fall in step, evidence that galaxies and their black holes evolve together.

How they did it

The review combined measurements from many multiwavelength surveys. Ultraviolet light traces young, massive stars, while infrared light captures the starlight that dust absorbs and re-emits; using both avoids missing hidden star formation. Madau and Dickinson converted each measurement to a common scale, plotted the star-formation rate per unit volume against redshift, and fitted a simple formula to the result. They then checked it against an independent record: the total mass in stars at each epoch, which matches reasonably well the sum of all the star formation that came before.

Why it mattered

The “Madau plot” is one of the most cited results in galaxy evolution, with about 3,000 citations in Semantic Scholar as of October 2026. It turned a scattered set of observations into a single, testable curve that every simulation of galaxy formation must reproduce. Deep fields such as the Hubble Deep Field of 1996 were essential to reaching the early part of the curve, and the Hubble Space Telescope remains a key source of such data.

What we know now

The universe’s most productive star-forming era is long past: we live in a time when star formation is fading. That decline is the first step toward the end of the Stelliferous Era, the age of stars described in the 1997 far-future study by Adams and Laughlin. At the other end of the curve, JWST is now finding bright galaxies very early, such as JADES-GS-z14-0, confirmed in 2024, extending the measurement toward cosmic dawn. Our galaxies guide explains how galaxies formed and changed.

Who wrote it

Piero Madau and Mark Dickinson wrote the review together. Dickinson was also a co-author of the original Hubble Deep Field paper, linking this review to the deep fields that made it possible.

Read the original

Madau, P. and Dickinson, M. (2014). “Cosmic Star-Formation History.” Annual Review of Astronomy and Astrophysics 52, 415-486. doi:10.1146/annurev-astro-081811-125615

Free to read: the arXiv preprint.