Contribution to cosmogony
An early paper of his made an interesting use of the Anthropic Principle. In trying to work out the routes of stellar nucleosynthesis, he observed that one particular nuclear reaction, the Triple-alpha process, which generated carbon, would require the carbon nucleus to have a very specific energy for it to work. The large amount of carbon in the universe, which makes it possible for life to exist, demonstrated that this nuclear reaction must work. Based on this notion, he made a prediction of the energy levels in the carbon nucleus that was later borne out by experiment.

His co-worker William Fowler eventually won the Nobel Prize for Physics in 1983 (with Subramanyan Chandrasekhar), but for some reason Hoyle’s original contribution was overlooked, and many were surprised that such a notable astronomer missed out. Fowler himself in an autobiographical sketch affirmed Hoyle’s pioneering efforts:

The concept of nucleosynthesis in stars was first established by Hoyle in 1946. This provided a way to explain the existence of elements heavier than helium in the universe, basically by showing that critical elements such as carbon could be generated in stars and then incorporated in other stars and planets when that star "dies". The new stars formed now start off with these heavier elements and even heavier elements are formed from them. Hoyle theorized that other rarer elements could be explained by supernovas, the giant explosions which occasionally occur throughout the universe, whose temperatures and pressures would be required to create such elements.

Rejection of the big bang
While having no argument with the discovery of the expansion of the universe by Edwin Hubble, he disagreed on its interpretation: Hoyle (with Thomas Gold and Hermann Bondi, with whom he had worked on radar in World War II) argued for the universe being in a "steady state". The theory tried to explain how the universe could be eternal and essentially unchanging while still having the galaxies we observe moving away from each other.

The theory hinged on the creation of matter between galaxies over time, so that even though galaxies get further apart, new ones that develop between them fill the space they leave. The resulting galaxy is in a "steady state" in the same manner that a flowing river is - the individual water molecules are moving away but the overall river remains the same. The theory was the only serious alternative to the Big Bang which agreed with key observations of the day, namely Hubble's red shift observations, and Hoyle was a strong critic of the Big Bang.

Ironically, he is responsible for coining the term "Big Bang" in a BBC radio programme, The Nature of Things while criticising the theory; the text was published in 1950. Hoyle and other steady-statesmen offered no explanation for the appearance of new matter, other than postulating the existence of some sort of "creation field", but argued that continuous creation was no more inexplicable than the appearance of the entire universe from nothing, although it had to be done on a regular basis.

In the end, mounting observational evidence convinced most cosmologists that the steady state model was incorrect and that the Big Bang was the theory that agreed best with observations, although Hoyle clung to his theory, mostly through criticizing the accuracy of astronomers' observations. In 1993, in an attempt to explain some of the evidence against the steady state theory, he presented a modified version called "quasi-steady state cosmology" (QSS), but the theory did not capture a significant audience.

The evidence that resulted in the Big Bang's victory over the steady state model, at least in the minds of most cosmologists, included the discovery of the cosmic microwave background radiation, the distribution of "young galaxies" and quasars throughout the Universe, a more consistent age estimate of the universe (for some time, to the considerable embarrassment of the Big Bang theory, the rocks in the earth appeared to be older than the universe) and most recently the observations of the COBE satellite, which showed that crucial disturbances in the early universe allowed for the creation of galaxies.

Media appearances and scientific honours
Hoyle appeared in a series of radio talks on astronomy for the BBC in the 1950s; these were collected in the book The Nature of the Universe, and he went on to write a number of other popular science books. He wrote some science fiction; most interesting is The Black Cloud in which it transpires that most intelligent life in the universe takes the form of interstellar gas clouds, who are surprised that intelligent life can form on planets, and a television series A for Andromeda. In 1957 he was elected a Fellow of the Royal Society, and he was knighted in 1972.

Rejection of chemical evolution
In his later years, Hoyle became a staunch critic of theories of chemical evolution to explain the naturalistic Origin of life. With Chandra Wickramasinghe, Hoyle promoted the theory that life evolved in space, spreading through the universe via panspermia, and that evolution on earth is driven by a steady influx of viruses arriving via comets.

In his 1981/4 book Evolution from Space (co-authored with Chandra Wickramasinghe), he calculated that the chance of obtaining the required set of enzymes for even the simplest living cell was one in 1040,000. Since the number of atoms in the known universe is infinitesimally tiny by comparison (1080), he argued that even a whole universe full of primordial soup wouldn’t have a chance. He claimed:

The notion that not only the biopolymer but the operating program of a living cell could be arrived at by chance in a primordial organic soup here on the Earth is evidently nonsense of a high order.

Hoyle compared the random emergence of even the simplest cell to the likelihood that "a tornado sweeping through a junk-yard might assemble a Boeing 747 from the materials therein." Hoyle also compared the chance of obtaining even a single functioning protein by chance combination of amino acids to a solar system full of blind men solving Rubik's Cube simultaneously.

These analogies have been rejected by biologists as a straw man argument. Richard Dawkins, for example, wrote in The Blind Watchmaker:

“If he'd said 'chance' instead of 'natural selection' he'd have been right. Indeed, I regretted having to expose him as one of the many toilers under the profound misapprehension that natural selection is chance.”

Some speculate that evolution of complex systems can occur by means of a ladder of stratified stability. The Nobel Prize-winning chemist Manfred Eigen (beginning in 1971 with an influential theoretical paper) and his collaborators have considered in some detail how a genetic code could get going.

Other controversies
Further occasions on which Hoyle aroused controversy included his questioning the authenticity of fossil Archaeopteryx and his condemnation of the failure to include Jocelyn Bell in the Nobel Prize award recognising the development of radio interferometry and its role in the discovery of pulsars. Hoyle played an important role in determining the nature of the pulsing radio signals (from the pulsar), but was also excluded from the prize. Hoyle had a famous heated argument with Martin Ryle of the Cavendish Radio Astronomy Group about Hoyle's Steady State Universe which somewhat restricted collaboration between the Cavendish Radio Astronomy Group and the Institute of Astronomy during the 1960s.