Many of the equations of physics include a dimensionless physical constant, included to make the equation match real-world measurements.
Mathematical modelling of the universe, beginning with a hot big bang, and using the known laws of physics, has shown that if any of several physical constants were only slightly different to their measured values the universe would not be conducive to the establishment and development of matter, astronomical structures, elemental diversity, or life as it is presently understood. This observation has come to be known at the 'fine-tuning' of the universe.
A simple (but not particularly good) example is the strength of the gravitational force, which is described by the following equation:
Where...
Fg = force of gravity (N)
G = universal gravitational constant = 6.673 x 10-11 N m2/kg2
m1 = mass of object 1 (kg)
m2 = mass of object 2 (kg)
r = distance between centre of mass of objects (m)
If the value of G was much higher, the stronger force of gravity would have caused the universe to collapse on itself too quickly for life to have appeared. If the value of G was much lower, the force of gravity would be too weak to produce galaxies or stars, which are essential for life.
British physicist Stephen Hawking held the prestigious position of Lucasian Professor of Mathematics at the University of Cambridge between 1979 and 2009. In his best known book Hawking observed:
"The laws of science, as we know them at present, contain many fundamental numbers, like the size of the electric charge of the electron and the ratio of the masses of the proton and the electron... The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life."
Stephen Hawking, 1988. A Brief History of Time.
After noticing a great deal of fine-tuning in his research into the origin of the elements, Fred Hoyle (who proposed a naturalistic theory of cosmology in 1948) remarked:
"A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question."
Fred Hoyle 1982. Annual Review of Astronomy and Astrophysics
In the last few decades physicists have realised that life in the universe is incredibly unlikely... and yet we are here. The 'fine-tuning' idea evokes a rather crude image of God carefully setting the many dials of his universe-making machine to the right levels for the universe to eventually bring about life. This image is more deistic than theistic, however, it does reveal the purposefulness of God in creation.
Naturalists face the challenge of mounting a convincing argument for the conditions necessary for life in the universe arising solely from chance and chemistry. They do so firstly by suggesting that a few of the physical constants are not as fine-tuned as generally thought and secondly by postulating the existence of multiple universes.
A universe made for me? Cosmos
Argument for fine-tuning Biologos
Argument against fine-tuning Victor J. Stenger