If you must—absolutely must—search for traces of god in the universe, a great place to start is with its constants. There are several absolutely crucial values for forces, masses, and ratios that hold true everywhere in physical existence (or should hold true) that we typically consider fundamental. That is, they don’t come from first principles, but rather measurements made in a laboratory. Examples include electron mass and charge, Avogadro’s constant (a scaling factor between macroscopic and atomic scales), the Boltzmann constant (relating energy to temperature), and the universal gravitation constant, aka “G.” Also: the speed of light, c.
These numbers are never supposed to change. You might say that they are nature itself, if such a thing as “nature itself” were to exist. The numbers behind the constants look ugly and arbitrary, like G, which is 6.6726 × 10−11. But that ugliness is more of a function of the units we impose. With G, the units are m³·kgˉ¹·sˉ², which is some combination of distance, mass, and time. We could apply different units to G through some equivalency and wind up with a really nice number, like 1 (the nicest number actually).
Ultimately though, "1" is just as ugly and arbitrary as 6.6726 × 10−11. There's no good reason for the strength of gravity to be a whole number. 1 with the same units as 6.6726 × 10−11, however, would be a force of gravity so strong it would be almost impossible to comprehend. The important thing is that 6.6726 × 10−11 (with the correct units) is pretty much the only value of the universal gravitational constant that might allow a universe with life. Too much smaller and mass wouldn't have come together in galaxies; too much bigger and everything in the cosmos winds up as one lump. Same with all of the other constants: much variation means a dead universe, at least by any way of living we can conceive.
Same with all of the other universal constants: too much variation means a dead universe
Science is understandably very interested in the idea that constants might change in the universe. The dials are set for life right now, but what if they change over time and space? I probably get a paper validating the speed of light about every other week in my inbox, and the fine-structure constant remains a subject of fervent speculation and experimentation. That one constant (otherwise known as the coupling constant) contains three other more fundamental constants—charge on the electron, velocity of light, and Planck's constant—and showing some variability in it would give some pretty big bang for the buck. Papers in 2010 and 2011 made strong cases for the fine-structure constant being variable over space and time.
In 1937, Paul Dirac made a case for the strength of gravity being variable over time as well: as time progressed and the universe expanded, G gets smaller. This is based on some interesting observed coincidences between the ratios relating forces and time. Just coincidences, however. A better reason for measuring G is simply that it’s very hard to do. Most attempts come up with different values, and the official value of G is an average of them. Usually measurements aren’t very different, but a pair of recent attempts, one in 2001 and another this year, is quite different. Usually you’d discount a wacky value as an error, but in this case researchers have two different measurements that are very different from the official value, but are very close to each other.
The new value is 240 parts per million bigger than the latest official value, set in 2010. This would be 6.6742 × × 10−11, rather than the currently accepted 6.6726 × 10−11. It’s a significant deviation. What’s more, the newest measurement, courtesy of Terry Quinn of the International Bureau of Weights and Measures, was designed to mimic the 2001 measurement, but with every possible source of error removed an checked against a second method. They should be different, but aren’t. Either both experiments made the same dramatic and very, very hidden error, or gravity is fluctuating.
If it’s the case that the strength of gravity is changing, then there is something else, some other field, influencing it. Gravity in this scenario could be the result of something that’s not quite new but very unknown: dark energy. For now, we can only assume an error and wait for some better verification from another duplicate experiment with even closer scrutiny paid to potential sources of errors. A sigma-5 result demonstrating variable gravity would take a lot of work and verification, and would result in basically a rewriting of astrophysics.