Discovering a quantized theory of gravity is possibly _the_ major open question in physics atm. We presume there's a 'graviton' of some sort, but have not observed it yet.
These gravitational waves are predicted by (completely non-quantum) general relativity. Einstein predicted their existence in 1916, but thought we would never have good enough detectors to measure them.
The light is affected only because the distance it has to travel changes when spacetime compresses and expands. So the time it takes from A to B changes, but also the wavelength of the light.
What is used in Ligo etc. is interference. They shoot two perpendicular laser beams that collide in a point. Ordinarily, the lasers interfere at this point and everything is aligned so they cancel each other out almost perfectly. But when a gravitational wave changes the length in one of the arms, the interference isn't perfect anymore and you can detect the laser signal.
To a very very good approximation, a gravitational wave front hitting Earth is a flat plane. This means the detectors cannot see waves that hit the arms at close to 45°, as well as waves that hit the Earth's surface close to vertically at the detector location.
So the indication that "gravity wave happened" is wavelength change? Freaky stuff, I really have a hard time wrapping my head around all this, even after reading layman intros.
Mechanical analogy: there are two very long very fine pitch helical gears that are both suspended from one end and mesh perfectly at the other end. When the gravitational wave makes one gear undetectably longer, we can easily see that the gears no longer mesh.
The statement is also only true for perturbations with respect to a fixed background metric. In principle it is possible for space-time to expand much faster than the speed of light (this is believed to have happened just after the big-bang).
Sufficiently "foamy" ones should act like waves passing through material and cause interference based losses while sufficiently strange waves will travel faster than light, a la the hypothetical warp drive using negative mass.
Last year we got the first expirmental confirmation of this.
The nomenclature here really sucks, because colloquially theory and hypothesis are essentially synonyms. However, it makes no sense to talk about the hypothesis of gravity. This discussion comes up most often around claims like "The theory of evolution is just a theory".
http://adsabs.harvard.edu/abs/1982ApJ...253..908T
But the work on the gravitational wave detectors started much earlier, some fundamental calculations to support the current project were made already in the 1967, 50 years ago! That scientist (Rainer Weiss) got a half of the Nobel Prize in Physics this year for that:
https://www.nobelprize.org/nobel_prizes/physics/laureates/20...
Richard Feynman contributed his (valid) argument in support of the energy actually carried by the gravitational waves at the first American conference on general relativity, GR1, in 1957, 60 years ago:
https://www.forbes.com/sites/startswithabang/2017/03/07/how-...
Regarding the false understanding of the term "scientific theory" by the non-scientific public:
"A scientific theory is an explanation of some aspect of the natural world that has been substantiated through repeated experiments or testing [emphasis mine]. But to the average Jane or Joe, a theory is [wrongly] just an idea that lives in someone's head, rather than an explanation rooted in experiment and testing [the actual scientific meaning]."
https://www.scientificamerican.com/article/just-a-theory-7-m...
The gravitation is also "a scientific theory."
The gravitational waves are the consequence of the General Relativity, the theory introduced in 1915 by Einstein (102 years ago), but which was also based on the centuries of the previous observations and calculations i.e. all the discoveries of the gravitation (Newton 1687, 330 years ago), electricity, magnetism, electromagnetic waves (more than 200 years ago), etc.
"Though these words [like "theory"] may be routinely misunderstood, the real problem, scientists say, is that people don't get rigorous science education in middle school and high school. As a result, the public doesn't understand how scientific explanations are formed, tested and accepted."
That I have to write all this is a kind of confirmation of that statement.
Just the same, the science of global warming is also based on the scientific observations and valid theories since 1824 (almost 200 years ago):
https://en.wikipedia.org/wiki/History_of_climate_change_scie...
Usually this distinction isn’t really a big deal, but in some cases - quantum mechanics, for example - there’s a big difference between the two, with multiple interesting interpretations to consider.
When we don’t make this distinction it creates an opening for people with poor understanding (or, occasionally, bad motives) to nitpick extremely well-established theories on the basis of quibbling about interpretation. I worry about this with respect to climate change specifically: deniers come up with a million reasons that climate change may be partially natural, or that this or that industry may be unfairly maligned, but we can’t get sucked into those debates so much that we forget the big picture painted by the data and models we have.