Motivation behind the theory of cosmological perturbations What is the main motivation behind the theory of cosmological perturbations? Is it the observational data, observational hints, or perhaps the theory of inflation?
 A: None of those. If you mean by motivation what it means in English, what was the reason for doing perturbations, it's more or less straightforward. 
It was to try to find approximate solutions to how deviations from an ideal homogeneous and isotropic universe evolves. Since people figured that probably gravity had something to do with it (not a very hard thing to think), and in the large going back to the past the universe still looks homogeneous and isotropic, but we also do see very strong inhomogeneities in the 'small', like stars, galaxies and clusters, they went to earlier cosmological times and put in small perturbations and saw how they grew. 
Even before cosmology there were perturbation calculations in Newtonian gravity to model and help determine how stars and galaxies formed. 
So perturbations is just a normal way of doing the physics of changes in some semi-stable solution, and see how other things happen, particularly where exact solutions with those kinds of irregular distributions are just not possible. It was not just Einstein, there is also the raw numbers of particles and bodies, and you need to also include the nuclear 
and electromagnetic interactions.  
The only reason inflation enters in is because it is a way to get to an initially mostly homogeneous, isotropic, and flat universe. The the question is what are the initial sources of the perturbations, and at those energies and temperatures it came down to quantum fluctuations of the fields, with sizes approximately the Planck size. 
From that point on you can treat cosmology without reference to inflation. Some people simply call that post-inflation the beginning of the Big Bang. 
