Time is reversible according a theory put out by stephen hawkins. He said that as the universe expands, time flows in one direction and we remember the past, but not the future. After the universe is done expanding, the universe starts to contract via graviattaional forces and upon contraction, we would remember the future, but not the past. This of course would make sunday confessions obsolete, as you would not remember your past sins.
As far as time and gravity, yes they are related. They are only the same though the same way you would consider light and heat the same. The whole universe, even our thoughts, are made of energies. ALL energies are connected and be converted from one form to another. The basics are like how a magnetic field can create electricity, enough electricity can create light, enough light can create heat (or enthalpy), heat can create pressure, pressure can create heat or electricity or light, etc.
Gravity, time, thoughts, memories are also in that mix and can be converted to and from other forms of energy. If we live in a universe where energy is conserved within a system, then I would have to say that the expansion of universe with acceleration that scientist are able to measure is due, in part, from mankinds population expansion, which in turn expands the amount of thought energy and memory energy within the universe. While thoughts and knowledge increase, the energy for those thoughts is not created out of nothing in a closed system. It comes from somewhere, and being that the universe is expanding with acceleration, that would mean that as we continue to expand, we are approaching the speed of light, and as we do that, time slows for the physical world. For the mental world, it maintains the same energy dynamic, and thus time seems to go faster the older we get (because physical time is slowing down as we get closer to zinging through the U at the speed of light.
If on the otherhand, we live in an endless universe, where energy can be created, then I would have to say that it is mankinds endless thought energy that is the base energy that starts it all. After a thought is conceived, the energy is converted into another energy form (maybe time, maybe gravity, for sure something very small and mostly undetectable, like the energy of thought itself). This thought energy may be the k constant that Einstein needed to balance his Relativity equations.