Normally push gravity is associated with LeSage. However LeSage, being particulate has its problems, including not being able to explain how the mass of an atom doesn't increase over time. But by remodelling push gravity as a wave EMR based model one can avoid these theoretical problems. To do this one has to discard any relativistic or Big Bang assumptions.
As the non expanding universe is infinite in size and age, all matter will have relative motions between different regions of space. And one can then postulate that mass in one part of the universe can move at many times the speed of light towards or away from another. This in turn means that emr emitted from one part will also have great relative speed differences to another. So that from any one point an observer will be experiencing isotopic radiation with radiation speeds of many times less than or greater than c. It is this wave emr radiation that in total can be the basis for push gravity. It pushes in and passes through all mass from all directions. Imbalances occur when an observer is near any other mass. For instance the moon experiences from among other sources, a relative imbalance of this push gravity radiation from earth. More radiation pushes the moon down towards the earth than comes up through the earth. Hence an imbalance and the moon is 'pushed' towards the earth.
It is worth pointing out that the push model has no definite speed of gravity but then again it isn't infinite. It must be a range of finite speeds but still on average, much greater than c.
To avoid the theoretical pitfalls of a particulate LeSage gravity this emr based wave gravity must not be absorbed by atoms. It must pass through. Modelling how exactly it can interact with mass while it passes through can only be speculative, but the best scenario is that some directional anisotropic gravity radiation that passes through the atom gets re-radiated isotropically as it passes through. Explaining not only the actual push mechanism but also the other observed forces associated with atoms. Like the strong and electroweak and magnetic forces. While also still being able to explain how no wave energy is stored in the atom itself as it passes through.
Plus, as this is a wave based model, the atom itself can be thought of as a standing wave or nodal point in this infinite sea of energy. Something that is in fact a more correct explanation than other models like the particulate Standard model. Because as the closer we get to looking in macroscopic detail at atoms and electricity, the more wave like and resonant these phenomena appear. As a wave only push model describes.
A good way to visualise a push model is to use the analogy of a vibrating tray of water. Notice that raised nodal points of water appear. These are standing waves in the water created by the passing wave energy from the vibrations. They are analogous to the atom. And like the atom, these raised nodal points in the water are created by energy passing through. No energy stays at one point and builds up. Just as a wave only atom is the sum of many different frequencies of passing wave energy interfering with each other and creating a standing wave nodal point at a specific point in space. Maybe studying vibrating wave tanks would increase our understanding of this model. Research could see if manipulating these nodal points in the vibrating water could create effects similar to gravitational , strong and electroweak etc mechanisms.
One criticism of a push model, is that gravity has to be instantaneous to make its predictions match the observed orbital motions of planets etc. And push gravity by its nature does have to have a finite speed as I have mentioned earlier. But if one looks at the nature of a push model it becomes apparent that in fact the push mechanism will give instantaneous effects, as if it had an infinite speed. This is because if one looks at any point in the gravitational field of any object like a planet, it will at any point in its gravitational field already have the pressure imbalance I have mentioned earlier. Some wave gravity will already be at that point pushing up and more will already be at that point pushing down. You don't have to move into a new position in a orbit around earth to wait for earth to detect you and then reach out at a finite speed to pull you in. There already is push gravitational radiation pushing and pulling at any point in any gravitational field.
An important analogy would be: If you move across the paths of light rays at a distance from a light source, you don't have to wait for light to travel out at c from the source each time you move to a new position. *There will already be radiation* at each point in your path that has already left the source and travelled out to you.
This is an important distinction because it allows a push model with a finite speed to always have an instantaneous gravitational effect at any point in any gravitational field.
Another criticism of push gravity is that to have this imbalance occur in a gravitational field and be able to explain the larger fields near stars then it must infer a sea of great invisible energy permeating the universe which isn't normally detected. In other words each observer would have tremendous forces travelling through their bodies from all directions. This is an unfair criticism as it comes from theorists who at the same time postulate EXACTLY the same thing when speculating about quantum foam. The invisible sea of energy popping in and out of existence at any point in the vacuum.