I wrote many times about kinetic and potential energy. A gravity is a potential energy. Mainstream claims the gravity is a metric curvature of the space. In String Theory are looking for a graviton mediating the gravity in an empty space. This direction of the math is not effective for now.
What curves the space if there is nothing ?

According to Casimir effect we know there is a minimum energy in a space. We call it Zero Point Energy, Vacuum Energy, Space-time, Ether, and many other words. There are oscillations (Schrondiger's Zitterbewegung) inwards schrinking with a positive energy and it causes inwards warping curvature of the space.

My suggestion is that the minimum space energy is because of the gravitational field. Every massive particle oscillate and this inwards shrinking oscillations are mediated by the Zero Point Energy or Virtual Particle Field or other words.

The density of the space oscillations between two masses is greater than behond because an inverse square distance. This shrinking oscillation causes a tension we call GRAVITY.

This idea shows an another picture of the shape of the gravitational field. It suggests an additional energetic field between masses (galaxies, galaxy clusters). Such a cylindrical consolidation of the energy in a Cosmic space far away behind a galaxy halo may explain a Dark Matter effect.
It will depend on mass distribution, shape of the galaxy and angle of the rotation plane of the galaxy according to another galaxies.

What retains my PC on the table is not the curvature of space. It's earth gravity.

What's the difference?

With or without space curvature, my PC remains on the table, attracted by earth's gravity.

As for space, perhaps not the space per se which is curvated. What is "curvated" is what is inside the space, call it vacuum's energy, ether or whatever, that changed it's distribution due to the presence of the mass.

The distribution of space's content has changed due to mass, not it's geometry.

But they could be the same thing.

One nit, it's not space curvature, it's space-time curvature. There is a difference.

If the space's content change it causes a change of the geometry too.
It is mainstream science.
The difference is between a String Theory (Mainstream today) - the particles are mediating all interactions in an empty space and Quantum Loop Gravity, Heim Theory where the discrete space-time field mediates the interactions and creates geometry.
How do you explain gravity if there isn't graviton ?
What are the particles build of if they move in an empty space ?

I disagree.
Take an euclidian space. fill it with glass with changing index.
Light bends kuz of changing index, not kuz of space geometry that remains euclidian. Am I right ??

We still didn't detect gravitons, nor ... gravitinos , deuh !!
No experimental evidence yet.

In a really empty space, ie. with no Casimir energy nor matter of any kind, than we have to admit a change in geometry to explain the light bending when passing near a mass.
The problem is, such an empty space is not physical. I must be filled with something.

An empty space is not physical. It must be filled with something, call it vacuum energy ( Casimir) or ether, or whatever.

You are right in this case but I wrote about a curvature of the space in a gravitational field. If you change a mass you change a gravitational field too. A stronger gravitational field changes a curvature of the space-time.

OK. Matter curvates S-T.
How about energy ?
Consider many laser beams focusing on a single point. We have here a concentration of energy. Does this point curvate S-T ?

Yes. The energy curves S-T. We have discus it earlier.
If two hipothetical Black Holes or Neutron stars collide one made of matter and another made of antimatter the result will be one Black Hole made of annihilated matter (energy).
In our Universe a Dark Energy makes a curvature of S-T so we have together with a baryon rest mass a critical density that is enough for a flat geometry.

Perhaps gravity is not a form of energy.