The duality I refer to is not the wave/particle duality, but the idea is the same: we see two apparently contradictory phenomena occurring at the same time.
Whether light is a particle or wave was debated for centuries, and the argument was finally resolved by recognizing it is both. In a parallel manner, Einstein famously “solved” his equations of GR and discovered that every possible universe would either contract or expand, depending on its initial conditions. When giant telescopes were developed, pointed skyward and the Hubble expansion was unveiled, the reaction was, “Ah hah! The universe is expanding after all!” But this is a case of not seeing the forest for the trees.
When we look to distances of less than about 5 Mpc, we do not see expansion. We see contraction. The Andromeda galaxy is on a collision-course with the Milky Way, and all the mass within the entire Local Group is caught in the local gravitational grip, pirouetting about the local center of gravity, slowly spiraling inwards. Throughout this local region, gas is contracting in myriad regions, forming new stars; and virtually every visible point of light in the sky is a center of local gravitational contraction, furiously radiating away energy as the gravitational field continues crushing matter in its ever tightening grip.
What model includes this?
Take any
mainstrea model that includes math, and you will see only one distance term. It is implied, but not stated, that r in the referenced equations is > 5 Mpc. If you use an r of less than that, say 1 Mpc, the approximate distance of Andromeda, you get an answer that is completely wrong, because our local region of the universe does not participate in the cosmic expansion.
Now we take this observation and apply the Copernican Principle: we assume there is nothing special about our position, and most observers in the universe see the same thing. And in fact, we can confirm the CP by looking carefully beyond the 5 Mpc inflection point (the distance at which contraction transitions to expansion): we see galaxies colliding and clusters of galaxies that are—by all appearances—caught in a local gravitational tango, same as we are in the Local Group.
The duality is there, staring us in the face. Like the cheating spouse: how could we miss it for so long? Like the wave/particle duality, it is not one or the other. The universe is not contracting or expanding, it is doing both: two-timing us! Space is expanding at the ends of the universe, to be sure, but it is contracting right before our eyes.
As for the math, again, it is simply missing-in-action
I have argued that if you include it in your model, local contraction will show up in GR—as currently formulated—as “dark energy.” But that is just my guess. All I know is duality is not in the mainstream models. If it were, you would not be asking what it is.
The duality is reality. Once you see it, it is drop-dead obvious and it becomes impossible to not-see. But it is not yet seen by the mainstream and is not included in any model.