Why hasn't the graviton been discovered yet? A thought experiment could shed some light on this question. Imagine a universe with only a Higgs field and nothing else. No strong, weak or electromagnetic interactions, no spacetime as we understand it. The basis of this universe is just the Higgs, so the only boson available is the Higgs boson. It's true the Higgs can decay into other particles, but let's focus on it while it is a Higgs.
Now, in such a universe, there should be no gravity, since there are no gravitons, right? (We performed a similar thought experiment in a previous post involving photons. Click here to read all about it.) Let's lay out the mathematics and see. First, we define the variables:
If we find gravity in our Higgs-only universe, that would explain why the graviton hasn't been found--it isn't necessary--so let's begin with the Higgs Lagrangian (L) at equation 1 below. At 2 we convert the Lagrangian to the Hamiltonian (H). To make the math less cumbersome we set the kinetic term equal to chi at 3.
We make a substitution at 4. Equation 5 is a Hamiltonian (H') with the same energy as H, but a different mass and kinetic energy. Equations 4 and 5 represent two adjacent fields whose centers of mass are r distance apart. At 6 we show the equality or conserved energy of the two fields. At 7 and 8 we equate the kinetic and potential energy differences.
Here is an overly simplified, crude diagram for illustrative purposes only:
As you can see the two adjacent fields are outlined with imaginary boxes and labeled blue (high kinetic energy/low mass) and red (low kinetic energy/high mass). The white dots represent the masses. Now, equation 8 fails to take into account distance r, so let's convert mass m as follows:
At equation 11 we have distance r where we want it. Equation 11 is the value of the kinetic-energy difference between the two fields. Classical kinetic energy is a function of velocity squared. What we want to know is the value of the velocity squared:
Now that we know the value of velocity squared, we can do one more step and determine the value of the gravitational constant for this Higgs universe (Gh):
We made a substitution at 14 above and end up with Newtonian gravity! And no gravitons! Equation 14 reveals that gravity is the net velocity squared of kinetic energy differences. If we divide both sides by another r, we get gravitational acceleration. Given these results, one could postulate that gravity is the net motion resulting from motion differences. And motion differences are caused by mass differences. Einstein suggested that matter curves spacetime. However, that assertion is very specific to our universe. A more general assertion is mass disturbs the status quo, whatever that may be, and causes kinetic energy variations. At the quantum scale, gravity does not seem to need its own boson. Information is passed using whatever boson is available. In this case, it's the Higgs.
Now, for extra credit, let's derive Einstein's field equations from equation 14:
If you are feeling ambitious, you can work backwards and derive the Higgs Langrangian from Einstein's field equations.
Update: Here is a video containing a mathematical proof that falsifies the graviton: