More on MOND and the octonionic theory

In what way might we think of Newtonian gravitation as the square of MOND?

To get some insight, let us write the acceleration a in a circular orbit as

a = [ GM / R^2 ] ( 1 + \beta (R) ]

The function \beta (R) depends on a and goes to zero for a >> a_0, thus recovering Newtonian gravitation. For a in the vicinity of a_0 we approximate the last bracket to a_0 / a, thus yielding MOND. At large cosmic distances, relativistic effects become important. GM/R^2 is replaced by its GR counterpart, and (1+\beta) becomes the MOND induced modification of GR. It is important to ask if dark energy is a manifestation of this MOND induced modification. Were this to be so, we will have a common original cause for flat galaxy rotation curves and cosmic acceleration, without dark matter or dark energy, and because GR and Newtonian gravity are limiting cases of a more general law of gravity. On the clusters scale MOND will need warm dark matter such as sterile neutrinos, or dark baryons.

What then is this more general law of gravity? Which we demand must come from first principles. The Left-Right symmetric octonionic theory proposes SU(3)_g X SU(2)_R X U(1)_g as would-be-gravity, or square-root-gravity, this is the right-hand counterpart of the broken L-R symmetric theory, whose left-handed counterpart is the standard model. The gauge theory of would-be-gravity on an 8D octonionic space-time is proposed as the more general law of gravity, which explains the origin of the critical acceleration a_0 and the emergence of GR, MOND, and Newton as special cases.

Cosmology and the scale a_0: In the L-R symmetric theory, the very early universe undergoes an inflationary expansion having a time-dependent cosmic acceleration a_0(t). This inflationary expansion is halted (and converted to a power law expansion) when significant seeding of density perturbations causes a quantum-to-classical transition, L-R symmetry breaking, and emergence of 4D classical spacetime. The gravitational acceleration in the vicinity of the seeded relativistic density perturbations exceeds the then a_0, and GR emerges from would-be-gravity as its square. MOND is the transition zone between would-be-gravity and Newton/GR. Thus would-be-gravity can seed the scale-invariant matter perturbations whose effect is seen in the CMB (hence relativistic MOND).

In today's universe, away from compact objects, would-be-gravity (relativistic MOND) dominates because accelerations are smaller than a_0 and tend to the current cosmic a_0. In this deep MOND regime there is space-time scale invariance, and the universe tends to de Sitter.

Would-be-gravity when squared yields GR at high accelerations and the condensation of SU(2)_L and SU(2)_R into 4D spacetime geometry is indicated. SU(2)_L mediated on small scales by heavy weak bosons is the weak interaction. The electro-weak symmetry breaking is in reality an L-R symmetry breaking same as

QCD Color + U(1)_em - Grav Color + U(1)_g

breaks from - breaks from

Weak SU(2)_L - SU(2)_R

It appears that if we do cosmology with the L-R symmetric octonionic theory and its emergent approximations, all will be well without cold dark matter and without cosmological constant as dark energy. In this theory the cosmological constant (zero point energy of vacuum) is strictly zero. Cosmic acceleration is caused by U(1)_g