The fine structure constant
is given by the ratio [alpha] = [e.sup.2]/[e.sup.2.sub.*], where (-e) is the observed electronic charge.
The terms [[DELTA].sup.i.sub.I], i = U, [kappa], [[alpha].sub.G], denote the threshold corrections due to unification scale ([M.sub.U]), intermediate scale ([M.sub.[kappa]]), and GUT fine structure constant
I will present 4 cosmological signatures produced by such a coupling: a violation of the cosmic distance-duality relation, a temporal variation of the fine structure constant
, a modification of the evolution of the CMB temperature and CMB spectral distortions.
The fine structure constant
, also known as alpha, has been both essential and confounding to physicists.
Ultra-precise atomic clocks can be used to verify Einstein's general theory of relativity as well as test whether constants of nature change over time, for example, the fine structure constant
, which describes the size of the electron energies of the atomic structure.
But the new study focuses on the fine structure constant
, also known as alpha.
It is known that since the fine structure constant
relates the three fundamental constants of c, e and h, not all of the latter can be fundamental at the same time.
Besides the numbers in the examples above, the author has commonly employed either the number or its decimal harmonic of the following: the comma of Pythagoras (CP = [3.sup.12]/[2.sup.19] = 1.0136432); the fine structure constant
(a = 1 / 137.036); musical pi (MP = 360/84 = 4.2857); the radian (180/[pi] = 57.29578); the square roots of 2, 3, and 5; the sizes, orbital periods, and distances of planets; geographical coordinates of ancient monuments and modern cities; and many other interesting topics.
He also discovered that the beta ratio is not only "the ratio between the magnitude of the mass of the proton over that of the electron" but also "the ratio between the magnitudes of all the other corresponding quantum attributes of the electron and proton." He found that the probable definition of the fine structure constant
is the ratio between the magnitudes of local inertia and the universal minimum and that this reveals the meaning of the mystery number 137.
where [m.sub.p] is the proton mass, [alpha] is the fine structure constant
, [e.sub.V.sup.R] is a low energy constant, [[partial derivative].sub.a]'s are model-independent radiative corrections, [[~.g].sub.A] is the axial coupling constant, and the correlation coefficients a, A, B are incorporated into the recoil corrections [C.sub.i]([E.sub.e]) .
The threat to the idea of an invariable speed of light comes from measurements of another parameter called the fine structure constant
, or alpha, which dictates the strength of the electromagnetic force.
Cahill  introduced an additional dimensionless constant that coincides with the fine structure constant
and determines the strength of a new 3-space self-interaction that can explain various gravitational anomalies, such as the 'borehole anomaly' and the 'dark matter anomaly' in the rotation speeds of spiral galaxies.