Let's take a look at these arguments to see how the reasoning goes.
The principle of conservation of energy is one of the solid pillars on which physics rests. Thus, a particle's rest energy (E), which is connected to its rest mass (m) via Albert Einstein's famous relation E = mc2, is constant over time'”and, thus, the speed of light (c) is also constant over time.
The observed redshift of distant galaxies indicates that'”when seen in a cosmic or 'global' perspective'”the Universe is uniformly expanding. However, 'local' structures, such as everyday objects, stars, and galaxies (that is, structures held together by electromagnetic or gravitational forces), do not expand in the same way.
If radiation escaping from the galaxy or received from other galaxies is neglected, the energy of a galaxy is conserved. That is, the energy principle implies that energy is 'locally' conserved.
In contrast, energy is not conserved 'globally' throughout the Universe. That is to say, in a large cosmic volume (containing any given number of galaxies'”that is, composed of many independent local structures) co-expanding with the Universe, total energy is not conserved.
This is so because radiation is redshifted during its voyage through intergalactic space. That is, the expansion of the Universe causes the photon's wavelength (Î») to stretch and the photon energy, hc/Î», to decrease.
(In the present theory, this is the whole story, while in theories where gravity and expansion are assumed to balance each other, things are more complicated. Things become particularly complicated when one attempts to use the theory for gravity'”general relativity'”to predict expansion. In Predictive Cosmology, where expansion is a fixed property of the Universe, such an attempt is not meaningful.)
Now, why should it be that energy is not conserved 'globally' throughout the Universe, but is conserved locally, and not the other way round?
What if we were to assume that the velocity of light (c) changes with time in such a way that energy, instead of being locally conserved, is conserved globally'”that is, total energy is conserved in a cosmic volume expanding with the Universe? In other words, what if
(implying that c increases very slowly to compensate for the comparatively much faster growth in radiation's wavelength Î») holds true for an expanding volume having a mass M and containing N background photons subject to cosmological redshift?
Clearly, building our theories on the principle of conservation of energy, we may imagine, as it seems, two mutually exclusive 'pictures' of the expanding Universe.
In the 'local picture' (with c constant), energy is not conserved globally (because of the redshifting of radiation due to the expansion) but is conserved locally.
In the 'global picture' (with c varying over time), energy is conserved globally but is not conserved locally (because the change in light's velocity, c, changes the rest energy of matter).
And, now comes the big surprise. It turns out that the two pictures are NOT mutually exclusive. One picture does not exclude the other!
Page 5 continues with a look at the beginning of the Universe.