I haven't got these terms clearly defined in my mind. The way I see it is that there is the expansion of galaxies due to the possible expansion of the 4D shape of the cosmos and also possibly due to the matter contained within it. Because I have started at a different place to everyone else i.e. assuming that Einstein's concept of space-time is wrong, then even the simplest terms need thorough clarification. So, in my mind, there are just two causes of the galactic expansion; (i) force due to matter (ii) 'outside' force acting on 4D topology of the universe.
What exactly do you mean by 'energy density'? That the amount of energy is fixed but that the amount of space that it fills is increasing??
Yes, the amount of energy is fixed in a given space at a point in time and the energy density becomes variable as the amount of space changes over time. When I refer to the energy in a given space I am including all forms of energy in that space including matter, electromagnetic radiation, dark energy, dark matter, everything that can be described as energy whether observed or theoretical.
See footnote 7 from the chapter 36 Cosmic Repulsion. Let’s start there in getting a common understanding of terms:
“The cosmological constant is comparable to the inverse of the square of length. For the physicists of the infinitesimally small, this length is interpreted as the distance scale at which the gravitational effects due to the vacuum energy become manifest on the geometry of space-time. They estimate that this scale is Planck length, or 10^-33 centimeters. For astronomers, the cosmological constant is a cosmic repulsive force that effects the rate of expansion on the scale of the radius of the observable universe, or 10^28 centimeters. The ratio between these two lengths is 10^61, which is in fact the square root of 10^122.”
Now go to pages 213 to 216 and read from the perspective of the footnote, i.e. the huge energy difference between the theories at the quantum level and the macro level. Let’s start with vacuum energy:
http://www.astro.ucla.edu/~wright/cosmo_constant.html
The cosmological constant is said to represent the force that the vacuum of empty space would have on an expanding universe within it. I’m not saying that there is any empty space or that our universe is expanding into empty space because I have formed my own opinion on that imponderable
. But the concept is that this empty vacuum which surrounds our finite expanding universe is in effect pulling at the universe causing the expansion. That is vacuum energy density, i.e. a constant force driving the expansion. It is called it the cosmological constant and represents that constant force of expansion that can be explained using the empty space concept.
The force is mysterious if you believe that our observable universe is all there is, i.e. that there is no such empty space surrounding it, but if you look for a way to explain that mysterious “dark energy” driving the expansion and especially the inflationary epoch during the first instant of expansion, then the concept of vacuum energy density is there for you. Vacuum energy density and negative energy density are the same thing.
Next, you use the term 4-D topology. Would you name the 4 dimensions that make up 4-D topology and say a little about it relative to 3-D space plus time? This question is just to be sure we have the same definitions as we discuss things.
And one more question for clarification. You mention the "expansion of galaxies due to the possible expansion of the 4D shape of the cosmos". Are you talking about the observed separation of the galaxies as in chapter 32, The Rate of Expansion?
I assume you don't mind if I make a reference to this thread in my
blog because it begins to show the origin of my ideas about the two levels of order. The similarity between quantum action and arena action is the idea I use to solve the energy discrepancy between the two levels. There is a connection between the two levels during the arena expansion when the quantum realm of the arena forms from the energy density of the expanded big crunch core. The core is the “source particle” and the energy of the quantum realm is extracted from the expanding core energy. The extracted energy retains its energy density in the form of matter while the rest of the core energy is devoted to the force of expansion called dark energy. The energy density of the dark energy portion decreases as the space it occupies increases, while the energy density of the matter is locked into the space required for matter to function properly. Matter doesn’t expand as the observable universe expands.