# The universe expands

Nowadays standard cosmology assumes the empty space itself between the galaxies is expanding and drives them away from each other. The newly formed empty space distinguishes itself in nothing from the old, already present space and will expand at precisely the same rate.

We assume space is uniformly expanding and the rate of expansion is constant in time. The universe is ”steady in expansion”, it always looks as expanding as ever, no matter WHEN you look to the sky.

After a certain time delta-t the distance between any two points of space has doubled. After another time delta-t the distance between any two points of space has doubled again. The doubling every time delta-t is an exponential expansion. When followed backwards in time the galaxies half their speed every interval of time delta-t. They will finally merge but they will never actually come to a complete standstill with respect to each other.

In our idealized expansion our galaxies have no own movement, no proper motion with respect to the expanding frame.

This was the view until I started to find my own conclusions.

## Standstill

You are in your laboratory on earth. When you look at the sky you see the galaxies receding from you in all directions and receding faster when further away. If there was a galaxy in every possible place then every possible velocity would be possessed by precisely one galaxy. All galaxies seem to recede from you. They recede slower when more nearby and when such nearby they actually reached you, their speed is zero. You are standing still with respect to the universe.

Distance is measured by redshift. When the *distribution* of galaxies over space is uniform and *curvature* is zero, then the number of galaxies of a certain *redshift* is proportional to r (r = distance to you). You can count this. The frame of standstill then is the frame that at each of its points has such a velocity that the counted distribution is maximal isotropic (in all directions the same). Call this the Galaxy Frame of Expansion, in brief the Galaxy frame.

The overall curvature might be zero, denoted by = 1. But observations indicate the distribution is not completely uniform and observed large scale streams of galaxies might spoil the simple picture further.

The 2.7 kelvin background radiation (CMB or Cosmic Microwave Background) provides another frame of standstill. We are immersed in the background radiation as in a gas and one can stand still relative to the gas. That is, the frame of standstill is the frame with, at each of its points, a velocity such that the CMB radiation in all directions resembles the best a Planck curve; a velocity such that the CMB is as isotropic as possible with respect to its Planck curve spectrum. Call this the CMB frame. Mind eventually present large scale “streams”of the “gas” might spoil the simple picture.

The CMB frame is by no means Lorentz invariant. It is possible to move relative to the background radiation with such a speed that in front of you its temperature is enlarged to 10 K. Oké, behind the temperature drops to virtually zero, but the average overall temperature will be significantly higher than 2.7 K. The background radiation isn't isotropic anymore. There is only one relativistic invariant radiation field: intensity frequency^3, see THE FIELD OF ALL POSSIBLE FREQUENCIES.

There should be a 2 kelvin neutrino background radiation and a 1 kelvin gravitational wave background radiation, providing still more frames of locally standstill. (Call them the Neutrino frame and the Gravitational wave frame.)

At the very first moments after the Big Bang the elementary particles that will become the frames of galaxies, CMB, neutrino and gravitational waves, are thought to drag each other along in one big expanding motion. When one after the other frame separates, they *might* evolve a little different from then on. One can separate the frames in observation and if one does, is there already something found? What are the relative velocities of the frames at our location? For observations, what is taken the best as our location, the Sun, or our Galaxy as a whole?

## The Big Bang

According to the first chapter of TONE, mass absorption from the Higgs field curves space and the subsequent action of gravity curves it back. Finally gravitation does not curve spacetime. Whatever gravitational action there is, spacetime remains flat. Take also into account the described existence of the frames of galaxies, CMB, neutrino and gravitational waves. Then it seems to me that the view of the Big Bang that fits the best, is *an ordinary explosion occurring in already existing flat empty space*. The Big Bang is not a fundamental feature of spacetime. Light waves from distant galaxies no longer arrive while still expanding, as described in the first paragraph of this page.

In our universe as it is now, there is no preferred location where the Big Bang occurred, all locations are equally valid. There is no preferred center of the universe. The location of the universe is indefinite, 100 percent undetermined. But locally there always is a preferred *velocity of the universe*, locally one can stand still with respect to the universe. Locally the velocity of the universe is determined 100 percent. This is in accordance with the Heisenberg uncertainty relations. Coincidence? I mean, this velocity of the universe is not a fundamental feature of the vacuum, it only is an observed fact and *could* have been different, isn't it?

If there was an elementary particle in every possible place and no particle would have any extra velocity relative to the expanding frame (every particle locally stands still with respect to the expanding universe), then every possible velocity would be possessed by precisely one particle. So after the Big Bang, as soon as expansion as such is confirmed, the particles obey the demands for fermions (each particle a different state, in this case a different velocity). Then it very well might be at the Big Bang, when started out as a bunch of innumerous elementary particles much nearer to each other than e.g. 0.9 fm, that is chosen for expansion as the only possible way to obey the fermion demand. The bunch of particles might be only quarks, see TONE, e.g. the chapter 4 conclusions and chapter 5 conclusions and the Epilogue.

SR still holds. So the model of the expanding universe is I think the best that of Milne, a uniform, isotropic, homogeneous and constant expansion - the uttermost simple expansion there is - of an empty universe, wherein SR is taken into account. Added to the model of Milne are decelerations of the expansion due to gravity in the forward time evolving areas and accelerations of the expansion (as we observe them) in backward time evolving areas.

The previous page of the storyline EXPANSION OF THE UNIVERSE, paragraph The beginning of the universe, shows at the very first instant the expansion of the universe is not driven by gravity. The proton at page 5 of NET FORCES IN QCD chooses the force between quarks and gluons within 0.9 fm to be proportional to distance and zero at zero distance. So at the very first instant the expansion of the universe is not driven by the strong nuclear force either. At the very first instant it must be driven electromagnetically alone. And as soon as the particles of the universe were at mutual distance of about 0.9 fm the strong nuclear force comes into play to serve the matter-antimatter annihilation further.

A well-mixed cloud of matter and antimatter particles constitutes a *foam* of very small bubbles (small areas of space), each bubble more or less as large as the particle in it that is holding up the bubble. The matter areas go forward in time, the antimatter areas go backward in time, that's the assumption in the second chapter of TONE. The foam is supposed to embody a state of no net elapse of time. In each area Higgs field absorption and gravitation is active, respectively forward or backward in time. One of the first things that occur then is that matter and antimatter separate in more distinct areas. Matter attracts matter, antimatter attracts antimatter (see page 1 of FORWARD BACKWARD TIME DIRECTION, item 1), but matter and antimatter attract each other less. A matter and an antimatter mass of equal size will not even deviate each other's path at all, see Dark and bright planets and stars of equal mass. So matter-antimatter separation is expected to occur by gravitational forces, but it is not a very fierce force.

The Big Bang was a matter-antimatter explosion accelerating the matter and antimatter. During acceleration the accelerated matter experiences the surrounding vacuum as having a temperature proportional to the acceleration ( Davies-Unruh equation). This is supposed to hold in forward matter areas as well as in backward antimatter areas.

About 4 * 10^5 years after the Big Bang matter and radiation decoupled. The radiation then was equal to the black body radiation of a temperature of 4000 K, a little bit cooler than the outer surface of the Sun. When empty space itself is not expanding, this radiation up until now might have been diluted, but its temperature would still be according to 4000 K. The observed temperature of the CMB is 2.7 K, about a 1000 times smaller. This indicates the wavelengths of the CMB radiation *are* being stretched in the course of time, most probably still because space itself is expanding.

How does that work? I hope conclusions like mine about gravity come to the rescue, where all effects of Einsteinian curvature *are* impinged on matter and radiation *as if* spacetime is curved, see TONE paragraph 1.1, 1.2 and 1.3. That the act of gravity itself is constantly flattening the curvature back to zero doesn't erase any of the curvature-mimicking effects.

But the expansion of the universe is not *gravity* that tends space to shrink. This is *expansion*. Is it a group of particles, white gluons maybe, created at the Big Bang and then - obviously when matter and radiation decouple - being absorbed by the vacuum, causing a fierce expansion of space? At least in the forward time evolving areas?

## Velocity

Let's enter a rocket frame passing nearby with a constant and high (but not relativistic) speed, e.g. 100,000 km/sec. Your friends at home in the earthly laboratory see that in the sky there is precisely one galaxy having the same velocity as you now. (We neglect for the moment the *voids* and assume for the moment that everywhere you look there is a galaxy available.) It is in front of the rocket on the straight line of the rocket’s track and it is further away when the rocket frame velocity is higher. In your rocket you observe this galaxy as the only one standing still relative to you.

Will you in your rocket observe the distributions of the galaxy velocities - spherical up until now - be distorted? Egg-shaped or crushed to disk-shape or what?

No matter in what galaxy you are, you know you will see precisely the same picture of the sky: all galaxies recede from you as if you are in the center of the universe *). Observed from the rocket, the distant galaxy standing still to you now is the new center from where all galaxies seem to recede. You know you would see if you would go there AND you are already standing still with respect to that galaxy. As observed in the rocket the expansion remains the same but it is off-center now.

*) This is philosophically remarkable: for centuries people have thought the earth is in the center of the universe and now when people actually *see* that they are, nobody believes it anymore!

Let’s call the new expansion center your *homebase*. It is the place where you in your current state of motion would be standing still. Standstill can be defined as the case when you and your homebase coincide.

## The Globular Cluster

Globular clusters generally look perfectly point-symmetric. If the cluster had any angular momentum, it would showed itself in *some* disc-shape properties in the cluster, I suppose. This can be tested by computer simulation. We take the globular cluster to have zero angular momentum. This fits in with the picture that the cluster did arise from a single cloud of gas that had no angular momentum.

When disordered motion, as in globular star clusters, is transformed into an ordered expansion by translocating stars, keeping their impulse vector lengths and directions the same, the result looks like a fireworks expansion. In a fireworks expansion as it is meant here, the velocity of one piece of firework is proportional to the distance to the expansion center. It looks very much like the expanding universe described above. Each possible velocity has its unique proper place. This space then is a version of the set of all possible velocities.

Let's start to convert the globular cluster to a fireworks expansion. First we make sure to stand still relative to the mass center of the globular cluster. Next we choose an expansion center and we choose a sphere around it of points of 1 m/s. Although an unnecessary step, we choose a convenient moment in the history of the globular cluster, where all stars have convenient velocities. Now we translocate each star of the globular cluster to its proper place in the fireworks expansion, keeping velocity properties (magnitude and direction) the same while translocating. We swiftly determine the mass center of the new fireworks star cluster and call it our *home base*. The home base has a certain velocity in the chosen fireworks expansion coordinate system. We speed up our frame of reference until our system stands still with respect to the home base. The fireworks expansion now expands from the homebase, the expansion center coinciding with the mass center.

The impulse (mass of cluster times speed of mass center) and angular momentum of the original globular cluster is zero. The impulse and angular momentum of the new fireworks star cluster is zero too. Only the energy still can differ. Now enlarge (or reduce) the whole picture as in a three dimensional photocopier until the energy (kinetic plus potential energies) of the stars in the original globular cluster and in the new fireworks star cluster are the same. This multiplication is just another translocation of stars, their velocity vectors remaining constant while translocating.

Is there another way? Suppose you translocate stars while maintaining its impulse, angular momentum and energy, thus constantly obeying conservation laws, does this work? Regard distance r between mass m of the star you translocate and the mass center of the globular cluster. To obey angular momentum conservation law mvr = constant, the velocity magnitude must change while translocating. After translocation, r has increased by a factor b, r(before) times b = r(after). Since r in mvr has increased by factor b, you must divide v by b in order to keep mvr at constant. That is, the *component of v perpendicular to r(start)* has to be divided by b; the velocity component along r(start) remains unchanged.

Since the velocity has changed now, the *impulse* mv changes too, as does the *kinetic energy* mv/2 and the *potential energy* GMm/r, where M mainly is the mass of the globular cluster “below” the translocated star. The shell around the mass center “above” the star tends to cancel itself out, see A sphere of free falling clocks, page 1 of NEG.

Well, this is not my strongest point.

NDER
ONSTRUCTION,

eventually.

## Sphereworld

Larry Niven has written a book named *Ringworld*. There they’d build a huge ring that rotates around a star, the star is in the center of the ring. The rotation is such the centrifugal force provides a gravitation on the inner surface of the ring like on the earth. Something the like can be done with the expansion of the universe. Suppose you chain a large circle of galaxies in such a way they cannot fly away from each other no more. The expansion of the universe tries to draw them further apart. The chain effectively prevents this. The result is a force on the chain that is a kind of gravitation. Instead of galaxies on a circular chain we build a solid sphere just somewhere in empty space. Take its magnitude such that, when standing on its inner surface, the experienced gravitational force is 1 g. The sphere doesn’t rotate, no centrifugal forces arise.

When you start with a first sphere of a certain diameter, you construct on its surface a second sphere. Then you dig up the parts of the first sphere and use them to build the third sphere on the surface of the second sphere. And so on until the desired magnitude is reached.

It *will* take some time.

You stand on the inner surface of the sphere. What forces act on you? For convenience, assume there are no stars in the volume in the sphere, or other matter. How large is the gravitational force F excerted on you by the mass M of the sphere? Inside a perfect sphere holds F = 0, outside the sphere F is as if M is concentrated in the sphere’s centre. (Gauss’ Theorem, holds too in GR).

Well, since you reside on the inner surface: F = 0. But in case you want to get out, let’s calculate.

The radius of the sphere is r, the gravitational constant = G.

F exerted by M on 1 kg of you-just-outside-the-sphere

= G * 1 * M / r (Newton’s gravitational law)

= ( G / r ) * 4 r * U,

where U is the mass of a “unit column of the sphere”, a column of 1 square meter outer surface times the depth, or thickness, of the sphere

= 4 G U

= 8.4 * 10^-10 * U

The gravitational force of the sphere on you is proportional to its thickness (and mass density) and is independent of its size.

Make U as small as possible for practical use, e.g. construct the sphere of a kind of spider web with still stronger and lighter treads and larger holes, but not that large that one of our spaceships would immediately fall through it.

On the inside surface of the sphere one feels a one-g gravitation, which in fact is the accelerated expansion of the universe. A spaceship is standing there on a large hatch and the hatch is opened to the outside. The spaceship, free floating now, leaves the sphere by the one-g of the expansion of the universe at the sphere’s surface. Suppose one let fall the whole sphere along with the spaceship. One has to accelerate the sphere then. The parts of the world on the inner surface of the sphere in the neighbourhood of the ship will be weightless, exerting no force anymore on the sphere’s inner surface. On the other hand, at the other side of the sphere one expects a doubled gravitational force to be felt there. These combined forces make the sphere to counteract acceleration. The acceleration of the sphere will be undone and the sphere is free floating again.

(In fact correcting disturbances travel with light speed or slower along the sphere’s surface, effectively causing the surface to vibrate.)

## Summary for an accelerated expanding universe

*1) Is there a preferred system of ”standstill” in the universe?*

Yes, there is: the set of all velocity states where you coincide with you homebase. The preferred system of standstill expands, but locally a standing-still frame can always be found.

*2) Is there a force acting to bring you to a standstill with respect to this preferred system?*

No, there isn’t. When you have a velocity you will maintain to have that velocity. It is taken along with the expansion of the universe and increases with it. Everywhere you are the constant value of your speed will be added to the zero standstill velocity (see 1) in that location.

Especially a small velocity increment *d*v will be maintained while taken along with the expansion and so a lorentz invariant field of all possible velocities can be constructed in the expanding space of the universe too.

*3) Is there a force opposing acceleration?*

Yes, there is, for each coherent object occupying some space that expands, see *Static curvature of space tends a gas to cool down* in the column at the right. However the force is *very* tiny for the small spaces occupied by the elementary particles, it in principle keeps them at constant speed when no other forces are acting on them.

*4) Is this force explaining the first law of Newton, ”A mass where no forces are acting upon, maintains its velocity”?*

No, I don’t think so. It could if it wasn’t for the weakness of the force. But the principle is worth remembering, it might work in other cases.