The Hubble Expansion & Deep Space Anomalies
By Craig Hanks
Estimates for the lifespan of our Universe, when more than 99.99999999 percent of galaxies have receded beyond our ability to see, ranges in the trillions of years; according to many scientists discussing cosmology as contributors to science programs on Television. The actual figure for galaxies is about 140-billion years from now; a figure that is dictated by the current accepted Hubble expansion velocity of 71-km/sec/megaparsec.
Our universe is presently considered to be about 13.8-billion years old. It contains around 200-billion galaxies and nearly five times more unseen mass surrounding each galaxy in the form of dark matter. Quite a lot of matter; and essentially all of it is measured to be receding from our present position, in an ever expanding universe. In about 140-billion years our universe will consist of one large elliptical galaxy formed from the gravitational combining of our local cluster of galaxies; it will be a universe of stars, not galaxies.
This expanding universe theory follows from research in the 1920’s of the red-shifted light of distant galaxies, and resulted in the discovery of the Hubble Constant, which gives the velocity for the expansion of the universe as increasing by about 71-kilometers per second per mega-parsec. A mega-parsec (mps) is a distance defined as 3.26157-million light years. Since the velocity of expansion increases with distance, the 71-km/sec velocity at 1-mps becomes 710-km/sec velocity at 10-mps, 7100-km/sec velocity at 100-mps, and so a velocity of recession of 300,000-km/sec, which is C, the velocity of light, occurs at 4225.35-mps distance; which is derived by dividing 300,000-km/sec by 71-km/sec/megaparsec. The size of our universe and what we actually see are defined by the two velocities, 71-km/sec/mps and 300,000-km/sec.
Spatial expansion has, for all communication and measurement purposes, placed every observer at the center of their own universe. Essentially all that we see beyond our local group of galaxies is vacating our universe. Looking back does not necessarily mean seeing anywhere near a beginning.
Though the velocity of expansion continues to increase without an end, it becomes irrelevant to us beyond 4225.35-mps, because we have no way of measuring, witnessing, nor communicating with anything that is receding from us at a velocity greater than the velocity of light. So 3.26157-million light years per mps, multiplied by, 4225.35-mps, gives a distance of 13.78-billion light years, which is the maximum radius of our observable universe for a Hubble expansion velocity of 71-km/sec/mps. This does not mean that the Universe is only 13.78-billion years old.
Although looking back in time is the most popular way of thinking about distant galaxies, it is also valid to say we are only looking away from our position on Earth as observers; and only measuring spatial expansion relative to Earth and a recession radius of 13.78-billion light years, irrespective of any beginning. It is quite a coincidence that the estimated age of the universe is 13.8-billion years and the estimated distance that we may look back is also 13.8-billion light years.
The time to double the expansion distance between any two celestial points, not encumbered by gravity, is dependent on the given expansion velocity. Consider the expansion of matter at 1-mps going to 2-mps with a velocity change of 71-km/sec, relative to Earth. The expansion velocity of 71-km/sec at 1mps increasing to 142-km/sec at 2-mps gives an average velocity of 106.5-km/sec over a distance of 3,261,570-light years. Since velocity is changing with distance in spatial expansion, and not time, we can surmise that the physics of this phenomenon requires some definition. In standard physics:
A = V / T = dv / dt (velocity changes with time)
In spatial expansion:
A = V / X = dv / dx (velocity changes with distance.)
So, dv / dx = (km/sec) / km = sec-1 (which is the Hubble Parameter.)
(71 km/sec/mps) / (3.0857×10^19 km/mps) = 2.301×10^-18 /sec
The Hubble Parameter will give us the velocity of any displacement, in km/sec; simply by multiplying this parameter by the distance in kilometers of any chosen displacement. This parameter figure is simply the change in expansion velocity per kilometer due to spatial expansion. The Hubble Parameter requires that distance be integrated with velocity to obtain time of expansion between two points. For example, doubling the distance from 1-mps with V=71-km/sec, to 2-mps with V=142-km/sec; in one iteration: Vaverage = ( Vf + Vi ) / 2
T = Xkm / ( Vave km/sec x Tsec/year ) = Tyears
T = 1-mps in km / (106.5 km/sec x 31,536,000 sec/year) = 9.188×10^9 years.
In two iterations; 1-mps (V=71km/sec) to 1.5-mps (V=106.5km/sec) plus
1.5-mps (V=106.5km/sec) to 2-mps (V=142km/sec)
T1 =.5-mps in km / (88.75km/sec x 31,536,000 sec/yr) = 5.513×10^9 yrs.
T2 =.5-mps in km / (124.25 km/sec x 31,536,000 sec/yr) = 3.938×10^9 yrs.
T = T1 + T2 = 5.513×10^9 yrs + 3.938×10^9 yrs = 9.45×10^9 years.
Dividing the distance from 1-mps to 2-mps into smaller and smaller increments yields a limiting timespan of T = 9.55245×10^9 years to double that distance via expansion; and the doubling of further celestial distances such as, 20 to 40-mps, 100 to 200-mps, 2112.5 to 4225-mps, 4225 to 8450-mps, all calculate to 9.55×10^9 years. The limit calculation of 9.55×10^9 years is 3.97% longer than the initial calculation of 9.188×10^9 years. The average expansion velocity over any distance is reduced by the unusual nature of this spatial expansion velocity increasing only as a result of increased distance. Having less space created in the first half of any distances chosen, than the second half, the Hubble expansion velocity of 71-km/sec/mps, average velocities are reduced by 3.97% in order to calculate the correct expansion time between any two celestial points.
Although the Hubble expansion velocity may not be truly linear (constant over time), the values and calculations made here will assume a linear expansion. So if the expansion velocity is C, at 13.78-billion light years distance, it is.5C at 6.89-billion light years distance (half of the radius of the observable Universe, or 2112.5-megaparsecs; 2112.5-mps x 71-km/sec/mps= 150,000-km/sec, or.5C). I have chosen to use this.5C expansion velocity distance in a number of my calculations because it is an observable distance at which we can measure and verify the red-shifts of matter and the expansion of space. The Hubble expansion velocity of 71-km/sec/mps allows us to calculate that every 9.55-billion years, the expansion of the Universe relative to Earth, doubles for all points beyond the gravitational effect of the local group of galaxies. The key distance and expansion velocity, 6.89-billion light years and.5C, will allow me to develop a timeline of expansion until only our local cluster of galaxies is left in the visible Universe.
If the first principle in our timeline is a.5C velocity increase, for matter located today at 6.89-billion light years distance, expanding to 13.78-billion light years distance in 9.55-billion years; the second principle is that for a sphere of radius R, a second concentric sphere of radius R/2 (one-half R) contains 1/8 of the volume of the sphere of radius R. So in our present Universe with a radius of 13.78-billion light years, a sphere of radius 6.89-billion light years (one-half 13.78) represents 12.5% (1/8) of all matter we estimate to exist. Such that 87.5% of all matter is presently receding at.5C or greater velocity and will increase its expansion velocity to C or greater in the next 9.55-billion years; causing it to disappear from measurement and interaction. Also, in the next 9.55-billion years the remaining matter in the smaller sphere of 6.89-billion light year radius will expand to fill our visible Universe of 13.78-billion light year radius, while decreasing its density by 7/8ths. In a further 9.55-billion years another 87.5% of the remaining 12.5% of matter will disappear. By the time our Universe increases its estimated age to 32.88-billion years, only 1.56% of what we currently see will still reside in our viewable universe; 98.44% will disappear in the next 19.1-billion years, strictly due to the Hubble expansion velocity; while the remaining 1.56% will have expanded to fill a Universe of 13.78-billion light years radius and be 1/64 as dense as it is today. If we simply calculate the disappearance of 87.5% of our Universe every 9.55-billion years of additional age, we will find that at:
42.43 Billion Years only.195% remains visible
51.98 Billion Years only.024% remains visible
61.54 Billion Years only.003% remains visible
71.09 Billion Years only.00038% remains visible
80.64 Billion Years only.000048% remains visible
90.19 Billion Years only.000006% remains visible
99.74 Billion Years only.0000007% remains visible
109.30 Billion Years only.00000009% remains visible
118.85 Billion Years only.00000001% remains visible
128.40 Billion Years only.0000000014% remains visible
137.95 Billion Years only.00000000018% remains visible
(Approximately 36 galaxies out of 200-billion)
This math does not entertain the notion that the Hubble Expansion Velocity may be increasing in an accelerating expansion. In either case, the notion that it will take trillions of years for the galaxies to recede beyond our view is wrong.
The space located 1-megaparsec from us today will expand to 4225-mps, in about 140-billion years, if we ignore gravity in our local Virgo Supercluster. The local gravity will muddy the time for members of this supercluster to either expand beyond the visible horizon or combine to form one very large galaxy.
Even though gravity has clumped galaxies into clusters, superclusters and filaments, the average mass density of matter per unit volume would allow us to make better calculations regarding the velocity of expansion and age of the universe. Obviously as the universe expands the density decreases, however it is the rate at which density is decreasing that is shocking. Gravity and the proximity of galaxies to each other place age limits on both galaxy formation, their separation by spatial expansion, and the age of our universe.
The previous few paragraphs looked at galaxy numbers and mass density declining in the future relative to a population of 200-billion galaxies. Since our observable universe is calculated to be 13.8-billion years old, we can estimate that 9.55 billion years ago, our observable universe may have had eight times the number of galaxies in it, as today, (approximately 1.6-trillion), and it may have been 8-times more dense than today. 1.4-trillion galaxies may have receded beyond our view in the last 9.55-billion years; while the mass density of galaxies near us would have dropped to 12.5% of the mass density of galaxies 9.55-billion years ago. Studies of deep space regions are revealing large numbers of galaxies at extreme distances. If galaxy mass density at extreme distances is the same or greater than galaxy mass density nearby, then the loss of observable galaxies calculated above is true. However, for spatial expansion to be true, we should measure higher mass densities of galaxies with greater distance. This is one of three testable hypotheses offered in this paper to test the validity of spatial expansion. The density I refer to is total mass, not specifically galaxy quantities. If it takes the mass of 100-dwarf galaxies to equal the mass of a galaxy like the Milky Way today, then seeing 100-times the number of galaxies at 10-billion light years distance, and they being predominantly dwarf galaxies, does not indicate increased density of mass in the past. This would be problematic for spatial expansion.
Galaxies are also dealing with expanding space within them, possibly shaping them along the plane of their central black hole’s spin. Our galaxy at 50,000-light year radius is dealing with 1.1-km of new space every second between the center and the rim, in all directions. If our galaxy has been around for 13-billion years, galactic gravity has had to deal with 47,000-light years of expansion at its present rim radius of 50,000-light years. A significant amount of expansion over a reasonable time-span. Perhaps spatial expansion can account for some of the effects attributed to dark matter and dark energy with respect to galaxy formation, geometry, and various internal motions.
The galactic radius of 50,000 lt yrs, times the Hubble Parameter, yields,.4730×10^18km x 2.301×10^-18 /sec
Which = 1.088 km/sec; or 1.088 km of new space every second between our galactic center and its rim, at all points.
13 billion years of expansion at = 4.0997×10^17 sec x 1.088 km/sec =
4.46×10^17km. Which divided by the 9.461×10^12km/lt yr = 47,147 lt ys.
The continuous expansion of space for all reference frames presents some interesting facts about what we are measuring, what we are seeing, and what is actually occurring.
If a spaceship left a galaxy located 6.89-billion light years away,2112.5-mps from us today, where the galaxy is receding from us at.5C, and the spaceship is traveling toward us at 150,000-km/sec, also.5C, that ship would not gain any distance on us. They would be leaving their galaxy, but only traveling in tandem with us and we would both increase our velocity relative to their galaxy by 71-km/sec/mps. In 9.55- billion years we recede from 2112.5-mps to 4225-mps from that galaxy and we would then be receding at 300,000-km/sec, velocity C, relative to that galaxy. While the spaceship has traveled to 2112.5-mps away from its home galaxy, where its energy expended velocity of.5C, plus its spatial expansion velocity of.5C, at 2112.5-mps, has it also moving away from its home galaxy at velocity C. So we are still travelling in tandem with that spaceship and we have both lost any possible connection with the spaceship’s home galaxy.
On the other hand, if a supernova occurred in a galaxy 6.89-billion light years away, we would also be receding from that light at.5C, (150,000-km/sec). As earth is carried 2112.5 mps by spatial expansion, the supernova light is aided by a portion of that spatial expansion occurring between earth and that galaxy is happening behind the supernova light, increasing its velocity relative to its galaxy toward earth. Because of spatial expansion this light has an effective velocity of (C+.5C) over its 4225 mps journey to earth, which gives a travel time of 9.55 billion years; the same as earth receding from 2112.5 mps to 4225 mps from the galaxy. As the supernova light reduces the distance between us it also reduces the portion necessary to overcome spatial expansion, so that it eventually arrives at our location at velocity C, as we would expect. Though it took 9.55-billion years for that supernova light to reach us; the information in that light is that of a supernova that occurred 6.89-billion light years distance from Earth. Since our recession velocity relative to that galaxy has increased from.5C to velocity C, in that 9.55-billion years, we may only observe and record its history for 9.55-billion years; but that history takes longer and longer to reach us.
Spatial Expansion slows celestial motion. If a galaxy is located 1.38-billion light years away, it is receding at 30,000-km/sec, 10% of the velocity of light. In 10 seconds such a galaxy has receded 300,000-km further away (1-second of light travel time); so the comings and goings and doings inside this galaxy that occur in 10-units of time (seconds, days, years) require 11-units of time to play out through our telescopes and instruments. The timespan for things to occur is lengthened 10% at.1C; and so a simple relationship plays out; celestial motions slow by the same percentage of time that is the percentage of the velocity of light that spatial expansion is calculated for such motions. For example, if the average galaxy near us rotates with a period of 200 to 250-million years, and Type-1A Supernovas shine with a specific light curve over a 6-week period, then the average galaxy at 6.89 billion light years distance (receding at.5C) would show galactic activity slowed by 50%; so the average galaxy at that distance would rotate in 300 to 375-million years and Type-1A Supernovas light curve would last for 9-weeks. Such lengthening of events are observable and measureable. If we measure distant galactic rotation motion and distant Type-1A Supernovas brightness to be lengthening with distance, then spatial expansion is proven over other theories; if we do not measure any lengthening of such motions and brightness with distance, then spatial expansion is disproved and some other phenomenon is needed to explain red-shifts of light increasing with distance. These are testable hypotheses.
Though the slowing of activity at distance occurs relative to the distance the galaxy was from the earth when such activity took place; the time and distance measured by red-shifts does not further lengthen such activity. So a galaxy located 6.89-billion light years from earth, receding at.5C, when a Type-1A Supernova occurs would require 9.55-billion years for that light to reach earth. That light would measure 9.55-billion light years distant and it would be 9.55-billion years old, but the information in that light would exhibit the lengthening associated with its recession velocity when it started out,.5C. So a galaxy, measured to be 9.55-billion light years away today, should be measured to be rotating in 300 to 375-million years, and Type-1A Supernova brightness should take 9-weeks to follow its normal curve (50% longer).
I am including a list of galactic rotation times at various distances, relative to nearby galaxies, as well as brightness periods of Type-1A Supernovas, that can be verified with current and future data.
An expansion velocity of.1C occurs at 1.378 bly distance; and lengthens galaxy rotation by 20-25 million years; and adds 4 days to the 42 day light curve of Type-1A Supernovas.
An expansion velocity of.2C occurs at 2.76 bly distance; and lengthens galaxy rotation by 40-50 million years; and adds 8 days to the 42 day light curve of Type-1A Supernovas.
An expansion velocity of.3C occurs at 4.13 bly distance; and lengthens galaxy rotation by 60-75 million years; and adds 12.6 days to the 42 day light curve of Type-1A Supernovas.
An expansion velocity of.4C occurs at 5.51 bly distance; and lengthens galaxy rotation by 80-100 million years; and adds 16.8 days to the 42 day light curve of Type-1A Supernovas.
An expansion velocity of.5C occurs at 6.89 bly distance; and lengthens galaxy rotation by 100-125 million years; and adds 21 days to the 42 day light curve of Type-1A Supernovas.
Although we cannot, at this time, see any galaxies at 13.78-billion light years distant, such a galaxy would reflect activity that occurred when such a galaxy was just under 9-billion light years from our galaxy; but requires 13.78-billion years to reach us. So 9-billion light years is the limit distance of actual galactic activity that we may observe; for a universe that is only 13.8 billion years old. The velocity of spatial expansion at 9-billion light years is 65% of C, 196,000-km/sec; and history at this distance is retarded by 65% also. I believe that the most distant galaxy that has been measured is located about 11-billion light year from us, which represents light heading toward us when that galaxy was about 7.7-billion light years from our galaxy. So, for example, if we were looking for light from galaxies located 10.3 billion light years away from us today, receding with an expansion velocity of.75C, because of spatial expansion we would have to wait until 17.2 billion years had passed, to see the activities of galaxies occurring at that distance today.
The idea that galaxies will slow the expansion via gravity needs to be re-calculated to account for the disappearance of galaxies that are moving away from us at velocities greater than C. If 87.5% of all light and dark matter will disappear in 9.55-billion years, then the gravity associated with those galaxies will also cease; as well as the remaining 12.5% of galaxies will expand and separate over vast distances to fill the same volume as our present universe.
We cannot look back to the beginning, and we cannot determine the age of the Universe simply by extrapolations from observations of red shifts; since the Universe is receding beyond our view at 9-Billion Light Years distance; a figure that will actually get smaller if the rate of expansion increases. We can however, calculate the mass density of galaxies at different times in the past and compare that with the mass density of galaxies near us today to calculate backward in time increasing density of matter until we arrive at the age of our Universe.
� February 2017 by Craig D. Hanks
This article is by Craig D. Hanks of Eugene, Oregon, USA.