Posts Tagged ‘acceleration’

Normal distribution applied to Milky Way galaxy M-Sigma relation and bulge star data

July 18, 2013

Image

This superposition is supposed to show how the M-sigma relation could be applied to a given galaxy (the Milky Way). The vertical blue lines represent the positions of + and – sigma, the standard deviation of the normal distribution. The horizontal green line is positioned at the points where the blue lines intersect the distribution curve. Values are read at the green line from the vertical velocity dispersion axis.

It is seen that the M-sigma velocity dispersion for the Milky Way is about 100-103 km/s which we can use to estimate the M-sigma mass of the MW central supermassive black hole.

Msigma

This graph was made by the author of  “The M-Sigma Relation” in Wikipedia. I am trying to track his identity. No luck yet.

Take a look:

Two ten-billion-solar-mass black holes at the centers of giant elliptical galaxies

McConnell, Nicholas J.; Ma, Chung-Pei; Gebhardt, Karl; Wright, Shelley A.; Murphy, Jeremy D.; Lauer, Tod R.; Graham, James R.; Richstone, Douglas O.

Nature, Volume 480, Issue 7376, pp. 215-218 (2011)

 “Observational work conducted over the past few decades indicates that all massive galaxies have supermassive black holes at their centres. Although the luminosities and brightness fluctuations of quasars in the early Universe suggest that some were powered by black holes with masses greater than 10 billion solar masses, the remnants of these objects have not been found in the nearby Universe. The giant elliptical galaxy Messier 87 hosts the hitherto most massive known black hole, which has a mass of 6.3 billion solar masses. Here we report that NGC 3842, the brightest galaxy in a cluster at a distance from Earth of 98 megaparsecs, has a central black hole with a mass of 9.7 billion solar masses, and that a black hole of comparable or greater mass is present in NGC 4889, the brightest galaxy in the Coma cluster (at a distance of 103 megaparsecs). These two black holes are significantly more massive than predicted by linearly extrapolating the widely used correlations between black-hole mass and the stellar velocity dispersion or bulge luminosity of the host galaxy. Although these correlations remain useful for predicting black-hole masses in less massive elliptical galaxies, our measurements suggest that different evolutionary processes influence the growth of the largest galaxies and their black holes.”

    


  Of course, M-sigma works best when it is confined to galaxies of a given class. Maybe giant ellipticals constitute another such class.

  The M-sigma relation (those widely used correlations) may be written[i],[ii] :

  (1)        

         a)   M  =  Mbh  =  3.1 (σ/200 km s-1)4 x 108  Mʘ  =  M.     

  A current study, based on published black hole masses in nearby galaxies, gives[iii]

         b)   M  =  Mbh  =  1.9 (σ/200 km s-1)5.1 x 108  Mʘ  =  M.

  (2)                  Solar mass [iv]  =   Mʘ   =    1.98855 x 1030 kg                                   

  (3)                    M   =  Mbh  =   M●   =   r* v2/κG  from eqn. (2) in the paper, by the Postulate

                 Mbh  =  r* σ2/κG  =  3.1×108 (σ/200,000 m s-1)4 Mʘ       

                                      vσ  =  “σ” by the Postulate

  or

  (4)                  Mbh  =  r* σ 2/κG  =  3.1×108 (σ/200,000 m s-1)5 Mʘ   =   M  

                 Milky Way mass, Mmw  =  7×1011 M[v]

                                                or     = 1–1.5×1012 M[vi]

                                             with “Dark Matter “ contributing  

   We cannot have it both ways. Either bulge stars obey standard Kepler (SK) or adapted Kepler (AK). Which?  Is it a mixture of SK and AK as in eq. (6) of

   the paper? The Author of the paper dislikes the mixture, as it appears in eq. (6). But, such questions are good. They make for lots more research.

   So, astrophysicists, cosmologists and their grad students should love the Postulate.

[ii]     Ferrarese, F. and Merritt, D. (2000), A Fundamental Relation between Supermassive Black Holes and Their Host Galaxies, The Astrophysical Journal, 539, L9-L12

[iii]    McConnell, N. J. et al. (2011), Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies, Nature, 480, 215-218

[v]        Milky Way Mass  7×1011 M   Reid, M. J. et al. (2009). “Trigonometric parallaxes of massive star-forming regions. VI. Galactic structure, fundamental parameters, and noncircular motions”. The Astrophysical Journal 700: 137–148, solar mass M  =  1.9891×1030 kg,   Mmw  =  1.4 x 1042 kg   computed by conventional methods

[vi]    Milky Way Mass including “Dark Matter” 1–1.5×1012 M McMillan, P. J. (July 2011). “Mass models of the Milky Way”. Monthly Notices of the Royal Astronomical Society 414 (3): 2446–2457.  solar mass M  =  1.9891×1030 kg,  Mmw  =  2-3 x 1042 kg  by conventional methods

Wikipedia, rotation velocity  =  v,  AVD

 

Estimates for the mass of the Milky Way vary, depending upon the method and data used. At the low end of the estimate range, the mass of the Milky Way is 5.8×1011 solar masses (M), somewhat smaller than the Andromeda Galaxy. Measurements using the Very Long Baseline Array in 2009 found velocities as large as 254 km/s for stars at the outer edge of the Milky Way, higher than the previously accepted value of 220 km/s. As the orbital velocity depends on the total mass inside the orbital radius, this suggests that the Milky Way is more massive, roughly equaling the mass of Andromeda Galaxy at 7×1011 M within 50 kiloparsecs (160,000 ly) of its center. A 2010 measurement of the radial velocity of halo stars finds the mass enclosed within 80 kiloparsecs is 7×1011 MBut, we cannot apply standard Kepler or a correlation diagram based on unadapted Kepler, to stars that obviously do not follow Kepler’s laws, as is exemplified by the flat MW velocity dispersion diagram. But we go ahead anyway as if we haven’t a clue and do not understand. Most of the mass of the Galaxy appears to be matter of unknown form which interacts with other matter through gravitational but not electromagnetic forces; this is dubbed dark matter. A dark matter halo is spread out relatively uniformly to a distance beyond one hundred kiloparsecs from the Galactic Center. Mathematical models of the Milky Way suggests that the total mass of the entire Galaxy lies in the range 1-1.5×1012 M.

 

Galactic rotation,    velocity = v,  AVD

The stars and gas in the Galaxy rotate about its center differentially, meaning that the rotation period varies with location. As is typical for spiral galaxies, the distribution of mass in the Milky Way Galaxy is such that the orbital speed of most stars in the Galaxy does not depend strongly on their distance from the center. Away from the central bulge or outer rim, the typical stellar orbital speed is between 210 and 240 km/s. Hence the orbital period of the typical star is directly proportional only to the length of the path traveled. This is unlike the situation within the Solar System, where two-body gravitational dynamics dominate and different orbits have significantly different velocities associated with them. The rotation curve (shown in the figure) describes this rotation.

If the Galaxy contained only the mass observed in stars, gas, and other baryonic (ordinary) matter, the rotation speed would decrease with distance from the center. However, the observed curve is relatively flat, indicating that there is additional mass that cannot be detected directly with electromagnetic radiation. This inconsistency is attributed to dark matter. Alternatively, a minority of astronomers propose that a modification of the law of gravity may explain the observed rotation curve. The constant rotation speed of most of the Galaxy means that objects further from the Galactic center take longer to orbit the center than objects closer in. But, in fact, they orbit faster than they would if they followed Kepler’s 3rd  law. This is actually the problem. If they orbited according to Kepler’s 3rd, they would orbit so slowly as they neared the galactic rim that the spiral arms would wrap backward multiple times around the galactic center like the mainspring of an old windup clock. So, we can actually see the anomalous velocity dispersion at work when we observe a spiral galaxy.

The Hyperbolic Black Hole Galactic and Universe Gravitational Field

February 4, 2012

The Hyperbolic Black Hole Galactic and Universe Gravitational Field

Figure 1   Proper Time versus Scale Factor a(t) or Hubble Distance, R and also versus Potential Energies, Expansion Velocity, and Acceleration with Dilated or Reduced “Root” Time or “Relativistic Time”

http://www.fotothing.com/Gak/photo/f7c4dd2a76b88a78fa2f590a8751b883/ 100/92-100

 image #100 in this series

http://www.fotothing.com/photos/f7c/f7c4dd2a76b88a78fa2f590a8751b883_fa2.jpg

image enlargement

Graph computed from equations given in Fig.2 for Hubble expansion of the universe in extensive units. With a proportional overlay of the associated potential energy state diagrams.

                Busy, Busy, Busy

This overly complicated ugly graph is really quite simple. The “underlying” set of curves, for which the legend applies, are composed as below and in

https://garyakent.wordpress.com

 First:

The “underlying” set of curves, for which the legend applies, are composed as follows:

1.) The straight black diagonal line represents expansion of the universe if it had occurred at the speed of light.

2.) The green curve represents the exponential expansion of the universe according to equation 3 against proper time, t, and the extensive variable R, below. It rises almost straight up at very very small values of t, then rises more slowly, nearly leveling off; then it rises again at a more sedate rate after about 2×10-14 u (time in geometric or natural units).

3.) The deep red curve refers to the slope of (2.), the velocity of expansion, i.e. the first derivative in units of U/u. It declines very steeply from an apparently infinitely high level very very early, passing through a minimum at extremely small t = 2×10-14u, whereupon it rises monotonically as shown. This is a unique and very fortuitous feature of this relation.

4.) The purple curve is supposed to represent the acceleration of (3.), i.e. the second derivative.

5.)  The sky blue curve represents “root time”, “reduced time” or “relativistic time”, t1, the (inverse e)th root of proper time, t where t1 = t(1/e)

An unexpected interaction between t1 and the rest of the exponential form produces a fortuitous minimum in expansion velocity, dropping to near zero when t is very small (which occurs much too close to the origin to show), which is a crucial feature of this graph (see the relevant plot in the image series, #97 at Gak on FotoThing.com).

This is due to the odd way that exp(B*t1) behaves at very small t. Otherwise there would be no time for the essential equilibration of temperature and density that is postulated by Alan Guth’s theory. Without such a peculiar minimum in the rate of expansion, because of how t1 works, there would be no initial exponential induction period as is assumed by Guth. If the parameter, e, is adjusted so that Hubble expansion decelerates overall, having negative or concave curvature, no such minimum in the expansion rate occurs at small values of t.

The curve (5.) is the key to the exponential equation and is the secret of why it works. Perhaps this reduced or root time may represent how proper time is vastly dilated especially as it rises from an ultra-massive physically real singularity at our initial proper time, when t = 0. For the inflaton particle is postulated by Guth to be a humongously strong gravitational point particle in the meta-time of a multiverse.

Now, this curvature parameter, e, can be adjusted to describe an open, flat or closed universe. It can be adjusted to show much less curvature or much more. So, the position and duration of the minimum that occurs very early for curve (3.) can be modulated.

But, changing parameters A or B will make (2.) completely miss passage through the point (1,1) on the graphical grid. This would not work at all because the universe with all its matter and energy must have mass/energy M == 1 µ at t = 1 u. So, here is another label for the abscissa.

When the vertical axis is interpreted as being the scale factor a(t), then the horizontal axis must be interpreted as having proper time t = 1u = 27.44 billion years (at least) because from the time of emission of light that became the CMB, to 13.72 billion years (until now, the Hubble time), our universe has expanded another 13.72 billion years (at least). If we insist that the horizontal axis t = 1u = 13.72 billion years, only the Hubble time itself, then the Hubble distance is only 13.72 billion light years or R = 1 U on the vertical axis.

Note that herein R = r, interchangeably. It does not matter how the axes are interpreted as long as one remains consistent.

The author worries that expansion velocity accelerates beyond the speed of light too soon. After over half of the universe lifetime from this point, by now we should have lost contact with the CMB. This can probably be fixed by choosing the parameter, e, so that the curvature of expansion in (2.) is rather a lot shallower. This should also move the point where its slope exceeds c by quite a bit to the right. Then, its effect could be viewed as being more benign.

According to Guth and the consensus of cosmologists and other astrophysicists who truly respect Inflation Theory, the universe was once a purely quantum entity. It still is. The very success of quantum theory is evidence that ours is a quantum universe. Why should the universe not follow a mathematically defined trajectory like this?

Second:

Overlain upon this graph is another graph with three more curves, a black, an orange red and a bright blue one.

orange red: the curve for potential energy (P.E.), from a graph of y = ln(x) representing the integral of 1/kr, where k = 1 m and x = r = t, representing either the Hubble time or the actual age of the universe (more or less).

Here, y is the vertical axis which is to be read as P.E. of the “inflaton” (or galactic) hyper-excited gravitational field or as whatever else may be the correct quantity, in natural units, depending upon which curve one is reading. Ideally, this ln(x) integral denotes the initially (near the origin) extremely high relative P.E. condition of the hyperbolic ultra-massive black hole gravity.

Hyperbolic gravity fields are allowed by GR if proper assumptions and boundary conditions are posited to find a metric, much like the Schwarzschild metric, for the space wherein is assumed to reside a singular black hole.

That is, this curve represents the “state” of the universe’s initial hugely massive “inflaton” point particle and its associated “inflationary” hyper-excited renormalizable 1/kr gravitational field. Every field always has an associated particle, so there would have been an inflaton particle and it should have been an hyper-massive or “excited” quantum point particle already possessing that “renormalizable” higher energy hyperbolic gravitational field. How could it have been else in the Everett multiverse which Guth explicitly posits?

Now, there is no question that, if one accepts Inflation Theory then, one must accept the multiverse and meta-time.

The author compares the implied transition from an evolving higher energy gravitational field state toward a changing ground state to a time dependent quantum transition or to a Tanabe-Sugano diagram in transition metal ligand field theory.

B.)   black: the curve from y = -1/x, the lower energy P.E. state of the universe under the ground state of its normal gravitational field, which was proportional to 1/r2.

P.E. being the vertical axis now, as in (A.), it is equal to -1/x or -1/r or -1/t (because the scale has r = R = t = 1 since this is all in natural or geometric units). The ln(x) = ln(r) = ln(t) curve and the 1/x = 1/r = 1/t curves have been translated so that P.E. (A.) = P.E. (B.) when ordinate x = r = t approx. = 0.34 and then the whole graph was re-scaled and vertically re-positioned to fit other abscissa or P.E. versus t constraints.

Originally, this point was (1,0) or the intersection of both curves, where

ln(x) = 0 and

-1/x +1 = 0

got from a pair of equally scaled graphical curves adapted from figures in a textbook definition of the natural logarithm.

This was not an arbitrary adjustment. It was done so that the orange red ln(x) curve approaches the origin at the same time that the sum of the (A.) orange red, and (B.) black, curves equals the bright blue curve of (C.) as it passes through the point (1,1).

Then, the intersection of (A.) & (B.), at the bright green circle, which used to be at the point (1,0), had to be translated so that its position with respect to the underlying Hubble time axis corresponded to 0.344 u, or 9 billion years ago in Hubble time, when the universe is seen to have begun to “re-inflate”, consistent with observations of “acceleration”.  So, there is only one way that the overlay curves could have been re-scaled and repositioned to meet these constraints.

bright blue: the superposition or linear sum or mixture of the gravitational potential energy states represented by curves (A.) and (B.).

Now, as was said before, (C.) had to be made to pass through the point (1,1) on the underlying graphical grid. That is, the total P.E. had to equal all the matter and energy in the universe at t = 1, the present, including “Dark Matter” and “Dark Energy”, so that M == 1µ at t = 1u. So, total mass/energy M is yet another label for the abscissa.

The orange red curve in (A.) is identified with Dark Energy, and it is seen to keep on increasing into the future while the associated scale factor, which is to be read on the abscissa as R or a(t) in this case, also increases. Then, with these simultaneous increases, the P.E. density of the universe remains constant as is indeed postulated for Dark Energy.

At the instant of the BB, the hyperbolic inflationary gravitational inflaton field of the inflaton point particle had a potential energy curve that would have looked like the orange red curve in (A.) but, no matter/energy had yet had a chance to follow this P.E. curve at the instant that the BB occurred. And, afterward it might have been forced to follow the black curve in (B.). The matter/energy in the universe could not actually experience any of the individual states represented by (A.) or (B.) but could experience only the superposition of states in (C.), bright blue.

Still, it is all consistent. The orange red P.E. curve continues to increase as it should and the black P.E. curve becomes “nearly” constant as it must while the bright blue total P.E. curve increases as the energy density of the universe must remain constant, just as theory demands.

See? Simple. (Yuk! Yuk!)  By comparison, this should make filing an income tax-return seem like a piece of cake.

This is what time dependent quantum transitions mean. This is what the multiverse means. We can experience only the final resultant of the waveform vector sets for all terms in the total probability density wave sum. We experience only the superposition, not the separate states.

Yet, some cosmologists describe Inflation Theory minus the point particle concept and sans a multiverse with no meta-time and also without the implication that the inflaton field must be an excited renormalizable gravitational field with its associated hyper-massive particle. So, the quantum nature of Inflation seems foreign. One can pick and choose the ideas one likes only in regard to congressional legislation in a hidebound committee but, Inflation Theory will never become that kind of law.

If the hyperbolic black hole gravitational field can be validated and extended to the entire universe this way, then we would have hard evidence for a kind of a multiverse.

Figure 2   Rules Sheet from TK Solver Plus for the “e-Model” of Inflationary Expansion of the Universe

The graphical series in Fig.1 was computed using the equations presented in this rules sheet.

#98 A  Equations for the mathematical model of inflationary Hubble expansion of the universe according to extensive variables.

 98 A  universe accelerating hubble expansion guth inflation

http://www.fotothing.com/Gak/photo/dd3000c76d3f16f595af18ef135cfad2/ 98/92-100

image 98A  in this image series

http://www.fotothing.com/photos/dd3/dd3000c76d3f16f595af18ef135cfad2_fab.jpg

image enlargement

This is the rules page from a UTS TK Solver Plus math program that was used to plot the exponential expansion curve shown in image 96. It depicts acceleration of Hubble expansion, the 1st and 2nd derivatives of this curve as well as a straight diagonal line showing a baseline of what expansion would look like if it occurred at the speed of light. Image 95, at FotoThing.com under Gak, shows a minimum in the 1st derivative curve, the expansion rate. The rate drops to near zero, indicating an extreme slowdown in expansion that constitutes a virtual pause at around 1^-14 to 3^-14 u or “universe time”, time in “natural units” or “geometric time”. This period lasts around 2 x 10^-14 u or 8,660 seconds (144 minutes) but is sensitive to somewhat arbitrary initial conditions like those chosen by Alan Guth in his first paper on inflation. This pause may have come earlier or later and lasted longer or shorter depending on these initial conditions. Such changes would have to be pairwise and in the correct sense or else the intersection with (1,1) will be lost.

Dark Matter is an unnecessary ad hoc fix

January 11, 2012


The singularity at the center of a black hole must be unique and have testable consequences.

Dark Matter is an unnecessary ad hoc fix to fill in the blanks in the Friedmann model under the FLRW metric. Galactic supermassive black-holes exist as true physical singularities according to the Kretschmann invariant and Schwartzchild’s analysis of his spacetime metric under GR. Therefore, as point masses, they must possess a hyperbolic (1/kr) gravitational field, NOT a field that falls off as 1/r2. Now, k = constant = 1m, S.I., for dimensional integrity. It is not true that GR cannot tolerate hyperbolic spacetime geometries. “The universe is hyperbolic.” said Albert Einstein in his classic paper of 1915. An hyperbolic field will give constant orbital acceleration to orbiting bodies as far from the center of a black-hole as we might like to measure. This means that bodies near the periphery of a galaxy should seem to move at constant velocity because rotational acceleration does not drop to near zero there as with a 1/r2 inverse square law, it becomes consant. This constant velocity distribution effect has actually been measured and has given rise to the notion of Dark Matter.

Gravitation does not fall nearest to zero between galaxies in a cluster either. So they too can bend light and affect redshifts in ways that mimic Dark Matter. The rotation of galaxies in clusters is also influenced by the black-holes that they contain with their 1/kr gravitational potential profiles. The not quite counterbalanced redshift effects in the Sunyaev-Zeldovich phenomenon are influenced by the hyperbolic galactic and galactic cluster gravitational fields that exist as light falls out of such clusters and super-clusters into a large void and as it climbs out of it again after the universe has expanded by another billion light years or more.

Scientists are mapping, not Dark Matter, but the huge extent of the network of hyperbolic galactic and super-galactic gravitational fields that behave like Dark Matter because of the mathematical properties of the hyperbolic gravitational field are similar to that expected for Dark Matter.

Primordial massive and supermassive black-holes with their 1/kr galactic gravitational fields can also mimic the “halos” of dark Matter that are postulated to have existed just after the big bang and before the emission of the cosmic microwave background. There is nothing that Dark Matter explains that cannot be accounted for just as well or better by the hyperbolic black hole gravitational field.

The hyperbolic 1/kr supermassive black-hole galactic gravitational field explains “the Dark Matter Effect” without Dark Matter and it is more parsimonious and is a falsifiable hypothesis, unlike Dark Matter which is revised every time no Dark Matter is found.

The conditions for validity of Birkhoff’s Theorem are not met for real black-holes. Therefore, Birkhoff’s Theorem does not apply. It sometimes may be used as a first approximation, but it cannot be depended upon as a rigid rule for precise calculations. “The physics near at the extreme curvature of a black-hole singularity is not well defined”. This covers Birkhoff’s too.

It does too matter how the internal mass is distributed if it is contained within a single point. Then, in fact, it is NOT distributed at all! This is the point of Kretschmann’s invariant and Schwartzschild’s GR analysis of the consequences of his metric. Ordinarily, the distribution would not matter. But, a singularity must be different. If this is not explicitly acknowledged in some way, then to say there is a singularity with such intense curvature of spacetime in its vicinity that the laws of physics must begin to break down is a meaningless fatuous gesture to humility. It is false humility if it has no ameliorating effect on professional arrogance. Please, do not just restate Birkhoff.

I contend there is a loophole here or a gross misinterpretation. The consensus interpretation of Birkhoff and of Schwartzschild/Kretschmann cannot both be true at the same time. There must be a measureable consequence of the presence of a singularity that is beyond imaginary untestable gedanken experiments. The test is the hyperbolic gravitational field. It results in a nonzero constant rotational velocity distribution effect in spiral galaxies, ellipticals, globulars and galactic clusters. This is easier to believe than Dark Matter.

The very same phenomena that are used to argue for Dark Matter can be used to argue for the hyperbolic field. So, it is testable. But, how do we choose between them? I think that Occam ’s razor is the principle of choice here. WIMPS and neutralinos and the other oddball particles that have been proposed require ad hoc additions to theories or their complete rewrites. The hyperbolic field is far simpler. All that is needed is acknowledgement that the black hole singularity is unique. No rewrite of GR. No undetectable new heavy particles that get given self-serving, revised, lower detection limits every time they are determined to be really undetectable.

There seems to be a tendency of cosmologists to think inside the box. They never really consider anything that is outside the consensus. So too do journal editors rely on  conventional wisdom. They would all have been supremely comfortable with the Pope’s decision to censor Galileo.

“Cosmologists are always wrong, but never in doubt.”   Lev Landau

Nobel Prize for Perlmutter & Riess

December 19, 2011

If one carefully reads the papers submitted to ArXiv astrophysics from after 1998, one sees that Saul Perlmutter’s and Adam Riess’s supernova research groups were not independent (as claimed) and that they were in serious communication. Perlmutter and Riess actually wrote a paper together before they could have otherwise come to cooperate.

They say that the data that the two groups got regarding the distances to supernovae type 1a and other bright extremely distant objects was not concordant at first. In order to force the two data sets to conform, they admit that they had to apply a mutual “adjustment”. This artificial factor was used by both groups to bring the data of each set into alignment with the other so that a smooth plot could be made that included all the data points.

The sense of this artiface alone is the sole “evidence” that they both cite for an accelerating rate of expansion of the universe. They might have applied the adjustment factor to the other data set in the opposite sense. Then, the universe expansion rate would have been seen as decelerating.

There was a choice to be made. A cynic might hazard a guess as to why they made the choice that they did. A cynic might also claim that P&R’s colleagues on the Nobel Committee were grossly biased because they were close friends and few in number. When a subcommittee reports to the full committee, though, their recommendation is often taken as Gospel. How often has the Nobel Prize award been found to be, if not unwarranted, uncompelling?

In college, we had to write laboratory reports on the textbook experiments that we did in lab. We were warned against manufacturing data. Our professors all said that this kind of “fudging” is a big “NO NO”. Ethical standards are not just for students. Still, as professionals who certainly are good scientists, Permutter and Riess, no doubt, think that they were perfectly well justified in applying their adjustment factor and did so in all honesty. But, the result is the same.

Gary’s Blog

April 1, 2010

Stephen Hawking cannot say whether God exists. All he can say is that there is no need for us to assume that He does.

Try this scenario on for size:

The existence of the universe is accounted for by the postulates of the inflationary Big Bang. Alan Guth mathematically defines an “inflaton” particle that was a child of a highly excited gravitational field. This extremely excited and energetic inflaton particle, being much like an excited radioactive nucleus in an atom or an excited particle in a particle accelerator machine, had to decay eventually. When it did so, matter and energy, in types that we know, were formed. The inflaton particle was a point-particle, that is, a point-mass having mass, gravitational potential energy and all other types of energy equivalent to the matter and energy that we can tally today all rolled up inside.

For a black-hole F = GMm/kr, k = constant = 1m (SI System), for dimensional purity. The inflaton particle possessed a hyperbolic 1/kr  gravitational field with gravity existing prior to the big bang. The prior existence is said because we live in a multiverse (See followers of John Archibald Wheeler)) and the inflaton was only one of many such particles that existed and do still exist in the meta-universe (see Hugh Everett).

The big bang happened. And, it will happen again for other inflaton particles and has already happened in many others of them, long “before” our inflaton decayed into our universe. In other words, we must postulate “meta-time” as well.

Since the gravitational field existed prior to decay of the inflaton, gravity being “leaky” (George Dvali, Lisa Randall), overflowing boundaries like those associated with an infinitely dense, infinitely intense gravitational field stemming from a point-mass, it had such a hyperbolic 1/kr potential profile. When the inflaton decayed, the 1/kr field began to collapse. It is still collapsing, transitioning to the 1/r^2 gravitational field that we see today. On a graph, we see that the equivalent hyperbolic potential energy curve is inherently greater than the equivalent 1/r^2 parabolic curve. So, the continuing collapse of the hyperbolic 1/kr field releases energy into the visible universe. The only way this energy can be manifested is by means of the expansion of spacetime.

This expansion is kinematically equivalent to our having all the discrete objects in the universe rushing away from each other. Most of the time, we should think about expansion kinematically to avoid confusion.

Now, a graphical look at hyperbolic exponential decay reveals that acceleration of expansion may still be occurring slowly, but it should be happening at an infinitesimally lower and lower rate (after all, expansion has been progressing for 13.72 billion years already and the manspring should have wound down quite a lot by now). This potential energy, bound up in the remaining remnant of the hyperbolic gravitational field, is real energy (with mass equivalent via E = mc^2). It accounts for the “missing mass” of the universe and the accelerating rate of expansion without invoking any new forces like quintessence.

The unique role of gravity in this scenario is a key. You might say that gravity is the only true force, all other forces being derived from it, and its status is fixed by this role. It is such a weak force and cannot easily fit into quantum theories because of its status as the “Ur” force. (Ur was the first true city in Western civilization).

This scenario is hypothetical, to be sure. But, it is no more speculative than Alan Guth’s original formulation of “Inflation” as a solution to the various paradoxes of the Big Bang theory. There is “speculation” and there is speculation. Some intriguing speculation is more robust and worthy than other kinds.

At any rate, we see here that there is no need for God in accounts of the origin of the universe. This does not mean that there is no God. But, if He exists, He must be infinitely bigger and more powerful than anyone ever thought. He presides over a multiverse, not a mere universe, and He has made meta-time as well as standard time. He must be truly almighty.

Gak