Case for a Local Big Bang: the ALIVE model

By Josh Havelka

“Everywhere”. The response a layman receives when they ask an astronomer where the Big Bang occurred in the sky is usually summarized with this word. From that layman’s predictably puzzled expression, the astronomer then reassures them that, indeed, while it is hard to imagine, this is what the data is telling us. They would then likely recount how the words “Big Bang” are a misnomer which creates an erroneous image of an explosion in space when it is in fact spacetime that expands and not the matter within it. “Like raisins in a rising dough”. If this cosmology neophyte were to press the astronomer further, the arguments against local Big Bang expansion normally condense into the following statements:

  1. We would have to be at the centre of where the Big Bang occurred to corroborate observations of galaxy redshifts in all directions, which is extremely unlikely and breaks the Copernican principle.

  2. The inverse square law inherent to a local Big Bang would result in a hotspot clearly indicating the Big Bang’s whereabouts which we don’t see.

  3. We would see a “dropoff” of galaxies at the “edgeoftheshell”, which we also do not observe.

  4. Local expansion is a Newtonian model which has been superseded by the immense success of General Relativity.

This article aims to vindicate the instincts of that theoretical layman by refuting these widely held beliefs and by providing a framework for a type of local Big Bang expansion known as the “Absolute Linearly Increasing Velocity Expansion” model, or the ALIVE model for short. By reevaluating the first principles of cosmology, namely the origin of galaxy redshift from recession velocity and the origin of the Cosmic Microwave Background (CMB) dipole, it is hoped another perspective can be explored which seems absent from both the literature and popular science discussions.

Velocity Gradient and the Inverse Square Law

There’s a geometric phenomenon where the combination of a linear velocity gradient and the inverse square law creates a vector field with qualities that may be of interest: consider an explosion of dots, 60 degrees of which are shown in our dot model below, one second after they have exploded. The outer row travels 3.0 units per second, the middle 2.0 units per second, and the inner most row 1.0 unit per second. In other words they were expelled in a circular velocity gradient as a function of radius. Figure 1.0 shows the absolute reference frame of each dot travelling at their respective velocity anti-parallel to the origin.

Using simple Galilean transformations we can demonstrate in Figures 1.1-1.3 how three vantage points would observe every other dot with a recession velocity proportional to its distance and with a velocity vector field anti-parallel to their point of view. With these illustrations it is easy to see how this effect could be responsible for the phenomenon of Hubble Flow because all perspectives would conclude they were at the “centre” of the expansion just as they do in the current Lambda Cold Dark Matter (ΛCDM) model. Moreover it is impossible for any of the nine perspectives to determine which direction is towards, perpendicular to, or away from the origin point when only measuring recession velocities of the other dots; i.e. even though perspective C is closer to the origin than A and B, each would have no way of knowing their absolute velocities nor absolute positions by observing each other’s redshifts alone.

The ALIVE model, then, retains the Copernican principle by not requiring us to be at the centre of where the Big Bang had occurred in order to explain galaxy redshifts. It also asserts there is no such thing as cosmological redshift, it is instead Doppler redshift. 

Figure 1.0: A 60 degree wedge of 9 dots aligned in three rows. Each row is separated by one arbitrary unit length from the origin; each row’s velocity increases linearly as a function of radius; each row’s absolute velocity vector points anti- parallel to the origin. The dot model’s Hubble constant is therefor 1.0 unit per second per unit. Speed of light is instantaneous for simplicity.

Figure 1.1-1.3: Perspectives A, B, C, and their vector fields illustrating how each perspective would see recession velocities of surrounding dots. Note how velocities are proportional to distance but whose increase would asymptote at the speed of light

CMB Dipole and Great Attractor from a Universal Energy Gradient

Our Local Group is travelling towards a gravitational anomaly whose source is still unexplained nearly fifty years since this anomaly known as the “Great Attractor” [1] was discovered. Convergence of the peculiar velocities of the local superclusters to the CMB rest frame has also not been found and so far extends beyond this Great Attractor and perhaps even the Shapley Supercluster [2]. Which is to say, beyond the exact structures that were supposed to be causing a substantial portion of this gravitational pull. What’s more, the dipole in the sky-distribution of distant radio sources does not have a comparable amplitude with the CMB dipole, which challenges the assumption the hotspot in the CMB is caused by the Sun’s movement through space relative the CMB rest frame. Otherwise the radio dipole amplitude and the CMB dipole amplitude would match [3,4]. When we further consider the preferred axis (or the “axis of evil”) [5], and how the CMB dipole is not quite aligned with the bulk flow of the Local Group of which we are a part, and then add all these anomalies together, it seems reasonable to consider an alternative.

This gravitational bulk flow and the CMB dipole are two phenomena with one cause: physical differences in energy density. The same universal energy density gradient that arises naturally from the inverse square law inherent to a local Big Bang model; the same universal energy gradient which creates a global spacetime curvature towards the Big Bang without requiring large-scale structures to account for it. For this reason Alexander Kashlinsky and his team’s discovery of “Dark Flow” [6,7] is suggestive of a local Big Bang, and is perhaps the greatest observational evidence in support of the ALIVE model despite Dark Flow’s quasi-rejection by the cosmology community (Kashlinsky, Atrio-Barandela et al. made two counter-arguments of the Planck collaboration’s “disproving” of Dark Flow which can be found here: [8,9]). Regardless, there is still the mystery of the local bulk flows without convergence to the CMB rest frame out to at least 200 Mpc.

As primordial density perturbations condense into large-scale structures, the global peculiar velocities that initially point at the Big Bang, drift towards the centre of gravity of the nearest large-scale structure as it accrues more matter over time (in our case it’s the centre of gravity of the Laniakea Supercluster, hitherto believed to be a Great Attractor). In other words, in a local Big Bang model, the farther away we observe “dark” galaxy cluster bulk flows, the more we’d expect their peculiar velocities to shift away from their nearest superstructure and towards the Big Bang’s origin. And indeed, this is what is observed from Kashlinsky’s et al. research illustrated in Figure 2.0: blue is the closest sample of galactic cluster bulk flows, roughly aligned with the coordinates of the Great Attractor (and the Laniakea Supercluster’s centre of gravity), and red is the farthest sample of galactic cluster bulk flows which nearly points towards the CMB hotspot peak.

Figure 2.0: combined images of the CMB dipole with galaxy cluster bulk flow direction. Blue = clusters 0.8-1.2 Bly away. Green = clusters 1.2-1.7 Bly away. Yellow = clusters 1.3-2.1 Bly away. Red = clusters 1.3-2.5 Bly away ( Copyright: Nasa, Kashlinsky and his team;  P. B. Lilje).

So where did the kinematic dipole go if we’re still moving through space? The CMB is moving in tandem with us for it too is being pulled by the universal energy gradient back towards the Big Bang’s origin at the same velocity. It is therefor undetectable.

In summary, the Big Bang does have a hotspot. But it’s been described as entirely kinematic in origin despite accumulating evidence which disputes this interpretation. And there are observations of a global energy gradient from the inverse square law. But the Local Group’s inexplicable bulk flow, Dark Flow and the “the axis of evil”, are largely ignored. In any case, we can propound the galactic coordinates for the Big Bang as per the ALIVE model by simply recalling the peak of the CMB hotspot: (l) 264.0° (b) 48.3° (in galactic coordinates).

Thicker than the Observable Universe

A common argument against a local Big Bang model is how we cannot see a drop- off of galaxies in any direction which corresponds to the edge of the spherical shell of materials being strewn into space. Without the observational evidence of such a drop- off, the evidence for a shell and therefor a local Big Bang is negligible. While the ALIVE model indeed assumes our universe is in the geometric shape of a spherical annulus, otherwise known as a shell, the “where’s the edge?” rebuttal requires us only to imagine a thickness of the spherical annulus larger than the observable universe; one that, in all likelihood, is much greater than its current diameter of about 92 million lightyears. A dot diagram probably isn’t necessary but one has been illustrated anyways in Figure 3.0 for uniformity with the other rebuttals and because this is an unusually tenacious claim from even established professionals [10,11,12]. The ALIVE model, at sufficiently large enough scales beyond the observational universe, therefor must abandon the assumptions of isotropy and homogeneity due to the presumed existence of edges somewhere beyond our observational universe.

 

 

Figure 3.0: 60 degrees of a circular annulus of dots crudely demonstrating a thickness well beyond the observable universe, as indicated by the red circle.

An Absolute Motion Inherited Before t=0

Obviously there will be no attempt to refute General Relativity. We will not be bringing back the mysterious dust to explain the precession of the perihelion of Mercury, nor the luminiferous aether. But since the ALIVE model rejects spacetime expansion in favour of a linear velocity gradient arranged in a spherical annulus to explain redshift, it’s necessary to conflate General Relativity with our ostensibly Newtonian model of a local Big Bang because a counteractive force still needs to keep gravity from distorting global curvature into anything than what we observe: flatness (k=0). Gratefully it seems possible to do so when we fully dispense with spacetime expansion and reexamine the definition of the Big Bang at t=0 in that context.

A traditional definition of the Big Bang is when the Friedmann-Lemaitre-Robertson- Walker (FLRW) metric goes to zero, the Planck temperature is reached and General Relativity no longer functions to describe our universe. What a great stroke of luck it was to have our physics make sense the exact moment the universe began. In the ALIVE model however, space was not created in the Big Bang and so whatever existed before t=0 was itself positioned locally in spacetime and could be described classically as either static or in motion. The opportunity to marry General Relativity with the ALIVE model comes when we presuppose the pre-Big Bang energy was the latter; that matter and energy in our universe has an inherent absolute motion which it acquired before General Relativity becomes descriptive of our universe sometime when t<0. To say what caused this absolute motion is well beyond the scope of this article but one can imagine the possibility of a supermassive blackhole having a yet undiscovered equivalent of the Chandrasekhar limit, for example, which created a “meganova” if you will.

Believing that by rejecting spacetime expansion we are rejecting General Relativity is to believe the latter is mutually inclusive of the former. But this is not so. Alexander Friedmann, George Lemaitre, Howard Robertson, Arthur Walker and others derived their equations years after General Relativity was first published in 1915, at a time when there was still debate about the existence of galaxies apart from our own Milky Way, and well before Hubble flow had been formally discovered in 1929. Little was known about galaxies back then, let alone what creates their recession velocities.

The FLRW metric’s dependence on the cosmological principle should have been regarded as a placeholder until more astronomical observations were made, but instead, apparently in the absence of a more convincing alternative, has become a central feature of modern cosmology. Coming from an unremarkable author this may seem like arrogance, however it is only a reiteration of what many notable physicists have expressed, such as Steven Weinberg: “The real reason, though, for our adherence here to the Cosmological Principle is not that it is surely correct, but rather, that it allows us to make use of the extremely limited data provided to cosmology by observational astronomy”. He concludes, “If the data will not fit into this framework, we shall be able to conclude that either the Cosmological Principle or the Principle of Equivalence is wrong. Nothing could be more interesting” [13]. Nearly a hundred years of thought and effort has built on top of this placeholder often mistaken as a foundation, so it’s understandable why questioning the cosmological principle, or entertaining the idea of a radical yet simple alternative such as a local Big Bang model, may be unpalatable.

Unsavoury or not, Figure 4.0 shows a rudimentary schematic of the ALIVE model pre-Big Bang and post-Big Bang in order to visualize pre-Big Bang energy manifesting the relativistic universe we know today. A global absolute velocity arranged in a linear gradient as a function of radius would likely satisfy the counteractive force of gravity required to exist in a flat universe, as well as satisfy the phenomenon of Hubble Flow as demonstrated in Figures 1.1-1.3. The ALIVE model, in summary, contests that t=0 equates to the event of the Big Bang—instead, like to our inability to see beyond the opaque cloud of last scattering, t=0 only indicates some event at which General Relativity cannot peer any further into the past.

Figure 4.0: A red arrow symbolizes an absolute velocity which is inherent to the ALIVE model, the dots represent energy and matter in our current universe as it transitions from whatever energy came before t=0 (the fuzzy lines of the pre-Big Bang).

Brief Discussion & Conclusion

Until the 1960’s, a leading theory in opposition to the modern Big Bang model was known as the Steady State model. For years it asserted that, like the principles of isotropy and homogeneity for galaxies, time itself obeyed the cosmological principle and had no preference for either temporal direction. Curiously, much like the ΛCDM model’s requirement for spacetime energy to remain undiluted by its own expansion, the Steady State model required energy to appear from empty space as well—equivalent to one hydrogen atom per cubic kilometre per year. It was only until the ultra-deep field image was taken by the Hubble Space Telescope that the Steady State theory was thoroughly disproven many years later.

Upon reading this ALIVE theory, the professional who answered “everywhere” to our layman at the beginning of this article has surely found multiple problems with it. And it’s likely those holes would be genuine. It is hoped, though, that by recalling how most cosmological theories have had boisterous support despite glaring issues—e.g. in both the previously mentioned models a form of energy is inexplicably popping into existence—and by demonstrating the simplicity with which we can dispel common arguments against a local Big Bang that have even been made by leading physicists such as Alan Guth (who, in his book The Inflationary Universe, argued statements 1 and 2 [14])—we can at least humour our instincts. A seemingly universal gut feeling which, everything considered, might be the greatest proponent of the ALIVE model in the end.

In closing, it’s recognized these arguments are hardly rigorous from a physics perspective since there is an absence of physics. A proof is clearly not the intention of this text. Instead, the goal is to demonstrate how a local Big Bang, with the conditions of the ALIVE model, may satisfy many of the deficiencies in our understanding of the universe in ways the ΛCDM model cannot through a reexamination of the first principles of cosmology: namely, the source of redshift of receding galaxies and the source of the CMB dipole. Doing so requires a broad framework that oversimplifies the concepts into something like a dot model, while focusing on qualitative arguments rather than quantitative ones (for the time being) in order to break the ice, so to speak. Perhaps the most interesting implication of this ALIVE model is the physical location of the Big Bang in the sky: (l) 264.0° (b) 48.3° (in galactic coordinates) which is towards the Hydra Constellation.

Hopefully it goes without saying that this article, in no way whatsoever, aims to dismiss the remarkable work being done by the cosmology community whose efforts have ascended this scientific field into what’s been called a “golden era”. Of course these arguments herein do contradict many of the fundamental assumptions of modern cosmology, but this is being done solely with the spirit of inquiry in mind, not contempt.

References

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[2] Lavaux, G., Tully, R.B., Mohayaee, R. and Colombi, S. (2010). Cosmic Flow From Two Micron All-Sky Redshift Survey: the Origin of Cosmic Microwave Background Dipole and Implications for ΛCDM Cosmology. The Astrophysical Journal, 709(1), pp.483–498. doi:10.1088/0004-637x/709/1/483.

[3] Ellis, G.F.R. and Baldwin, J.E. (1984). On the expected anisotropy of radio source counts. Monthly Notices of the Royal Astronomical Society, 206(2), pp.377–381. doi:10.1093/mnras/ 206.2.377.

[4] Secrest, N.J., Hausegger, S. von, Rameez, M., Mohayaee, R., Sarkar, S. and Colin, J. (2021). A Test of the Cosmological Principle with Quasars. The Astrophysical Journal Letters, 908(2), p.L51. doi:10.3847/2041-8213/abdd40.

[5] Zhao, W., & Santos, L. (2017). The Weird Side of the Universe: Preferred Axis. International Journal of Modern Physics: Conference Series, 45, 1760009. https://doi.org/10.1142/ s2010194517600096

[6] Kashlinsky, A., Atrio-Barandela, F., Kocevski, D., & Ebeling, H. (2008). A Measurement of Large-Scale Peculiar Velocities of Clusters of Galaxies: Results and Cosmological Implications. The Astrophysical Journal, 686(2), L49–L52. https://doi.org/10.1086/592947

[7] Kashlinsky, A., Atrio-Barandela, F., Ebeling, H., Edge, A., & Kocevski, D. (2010). A New Measurement of the Bulk Flow of X-Ray Luminous Clusters of Galaxies. The Astrophysical Journal, 712(1), L81–L85. https://doi.org/10.1088/2041-8205/712/1/l81

[8] Atrio-Barandela, F., Kashlinsky, A., Ebeling, H., Fixsen, D. J., & Kocevski, D. (2015). Probing the Dark Flow signal in WMAP 9 yr and PLANCK cosmic microwave background maps. The Astrophysical Journal, 810(2), 143. https://doi.org/10.1088/0004-637x/810/2/143

[9] Atrio-Barandela, F. (2013). On the statistical significance of the bulk flow measured by the Planck satellite. Astronomy & Astrophysics, 557, p.A116. doi:10.1051/0004-6361/201321579.

[10] Gibbs, P. (1997). Where is the centre of the universe? [online] math.ucr.edu. Available at: https://math.ucr.edu/home/baez/physics/Relativity/GR/centre.html [Accessed 1 Jul. 2022].

[11] Ask an Astronomer. [online] Cornell.edu. Available at: http://curious.astro.cornell.edu/about- us/102-the-universe/cosmology-and-the-big-bang/the-big-bang/592-can-we-find-the-place- where-the-big-bang-happened-intermediate [Accessed 1 Jul. 2022].

[12] Wright, E. (1997). Cosmology FAQ: Where is center of the Big Bang? [online] astro.ucla.edu. Available at: https://astro.ucla.edu/~wright/nocenter.html [Accessed 1 Jul. 2022].

[13] Weinberg, S. (1972). Gravitation and cosmology : principles and applications of the general theory of relativity. Wiley, p.408

[14] Guth, A. H. (1998). The Inflationary Universe (First Paperback Edition). Basic Books, p.74-75