The Cosmic Filament Structure As Seeded By Inflated Primordial Gravitational Wave Interference

by Steven Gussman 

THE HYPOTHESIS

        Typically, the largest known structure of the universe, the cosmic filaments, are “explained” by the following argument: it is said that quantum fluctuations in the early universe were inflated during the inflationary epoch, seeding the locations where matter would clump in the universe.¹  I am proposing an alternative hypothesis that attempts a more precise and testable mechanism.  The philosophy of physics is simple: the early universe was a sea of interference between primordial gravitational waves.²  Being curvatures in space time, these waves were inflated during the inflationary epoch to cosmically large sizes.  At these scales, the light-speed propagation of these waves is relatively slow (it's as if the pseudo-random state of the interference pattern at the time of inflation was preserved as it was inflated).  This allowed time in the post-inflationary epoch for matter to be attracted to (or “fall into”) these large “frozen” gravitational wave amplitudes, thus seeding the filament structure of the universe.³  At this point, the primordial gravitational waves are no longer important because the filament-shaped gravity-well of the matter that fell into them is self-sustaining as the waves “slowly” move away from the matter (that is, the curvature that was due to the gravitational waves is replaced by the curvature associated with the mass that fell into it).⁴  As well as explaining the cosmic filament structure, confirmation of this hypothesis would strengthen the inflationary cosmology hypothesis itself; not only does it follow the same logic for generating larger-than-causal-scale homogeneity, but it directly requires the inflation of features of spacetime itself.  Further, it makes a precise prediction of an observable feature of spacetime prior to Big Bang nucleosynthesis (before the first 380,000 years of cosmological history),⁵ which the new class of gravitational wave telescopes could in principle look for.

BACK-OF-THE-ENVELOPE-CALCULATION

        The initial calculation involved in this model is to take the current dimensions of the cosmic filament structure, treat them as the amplitude and wavelength of giant gravitational waves, and scale them down, back through cosmological history, to predict what the cosmic gravitational wave background would have looked like, early on.  The cosmic filaments have a depth of A ≈ 20 Mly and a length of R ≈ 100 Mly.⁶  The depth will be taken to be the amplitude of the gravitational wave, with the length proportional to the time or distance between the source of wave emissions before they collided.  The cosmic microwave background (of the electromagnetic force) is known to have scaled by a factor of 1,000 in the post-inflationary epoch.⁷  By some estimates, the inflationary epoch is thought to have consisted of 85 doublings of the universe.⁸  Therefore the scale factor is:
s ≈ 10^-3 * (1/2)⁸⁶ ≈ 3x10^-29

Applying this scale factor to the present size of the observable universe (T = 13.8 Gly), and the dimensions of the filaments yields:⁹

T₀ ≈ (1.38x10¹⁰)s ≈ 4x10^-19 ly ⋅ 9.461x10¹⁵ m ≈ 4x10^-3 m

A₀ ≈ (2x10⁷)s ≈ 6x10^-22 ly ⋅ 9.461x10¹⁵ m ≈ 6x10^-6 m
R₀ = 10⁸s ≈ 3x10^-21 ly ⋅ 9.461x10¹⁵ m ≈ 3x10^-5 m

This basic model predicts the above order of magnitude for the original gravitational wave interference.  One quick sanity check is to compare these to the kinds of gravitational waves detected by LIGO.  The first detected signal from colliding black holes is supposed to have been three orders of magnitude smaller than a proton:¹⁰
l ≈ 8.6x10^-16 m ⋅ 10^-3 ≈ 9x10^-19 m

These were also supposed to have been “thousands of billions of times” larger at their source:¹¹
l₀ ≈ 9x10^-19 m ⋅ 10¹² ≈ 9x10^-7 m

10^-19 to 10^-7 is a large range, and my calculations fall just outside of it, suggesting that the primordial gravitational waves would have to have been quite energetic, and their sources somewhat close together (happily, the early universe would have been highly energetic and dense due to its much smaller size and the conservation of energy).

OBSERVATION

While on a walk in Shavertown, PA, I noticed someone's landscaping housed a stone with a wave-interference-like surface.¹²  As my mother remarked, the pollen had gathered in the crevices (which may have been what made the pattern catch my eye in the first place, given that it makes it far more noticeable).  In my model, the stone is the wavy fabric of spacetime and the pollen is the matter being attracted into its wells, creating the filament structure:

On another walk, at Hillside Farms, I noticed that the interference pattern in the creek was being projected by sunlight onto the floor of the body of water.  Here, the water is the fabric of spacetime, and the sunlight is the matter:

For my own observations along these lines, I filled a container with four quarts of water and created some wave patterns, using a camera's flash to project the wave interference pattern below.¹³  As you can see, something like the filament structure can be created in this way, though a more thorough analysis of the precise filament pattern and its ability to be created by wave interference is needed.  The first image was created by tapping the sides of the container:

The second by lifting the container and rotating it like an unbalanced top before placing it back down:

And finally, the third and fourth images were achieved by tilting the container and letting it drop, in both dimensions, one after the other:

NEXT STEPS

This small paper's scope is only to establish the basic philosophy-of-physics hypothesis, make an order-of-magnitude estimate of the primordial gravitational waves posited, and provide a proof-of-concept that general wave interference patterns and the cosmic filament structure look similar.  The immediate next step will be to read The Cosmic Web: The Mysterious Architecture Of The Universe by Richard Gott (Princeton University Press) (2016) for a survey of the relevant literature.  If the hypothesis still seems viable, some of the work that will need to be done includes: designing and performing a controlled experiment using the container, water, and light; making more careful and precise calculations using the most accurate available values; calculating what the gravitational wave background should have diminished to, today; comparing characteristics between my own and the hypothesized primordial gravitational waves of others; taking into account the potential effects of the time-evolution of the gravitational waves during the inflationary and expansionary epochs; and taking into account the potential effects of the time required for matter to fill the seeded volumes.

FOOTNOTES

1. Nobel-Prize winning theoretical physicist Sir Roger Penrose is skeptical of this, I believe even having called it “hand-waving”, see Fashion, Faith, And Fantasy In The New Physics Of The Universe by Roger Penrose (Princeton University Press) (2016). [This vague reference will have to do for now as I do not have the book in question with me as I stay in the PA mountains with my sister and brother-in-law. I plan on making the citation more specific upon returning to NJ].

2. Some may complain that this is too much of a general relativistic picture for the early universe, but A. perhaps the primordial waves were in some GUT-field which broke symmetry during inflation, leaving the gravitational component in the present epoch; and B. I am not the first to speculate about primordial gravitational waves (the BICEP-2 experiment was originally thought to have observed them before it turned out to be a misinterpretation of the data).

3. If gravitational waves contain both a positive / concave attractor well and a negative / convex repulsive curvature, the latter could be what keeps the the voids so empty. More likely, these regions are just deconstructively flat (not attractive nor repulsive). I do neglect here a complication from the motion of the waves which means that they should be expected to be a bit bigger than what's seen at the filament dimensions because the moving edges of the primordial waves would not be filled as nicely as the inner portions, creating a fraying, feathering diminishment of matter at the edges of the filaments.

4. Of course the constructive interference of the curvature associated with the gravitational waves and the masses attracted to them will be larger than the gravitational waves' alone, and their curvature contribution will leach away as those waves pass by.

5. Value from “Origins Of The CMB” (Berkeley) (https://www.universeadventure.org/big_bang/cmb-origins.htm#:~:text=The%20first%20light%20radiated%20after,all%20matter%20existed%20as%20plasma.&text=As%20the%20universe%20expanded%20and,bind%20to%20nuclei%2C%20forming%20atoms).

6. Values from “Galactic Filaments” (Swinburne University) (https://astronomy.swin.edu.au/cosmos/g/galactic+filaments). This page also includes a simulated image of the filament structure from Paul Bourke and Alexander Knebe which looks especially like the light shown through waves in water and projected onto the bed below (if you layered the pattern into the third dimension).

7. Value from “Origins Of The CMB” and using “Wien's Displacement Law” (Wikipedia) (https://en.wikipedia.org/wiki/Wien%27s_displacement_law) (note that I have not read this entire entry) which further cites “Wien Displacement Law Constant” (CODATA) (2018) (though I have not read this page). Considering light is an oscillation in the electromagnetic field, it stands to reason that the expansion of spacetime would only expand its wavelength and not its amplitude; for waves in the expanding fabric of spacetime, it seems appropriate to scale all of their features.

8. Value from “Inflation ” by Frank H. Shu (Encyclopedia Britannica) (https://www.britannica.com/science/cosmology-astronomy/Inflation#ref1070097) (note that I have not read this entire entry).

9. The calculations that follow use a conversion factor between lightyears and meters obtained from Google's conversion calculator.

10. Values from “Gravitational Waves Detected 100 Years After Einstein's Prediction” (Caltech) (2016) (https://www.ligo.caltech.edu/news/ligo20160211), “Scientists Make First Direct Detection Of Gravitational Waves” by Jennifer Chu (MIT) (2016) (https://news.mit.edu/2016/ligo-first-detection-gravitational-waves-0211), and “Proton” (Wikipedia) (https://en.wikipedia.org/wiki/Proton) (note that I have not read this entire entry) which further cites “Proton Size Puzzle Reinforced!” (Paul Scherrer Institut) and “Proton Structure From The Measurement Of 2S-2P Transition Frequencies Of Muonic Hydrogen” by Aldo Antognini et al. (Science) (2013) (though I have not read either of these works).

11. See “What Are Gravitational Waves” (Caltech) (https://www.ligo.caltech.edu/page/what-are-gw).

12. I suspect it must have originally been in water, and that the pattern is due to long-term erosion. Curiously, this seems to predict that the overall wave interference was not perfectly random over that time period, or it would have been expected to cancel out and merely shave the rock evenly.

13. The six quart container measures 8 3/8”x 8 3/8” x 7 1/4” and can be purchased on Amazon: https://www.amazon.com/gp/product/B001BZEQ44/ref=ppx_yo_dt_b_asin_title_o02_s00?ie=UTF8&psc=1. The camera-phone used was a Motorola Moto E 6. Waves were created by either tapping the sides of the container (which tended to make more container-shaped waves), rotating the container before placing it back down which created more natural looking waves, or tilting the container both ways and letting it drop which created initially container-shaped waves which would then create circular waves at the four corners due to their rounded shape; the hope is that where these meet, a filament pattern can be created. I will leave a rigorous experiment where such variables are kept track of for the future.