Alexander Franklin Mayer amayer@alum.mit.edu SensibleUniverse.net Interpreting SDSS extragalactic data in the era of JWST A Full-HD Digital Monograph J ames W ebb S pace T elescope (2022 – ) Sloan Foundation 2.5 m Telescope S loan D igital S ky S urvey (1998 – ) © 2023–2024 A. F. Mayer Study each page with care and attention to detail. 📄 Table of Contents 2 Review of the canonical cosmological model ............................................................................................... 3 JWST observations ................................................................................................................................. 7 Predictive models confronted by empirical data (6-page preview ) ................................................................ 12 MAGIC23 conference abstract @cern.ch .................................................................................................... 18 Two predictive cosmological models ......................................................................................................... 19 The Sloan Digital Sky Survey (SDSS) ......................................................................................................... 24 SDSS theta- z data ................................................................................................................................. 27 The new cosmological model ................................................................................................................... 72 Space-density of active galactic nuclei (NED AGN) ...................................................................................... 76 SDSS, 2dF, and NED AGN data suggest fractal cosmic architecture ................................................................ 85 2dF Galaxy Redshift Survey blueshifts ....................................................................................................... 92 SDSS Petrosian magnitudes (redshift-magnitude data) ................................................................................. 93 Summary ........................................................................................................................................... 101 ‘Dark matter’ ....................................................................................................................................... 107 Quotes .............................................................................................................................................. 108 The Astrophysical Journal ( ApJ ) .............................................................................................................. 111 Reproducibility .................................................................................................................................... 112 This is a dynamic document; click here for version check. page # v 2024-05-27-21z amayer@alum.mit.edu • SensibleUniverse.net This blue is reserved for clickable 🔗 Magenta is reserved for annotations. A links icon on any graphic denotes an associated link. This document has 200+ Internet links. Links are retrieved using 4ref.de 🐶 🔗 Study each page with care and attention to detail. 64, 102 • The most fundamental assumption of the Big Bang theory is that the observed cosmological redshift of galaxies is caused by the uniform expansion of space • Such an expansion would cause the space between galaxies to increase over time, which corresponds to a modeled general recessional velocity between galaxies • The wavelength of a receding light source is broadened towards the red end of the visible spectrum in proportion to recession velocity, and similarly by the modeled uniform expansion of space during light propagation; redshift is a dimensionless quantity designated by z that is applicable to photons of any source wavelength. • In a uniformly-expanding medium, each unit of distance expands at the same rate, thus the recessional velocity between points is directly proportional to distance ; doubling the distance between points corresponds to doubling their relative velocity. • Light travels at a fi nite speed; galaxies observed at greater distance (higher z ) are observed at greater lookback time , or farther back on the modeled cosmic timeline from the current ‘age of the Universe’ back to the origin of that timeline at T = 0 • If we reverse the modeled expansion, then all of the galaxies occupy a volume of space that becomes smaller and smaller over time, culminating in a hot and dense ‘singularity’ of space and time that Sir Fred Hoyle fl ippantly dubbed the “Big Bang” 3 ⎧ ⎪ ⎨ ⎪ ⎩ details next 3 pages ca • non • i • cal (adjective) : according to recognized rules or scienti fi c laws [historically, often found in need of correction]. Gyr : 1 billion (10 9 ) years Gly : 1 billion (10 9 ) light years or ~10 22 km ... amayer@alum.mit.edu • SensibleUniverse.net © 2023 A. F. Mayer The canonical uniform cosmic expansion — fundamentals The canonical uniform cosmic expansion ( A ) 4 Source of the canonical numerical values: Ned Wright’s Javascript Cosmology Calculator • L and N are equidistant from M , and the distance L – N is 2 d • L and M mutually recede at speed v • N and M mutually recede at speed v • L and N mutually recede at speed 2v d ↔ v , 2 d ↔ 2v , 3 d ↔ 3v ... n d ↔ nv v = H 0 · d v 2 d M L N d = a · D C d Big Bang light travel time (Gyr) comoving distance (Gly) Observer—Now 13.2 30.7 12.8 27.5 10.4 17.2 12.2 23.9 7.8 10.9 5.8 7.3 2.5 2.7 4.3 5.1 1.3 1.4 13.7 46.4 0 0 0 ∞ scale factor (1 + z ) –1 0.50 1 0.33 2 0.20 4 0.14 6 0.91 0.1 0.83 0.2 0.71 0.4 0.63 0.6 1 0 a z t D C 13.3 32.8 0.08 12 0.10 9 The scale factor ( a ) is the cosmic radius (i.e., the ‘size of the Universe’) relative to ‘now’ ( 1 ). The light travel time ( t ) is the di ff erence between the cosmic age ‘now’ and age at z . The comoving distance D C ( z ) to a particular object has a fi xed value over time, similar to the angle between two points on the surface of an inflating ball. The proper distance in a particular epoch is d = a · D C , so d and D C are equivalent ‘now’ , and the proper distance between galaxies at z > 12 was considerably less than 1/10 th of current values. The Hubble constant ( H 0 ) is the current-epoch ( a = 1 ) rate of expansion, typically measured in km/s/ Mpc © 2023 A. F. Mayer amayer@alum.mit.edu • SensibleUniverse.net H 0 = 69.6 km · s –1 · Mpc –1 ≈ 0.07 c · Gly –1 Ω M = 0.286 Ω Λ = 0.714 redshift ( z ) ⎧ ⎨ ⎩ 2v ⎧ ⎨ ⎩ The canonical uniform cosmic expansion (B) 5 © 2023 A. F. Mayer amayer@alum.mit.edu • SensibleUniverse.net BB! 1. JWST observes a GALAXY at z = 9 ; it has fi xed coordinate D C ≈ 30.7 Gly 2. We observe that GALAXY as it existed t ≈ 13.2 Gyr years ago (i.e., in our distant past). 3. At that time, the age of the Universe (i.e., the time since the Big Bang) was about 550 Myr ( T ≈ 0.55 Gyr ). 4. At that time, the Universe was 1/10 th ( a = 0.1 ) the current size. 5. At that time , its distance from the Milky Way was d = a · D C ≈ 3.1 Gly 6. Due to cosmic expansion, its light ‘chased’ the receding Milky Way... 7. and it took t ≈ 13.2 Gyr for that light to arrive at the JWST telescope. 8. At the current age of the cosmos ( T ≈ 13.7 Gyr ), that GALAXY is now at a distance of d = a · D C ≈ 30.7 Gly and receding at superluminal velocity ( v > c ). JWST ~30.7 z = 9 GALAXY now z = 0 z = 0.3 z = 1 9 a = 1 a = 0.5 0.1 a ≈ 0.77 d = a · D C ≈ 30.7 Milky Way D C ≈ 10.9 D C ≈ 3.9 D C = 0 ~0.55 T ≈ 5.9 T ≈ 10.3 T ≈ 13.7 d = a · 30.7 ≈ 23.6 d ≈ 15.4 ~3.1 t = 0 t ≈ 3.4 t ≈ 7.8 ~13.2 Milky Way 🕰 z : redshift a : scale factor D C : comoving distance (Gly) d : proper distance (Gly) T : cosmic age (Gyr) t : light travel time (Gyr) “lookback” In fl ationary epoch 10 − 36 ≲ T ≲ 10 − 32 sec Δ a ~ 10 26 Source of the canonical numerical values: Ned Wright’s Javascript Cosmology Calculator BB! VIEW ANIMATION 13.2 Gly ( Gyr · c ) H 0 = 69.6 km · s –1 · Mpc –1 ≈ 0.07 c · Gly –1 Ω M = 0.286 Ω Λ = 0.714 BB! The canonical cosmic timeline • From 2014–2022, the “ 1% Concordance ” model ( H 0 = 69.6 ± 0.7 , Ω M = 0.286 , Ω Λ = 0.714 ) gave the much-publicized, and ostensibly well-established ‘age of the Universe’ to be about 13.7 billion years , the value that most people today were either taught in school, read about in a magazine, or saw in a television program or Internet science video. • According to the latest (2022) reported “ precise measurement ” of the Hubble constant ( H 0 = 73.30 ± 1.04 ) and “a consensus Λ CDM with Ω M = 0.3 and Ω Λ = 0.7 ”, the modeled age of the Universe ✴ since the singularity has been revised, being reduced to ~12.9 Gyr. • The Λ CDM model with the foregoing parameters correlates the measured redshift of a galaxy ( z ) with the modeled age of the Universe in billions of years ( T ) at that redshift: 6 Big Bang Canonical age of the Universe (Gyr) ▪︎ [1% Concordance model] 0.94 0.87 3.32 3.08 1.56 1.45 5.90 5.49 7.94 7.40 11.27 10.53 9.40 8.77 12.41 11.61 13.72 12.86 0 ∞ 0.50 1 0.33 2 0.20 4 0.14 6 0.91 0.1 0.83 0.2 0.71 0.4 0.63 0.6 1 0 a z 0 0 T 0.37 0.35 0.08 12 JWST is observing galaxies at z > 12 ... 0.55 0.51 0.10 9 H 0 = 69.6 Ω M = 0.286 Ω Λ = 0.714 H 0 = 73.30 Ω M = 0.3 Ω Λ = 0.7 JWST © 2023 A. F. Mayer amayer@alum.mit.edu • SensibleUniverse.net Now Source of the canonical numerical values: Ned Wright’s Javascript Cosmology Calculator redshift ( z ) scale factor (1 + z ) –1 ✴ But NOW , a new published claim [ MNRAS (7 July 2023) ] is 27.7 Gyr! 🤨 7 Blue Dot — Section Mark & Return to Table of Contents • Companion paper: “Surveys with James Webb Space Telescope (JWST) have discovered candidate galaxies in the first 400 Myr of cosmic time. ... Here we identify four galaxies located in the JWST Advanced Deep Extragalactic Survey Near-Infrared Camera imaging with photometric redshifts z of roughly 10–13. These galaxies include the first redshift z > 12 systems discovered with distances spectroscopically confirmed by JWST in a companion paper. ” B. E. Robertson, S. Tacchella, B. D. Johnson, K. Hainline, L. Whitler et al., “Identi fi cation and properties of intense star-forming galaxies at redshifts z > 10”, Nat Astron (4 April 2023). Emma Curtis-Lake et al., Nat Astron (4 April 2023) 8 Fulvio Melina, “The Cosmic Timeline Implied by the JWST High-redshift Galaxies”, arXiv:2302.10103 [astro-ph.CO] (20 Feb 2023). “The so-called ‘impossibly early galaxy’ problem, first identified via the Hubble Space Telescope ’s observation of galaxies at redshifts z > 10, appears to have been exacerbated by the more recent James Webb Space Telescope ( JWST ) discovery of galaxy candidates at even higher redshifts ( z ~ 17) which, however, are yet to be confirmed spectroscopically. These candidates would have emerged only ~ 230 million years after the big bang in the context of Λ CDM, requiring a more rapid star formation in the earliest galaxies than appears to be permitted by simulations adopting the concordance model parameters. This time-compression problem would therefore be inconsistent with the age-redshift relation predicted by Λ CDM. ” 9 FULL ONLINE ARTICLE 10 “Deep space observations of the JWST have revealed that the structure and masses of very early Universe galaxies at high redshifts ( z ∼ 15), existing at ∼ 0.3 Gyr after the Big Bang, may be as evolved as the galaxies in existence for ∼ 10 Gyr. The JWST findings are thus in strong tension with the Λ CDM cosmological model. While tired light (TL) models have been shown to comply with the JWST angular galaxy size data, they cannot satisfactorily explain isotropy of the cosmic microwave background (CMB) observations or fit the supernovae distance modulus versus redshift data well. We have developed hybrid models that include the tired light concept in the expanding universe. The hybrid Λ CDM model fits the supernovae type 1a data well but not the JWST observations. ...” Ivo Labbé, Pieter van Dokkum, Erica Nelson, Rachel Bezanson, Katherine A. Suess et al., “A population of red candidate massive galaxies ~600 Myr after the Big Bang”, Nature (22 Feb 2023); https://doi.org/10.1038/s41586-023-05786-2 Also see: Michael Boylan-Kolchin, Nat Astron (13 April 2023). Rajendra P Gupta, “ JWST early Universe observations and Λ CDM cosmology”, MNRAS (7 Jul 2023); https://doi.org/10.1093/mnras/stad2032 1-min video James Webb Space Telescope ( JWST ) Something is amiss ; the distant Universe ( z ~ 10 ) apparently contains big, mature galaxies, where only “baby” galaxies are predicted to exist so soon after T = 0 JWST observations clearly put the Λ CDM standard model of Big Bang cosmology in jeopardy; has the model indeed failed? Image credit: NASA (Artist Impression) 11 First data release 12 July 2022 Throughout this monograph: Focal points appear in magenta Internet links appear in light blue Follow the data & no winking ... amayer@alum.mit.edu • SensibleUniverse.net webb.nasa.gov ‘While Hubble currently has the ability to peer billions of years into the past to see “toddler” galaxies, the JWST will have the capability to study “baby” galaxies, the fi rst galaxies that formed in the Universe.’ – esa potw1819a (7 May 2018) 😉 (references the controversial 2 Sept. 2023 N Y T article) Each model † is based on a distinct, known exact solution of the Einstein field equations. Model A: Einstein (1917) → Λ CDM model Model B: de Sitter (1917) → ‘RTG’ * model G μ ν + Λ g μ ν = κ T μ ν 12 amayer@alum.mit.edu • SensibleUniverse.net We will compare the predictive accuracy of two competing cosmological models. General Audience: Ignore the unintelligible equations —they don’t matter to you; they are like a foreign language ( 外語 ), and it is perfectly OK that you don’t know it. * Relativistic Temporal Geometry , motivated by Minkowski (1909) Pages 13 – 17 preview that comparison. † The three new ‘RTG’ predictive formulas are a logically consistent set (i.e., any one formula can be true if and only if all three formulas are true). • 🔗 🔗 🔗 🔗 0 : 0 0 5 0 : 0 1 0 : 0 2 0 : 0 3 0 : 0 4 0 : 0 5 0 : 1 0 : 2 0 : 3 0 : 4 0 : 5 1 S p e c P h o t o : z ( r e d s h i f t ) 0 : 2 0 : 3 0 : 4 0 : 5 1 2 3 4 5 1 0 2 0 3 0 G a l a x y : p e t r o R 5 0 g r i ( h a l f - l i g h t r a d i u s 3 - b a n d a v e r a g e i n a r c s e c ) Λ CDM predictive curves 13 0.32 0.08 0.02 amayer@alum.mit.edu • SensibleUniverse.net • Data: SDSS smallest galaxies 10 × reference petroR50_gri - - - Λ CDM curves H 0 = 69.6 Ω M = 0.286 Ω Λ = 0.714 “theta = size / D A ” - - - θ ̅ z data As per di ff erences in ‘measurements’ of ( H 0 , Ω M , Ω Λ ), such variation has no appreciable e ff ect on these curves. intercept 62 ← ⎧ ⎪ ⎨ ⎪ ⎩ Wright (2006) ~2.4M measurements Empirical reference curve (constant intrinsic-galaxy-size as per linear fi t to data points) The data does not support the model; the Λ CDM model fails catastrophically .* * This model is irreconcilable with the data. z -bin Apparent size vs. redshift 0 : 0 0 5 0 : 0 1 0 : 0 2 0 : 0 3 0 : 0 4 0 : 0 5 0 : 1 0 : 2 0 : 3 0 : 4 0 : 5 1 S p e c P h o t o : z ( r e d s h i f t ) 0 : 2 0 : 3 0 : 4 0 : 5 1 2 3 4 5 1 0 2 0 3 0 G a l a x y : p e t r o R 5 0 g r i ( h a l f - l i g h t r a d i u s 3 - b a n d a v e r a g e i n a r c s e c ) petroR50_gri 14 θ ( z ) = C ℓ ( 1 − 1 ( z + 1 ) 2 ) − 1 2 , C ℓ = 1 0.32 0.08 0.02 0.64 0.16 0.04 0.01 - - - θ ( z ) - - - θ ̅ z data amayer@alum.mit.edu • SensibleUniverse.net • Data: SDSS There are no free parameters to modify the curve; C ℓ merely shifts the curve up or down on the θ -axis. (remarkably, not an arbitrary #) The RTG predictive model fi ts the data. C ℓ = 2 C ℓ = 0.5 1 reference constants 69 ← N = 398 3.5k 8.3k 38.8k 34.7k 36.5k 7.1k Bin galaxies: [constant intrinsic galaxy size] Minimal-data measurement z -bin Apparent size vs. redshift V C ( z ) N ( z ) C u m u l a t i v e A G N c o u n t 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 9 C o m o v i n g v o l u m e V C ( V S m o o t s ) 1 0 3 1 0 6 1 0 9 R e d s h i f t ( z ) 0 0 1 0 1 1 1 0 The third and quite certain interpretation of the graph is that this redshift-volume model [ V C ( z ) ] is radically unphysical 3 ρ AGN 7.40E–5 Λ CDM: over time, AGN space density increases by >4 orders of magnitude. Another possible interpretation of the graph, is that ⋘ 1% of AGN that exist at higher redshift are observed and counted by the various astronomical surveys. 15 ρ AGN 1 ρ AGN = N ( z ) V C ( z ) Λ CDM Lookback: 140 Myr Λ CDM Lookback: 12.86 Gyr 6.42 H 0 = 69.6 Ω M = 0.286 Ω Λ = 0.714 1 2 Δ z bin = 0.001 [arbitrary units] The data does not support the model; the Λ CDM model fails catastrophically amayer@alum.mit.edu • SensibleUniverse.net • Data: NED 81 ← (for intercept) >4 orders of magnitude! Volume/ AGN vs. redshift Λ CDM: cosmic galaxy evolution over ~12.7 Gyr S 3 ( z ) N ( z ) C u m u l a t i v e A G N c o u n t 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 9 P r o p e r v o l u m e ( a r b i t r a r y u n i t s ) 1 0 3 1 0 6 1 0 9 R e d s h i f t ( z ) 0 0 1 0 1 1 1 0 S 3 ( z ) = C V ⋅ cos − 1 ( 1 z + 1 ) − ( 1 ( z + 1 ) 2 − 1 ( z + 1 ) 4 ) 1 2 S 3 represents the volumetric ‘surface’ of a Riemannian 3-sphere The fi t of this a priori theoretical predictive curve to the empirical AGN population data is equally remarkable to that for the theta- z data; there are no free parameters available to achieve this fi t. 16 Δ z bin = 0.001 same intercept amayer@alum.mit.edu • SensibleUniverse.net • Data: NED 82 ← C V = 9.7 E 4 (sets the intercept) Volume/ AGN vs. redshift The RTG predictive model fi ts the data. The interpretation of this graph is that AGN are accurately counted, even out to very high redshift, and that galaxy clusters comprise a fi xed percentage of AGN throughout the Universe. intercepts (0.32, 18.2) (0.32, 16.6) Redshift-magnitude curves modeling constant intrinsic brightness 17 Note: g -band data must exhibit 4000 Å break! Data: ~136k SDSS LRGs ( z -band) RTG: m ( z ) = C M − 2.5 log [ 1 4 π ( ( z + 1 ) 4 − ( z + 1 ) 2 ) ] + ε λ ⋅ cos − 1 ( 1 z + 1 ) − C M = 14.82, 13.22 ε λ = 0.5 C M = 15.17, 13.57 ε λ = 0 − − Λ CDM: m ( z ) = K M − 2.5 log [ 1 4 π D 2 L ] − K M = − 0.68, − 2.28 amayer@alum.mit.edu • SensibleUniverse.net • Data: SDSS 97 ← The SDSS Luminous Red Galaxies (LRGs) were speci fi cally selected to have similar characteristics, including their luminosity. extinction RTG constant-intrinsic-brightness model The RTG predictive model fi ts the data. Λ CDM constant-intrinsic-brightness model The data does not support this model.* * The Λ CDM model fails catastrophically https://indico.cern.ch/event/1153372/contributions/5200955/ 18 “Facts do not cease to exist because they are ignored.” – Aldous Huxley (1927) • of ~ 🔗 End of preview; Main Presentation • ⤺ Table of Contents What is Science? (2-minute video) – Yuri Ivanovich Manin , Talk on Computability , Northwestern University (c. 1995) “When I was starting out in mathematics, it seemed very important to prove a big theorem. Now, with more experience, I understand that it is new notions that are more important, for example, Alan Turing’s new notion of computability, which I shall discuss today.” 19 amayer@alum.mit.edu • SensibleUniverse.net I thank Dr. Michael Stephen Fiske , Ph.D. Mathematics, Northwestern (1996) for this quotation. • As per this quote that Dr. Fiske had previously shared with me, I contacted Yuri, and he then invited me to meet with him at his o ffi ce at the Max-Planck-Institut für Mathematik in Bonn on 14 August 2009. We spoke about mathematical physics in a cordial discussion for well over two hours in which I fi lled three whiteboards with equations and diagrams. Our discussion concluded with Yuri memorably re fl ecting on the fact that his contributions to fi eld theory represented a signi fi cant lifetime investment — read between the lines. Best Paper Award HICSS 2022 & 2023 ψ θ ψ x y z 20 Spherical coordinate system ( r , θ , ψ ) amayer@alum.mit.edu • SensibleUniverse.net The following page (21) presents Einstein’s 1917 exact solution of the fi eld equations in the form of a metric (i.e., an equation that measures distance). It is important to understand that the locally-de fi ned blue vector r here is the same dimension of physical space as the blue arc r on page 21, and that the dot at the origin here can represent any point on the circle. The interior region of the blue circle of radius R does not represent space; the other two space dimensions ( θ , ψ ), over which distances between galaxies can be measured, are not represented in the diagram. We call the Euclidean coordinate system on the left, which represents strictly-locally-de fi ned measurable 3-dimensional physical space, a tangent space Each such tangent space has a 4 th coordinate, t that represents time as locally measured in that space; t is mutually orthogonal to the three space coordinates in accord with the locally -applicable Minkowski metric d s 2 = x 2 + y 2 + z 2 + ( i c t ) 2 local Minkowski metric Note that i 2 = –1 This Euclidean coordinate system is valid only in the neighbourhood of its own origin at r = 0. page-21 preview r R s p a c e Milky Way Distant Galaxy ψ - θ Mathematics convention