The Massive Black Hole Bias: A Potential Origin for the Cosmological Redshift-Distance Relation without Universal Expansion

The Massive Black Hole Bias: A Potential Origin for the Cosmological Redshift-Distance Relation without Universal Expansion Gerasimos D Danilatos Version 8: 26 December 2025 https://doi.org/10.5281/zenodo.17855884 ESEM Research Laboratory 28 Wallis Parade North Bondi, NSW 2026 Australia [email protected] Abstract The inference of universal expansion rests primarily on the observed redshiftdistance relation for galaxies. We propose that this relation may arise not from expanding space but from systematic observational biases inherent in deepeld astronomy. At increasing distances, detection limits permit the observation of only the most luminousand thus the most massive and compactastrophysical systems. If the gravitational redshift of these objects is larger than traditionally estimated, a natural correlation arises: objects detected at greater distances will on average exhibit higher intrinsic gravitational redshift. This mimics the functional form of Hubble's law without invoking cosmic expansion. Furthermore, a reassessment of the concept of mass in Push Gravity (PG)a theoretical framework that resolves longstanding inconsistencies in standard mass determination and gravitational couplingsuggests that the gravitational inuence of compact bodies has been substantially underestimated. PG distinguishes between eective mass , the gravitationally active component, and black mass , the inert interior; the former is distributed within a thin, highly absorbing Total Absorption Layer (TAL) surrounding the latter. This reinterpretation alters the relation between luminosity, radius, and mass, and leads to Malmquist-like selection eects that systematically bias high-redshift observations. If correct, these eects imply that the cosmological redshift may be of gravitational rather than kinematic origin, and that the case for universal expansion requires re-examination. The present work develops this thesis and lays the foundation for a cosmology based on PG rather than on spacetime expansion. 1 Introduction The commonly accepted evidence for universal expansion stems from the observed correlation between redshift and distance in galaxies. This correlation is canonically interpreted as a Doppler-like eect resulting from the recession of galaxies embedded in an expanding spacetime. We examine an alternative possibility: the redshiftdistance relation may arise from selection biases connected with mass, radius, and luminosity measurements of distant astrophysical bodies. At large distances, only the most luminous systems remain above detection thresholds. Such systems are associated with the most massive objects or collections of objects: massive black holes, dense stellar populations, compact galactic nuclei, and gravitationally intense environments. This observational ltering introduces several Malmquist-type biases Malmquist (1920) and Teerikorpi (1984): 1. Only the most massive and luminous systems are detectable near the instrumental limits. 2. Their eective radii, gravitational elds, and distances are systematically underestimated under conventional assumptions. 3. Mischaracterization of their luminosity and gravitational environment propagates into distance and mass estimates, compounding the bias. 1 Recent discoveries have intensied these concerns. JWST observations demonstrate the existence of galaxies at redshifts z > 10 with stellar masses exceeding 1010M (Labbe et al. , 2023). These challenge formation timescales in the standard Λ CDM picture. Simultaneously, the Hubble tensiona persistent discrepancy between earlyand late-universe measurements of the Hubble constant (Riess et al. , 2024)suggests that the interpretation of redshift as universal expansion may be incomplete or misleading. In a series of works , Push Gravity (PG) proposes a new conceptualization of mass, radius, and gravitational interaction. PG distinguishes between the eective mass responsible for gravitational coupling and the black mass that constitutes an inert core. The eective mass resides in an extremely thin Total Absorption Layer (TAL) surrounding the black mass. As mass increases, the TAL becomes thinner while the radius increases, leading to signicant deviations from conventional density and radius estimates. This reinterpretation of mass distribution implies that many very massive objectsincluding those observed by JWSTare far larger than conventionally estimated. Their gravitational redshift may therefore be substantially higher than expected under standard GR assumptions. Because only such objects are visible at greatest distances, their enhanced gravitational redshift creates a built-in bias: the further we observe, the higher the redshift. An adequate understanding for the proposed Malmquist biases should extend beyond those analyzed by Butkevich et al. (2005) Thus, the observed redshiftdistance relation may be an artifact of Malmquist-type selection rather than evidence of cosmic expansion. Whereas a qualitative report entitled  Is the Big Bang an artifact? was previously made by Danilatos (2024), the aim of current paper is to explore this possibility quantitatively (Danilatos, 2025b). Notes: A condensed and formally structured subset of the present work, focused on astrophysical and cosmological implications, has been prepared for submission to a journal as an independent article but a preprint can initially be found in Danilatos (2025a). That journal version constitutes a stable snapshot intended for external scrutiny, while the present ZENODO document remains a living research manuscript subject to ongoing revision and numerical renement. Furthermore, a qualitative but informal version of the same subject was rst published under the title Is the Big Bang an artifact? by Danilatos (2024). 2 Prevailing Theory In the conventional framework, three principal mechanisms contribute to observed redshift: 1. Cosmological redshift arising from the expansion of space. 2. Gravitational redshift predicted by General Relativity (GR). 3. Doppler redshift due to peculiar velocities. Of these, only cosmological redshift accounts for the dominant component in the standard interpretation. Gravitational redshift is generally considered negligible in comparison. We review these mechanisms briey below. 2.1 Cosmological Redshift: Cosmological redshift is understood as the stretching of photon wavelength induced by the expansion of the universe. In the FriedmannLemaîtreRobertsonWalker framework, the redshift parameter z relates to the scale factor a(t) via 1 + z=a(tobs) a(temit). (1) Empirically, for nearby galaxies, this leads to the HubbleLemaître law υ=H0D, (2) where υ is interpreted as recessional velocity, D is the comoving distance, and H0 is the present Hubble constant. The tension between earlyand late-universe determinations of H0 (Riess et al. , 2024), and the unexpected abundance of massive, evolved galaxies at high redshift revealed by JWST (Labbe et al. , 2023) (Naidu et al. , 2022; Kokorev et al. , 2023; Gottumukkala et al. , 2024; Giulietti et al. , 2024) suggest that the interpretation of z purely as expansion may require revision. 2 2.2 Gravitational Redshift in General Relativity In GR, photons lose energy as they climb out of a gravitational potential well. For a static, spherically symmetric Schwarzschild eld, the exact gravitational redshift of a photon emitted at radius r is zgGR =1 r1−2GM rc2 −1. (3) Dene the compactness parameter x≡2GM rc2=RS r, (4) where RS is the Schwarzschild radius. Then Eq. (3) takes the form 1 + zgGR = (1 −x)−1/2. (5) As x→1 , the redshift diverges, which corresponds to the approach toward the event horizon. However, all observed astrophysical objects have x1 , even neutron stars where typically x∼0.4 . Thus the gravitational redshifts actually observed in nature are very small, with measured values typically ranging from z∼10−6 (solar surface) to z∼0.3 (extreme neutron star conditions). This is vastly smaller than cosmological redshifts ( z= 1  15 ). Figure 1 illustrates this behavior in the GR curve (red line). The additional curves in this gure result from and are explained by the continued work next. Consequently, within the observable universe so far, large redshifts cannot be attributed to gravitational elds under GR. The general-relativistic expression for gravitational redshift used here follows standard derivations in modern expositions (Carroll, 2004). 2.3 Newtonian Gravitational Redshift Before comparing with PG theory, it is useful to revisit the Newtonian derivation of gravitational redshift using the eective-mass concept for photons. This derivation extends beyond the classical escape-velocity argument of Michell (1784) and produces a closed-form, exact Newtonian expression for gravitational redshift. Because this derivation forms the basis for a subsequent extension, and for good measure, we present all the detailed steps for reference when needed: Let a photon of initial wavelength λr be emitted at radius r from a spherical body of mass M . Its local energy is Er=hc λr . (6) Assuming the photon carries an eective mass meff =E c2=h λc, (7) the innitesimal work done against gravity when the photon climbs by d r is d E=−GMmeff r2dr =−GM c2 E r2 d r. (8) Thus d E E=−GM c2 d r r2. (9) Integrate from r to ∞ : lnE∞ Er=−GM rc2. (10) Exponentiate: E∞=Erexp−GM rc2. (11) Convert to wavelengths: λ∞ λr = expGM rc2. (12) 3 Therefore, the Newtonian gravitational redshift is zgN= expGM rc2−1. (13) To compare with GR, retain the compactness denition x≡2GM rc2, (14) so that GM rc2=x 2 . Then Eq. (13) becomes zgN= expx 2−1. (15) As shown in Fig .1 (orange curve for Newton), even at the limiting case x= 1 the Newtonian redshift saturates at zgN(x= 1) = e1/2−1≈0.6487, (16) which is far smaller than typical cosmological redshifts. Therefore Newtonian gravity, like GR, cannot account for large observed cosmological redshifts under conventional interpretations. So far, both GR and Newtonian predictions do not support our claim stated at the outset. The GR curve diverges as x→1 , while the Newtonian curve approaches a nite value. In both cases, for realistic astrophysical objects, x stays well below unity, yielding redshifts far smaller than those observed in cosmology. The above derivation follows treatments that interpret photon frequency loss via energy conservation in a Newtonian potential (Catto, 2014; Okun, 2006). More importantly, it is based on the critical understanding in Section 7.5. 3 Gravitational Redshift in Push Gravity Theory Push Gravity (PG) revises the understanding of mass and its distribution within a gravitationally active body. The key PG insight is the distinction between: • eective mass Me  the gravitationally active component generally for all bodies variously distributed, but particularly concentrated in an extremely thin Total Absorption Layer (TAL) for very compact bodies, and • black mass  the gravitationally inert component generally for all bodies variously distributed in the interior that does not participate directly in gravitational absorption. Both are components of real mass, or hyle . In PG, the standard gravitational parameter µ=GM is replaced by µP G =GMe=ARg0R2, (17) where •AR is the absorptivity (dimensionless), •g0 is the universal maximum gravitational acceleration, •R is the physical radius of the compact body. This relation arises from the absorption dynamics in the TAL and replaces the conventional GM term throughout Newtonian-style gravitational interactions. Crucially, Me is not concentrated at a point, nor does it correspond to the total rest mass. Instead, it describes the eective action of the absorption layer. To compute the gravitational redshift in PG, one repeats exactly the same steps used in the Newtonian derivationbut replaces GM by the PG gravitational parameter from Eq. (17). This yields the exact PG redshift: zgPG = expARg0R2 rc2−1. (18) 4 Figure 1: Comparison of gravitational redshift predicted by GR (red curve), the exact Newtonian eectivemass model (orange curve), and PG plotted against compactness values x . The PG model produces a family of curves corresponding to dierent eective masses, here shown as labeled powers En , n= 1 →7 , representing compact objects with total mass n M . PG allows large gravitational redshifts even at moderate compactness, owing to its dependence on the physical radius R0 of the compact body rather than on the theoretical Schwarzschild radius alone. 5 Maximum Compactness in PG In PG, a maximally compact object is dened not by a singularity or coordinate pathology but by the saturation of absorptivity and surface acceleration: AR= 1, g(R) = g0. (19) Such bodies possess a limiting radius R0 for a given eective mass Me , determined through Eq. (17). The TAL becomes extremely thin, fully absorbing incident gravions mediating gravity. The interior mass becomes gravitationally opaque (no inertia, inert, gravitationally inactive) but not singular. Substituting AR= 1 and R=R0 into Eq. (18) yields zgPG = expg0R2 0 rc2−1. (20) Dene p=g0 c2, (21) so that zgPG = exppR0 R0 r−1. (22) This reveals that PG redshift depends sensitively on both the radius R0 and the emission radius r . In contrast with GR and Newtonian gravity, PG allows substantial gravitational redshifts even far from r=R0 , provided R0 is large enough. For a direct comparison, we can now dene the compactness factor by x=R0 r (23) and re-write the PG gravitational redshift as zgPG = exp(pR0x)−1. (24) Numerical Estimates Using a preliminary PG nding g0= 1.331942797 ×109m s−2, (25) we obtain p=g0 c2≈1.4819862273 ×10−8m−1. (26) Compact bodies of increasing mass yield increasing values of R0 in PG. We can now complement Fig .1 by illustrating the PG redshift in comparison to GR and Newtonian models. The PG redshift of Eq. (20) is shown against R0/r for a sequence of values of R0 corresponding to eective masses ranging from 1M to 7M . The resulting PG redshifts can exceed unity by large factors, reaching and surpassing the observed redshifts of JWST highz galaxies. In this framework, extremely large redshift values arise not from cosmic expansion but from intense gravitational elds associated with very massive objects whose radii have been underestimated in standard and prevailing analysis. These results challenge the interpretation that large observed redshifts necessarily imply cosmic expansion. 4 A Re-appraisal of Luminosity and Distance by PG Theory Given the distribution of eective mass in PG, especially for compact objects whose gravitationally active mass resides within a thin TAL, the conventional relation between luminosity, mass, and radius requires a fundamental revision. In standard astronomy, the intrinsic luminosity of an object is treated independently of its gravitational structure. In PG, however, the geometry and mass distribution of the TAL directly inuence both the emergent luminosity and the inferred distance. 6 4.1 Conventional Relation Between Luminosity and Distance The observed ux f , intrinsic luminosity L , and physical distance D of an astronomical object are related by the inversesquare law: f=L 4πD2. (27) Here, f= apparent brightness (ux) , L = intrinsic luminosity , D = distance . 4.2 Luminosity of Compact Bodies in PG For general absorptivity values AR<1 , the connection between AR , eective mass Me , and luminosity remains an open theoretical task. However, for maximally compact bodies satisfying AR= 1 , PG provides a clear simplication: the entire eective mass is concentrated in a thin TAL at radius R0 . In such cases there is no need to model radiative transfer from an interior volume; the luminosity is set by surface processes at the TAL. It is therefore plausibleand consistent with PG structureto assume that the intrinsic luminosity scales with the surface area of the absorption layer: L∝Me∝R2 0. (28) This contrasts sharply with GR-based compact objects, where luminosity is either severely suppressed or originates from accretion physics rather than a well-dened physical surface. Distance as a Function of Flux and PG Radius Substituting the proportionality L∼R2 0 into Eq. (27), we obtain D2∼R2 0 4πf ,⇒D∼R0 2√πf . (29) Thus, knowledge of R0 implies knowledge of distance. Determining the Radius R0 from PG Redshift The PG gravitational redshift for a compact body with AR= 1 is provided by Eq. 22 being rearranged as 1 + zgPG = exppR0 R0 r, (30) Taking natural logarithms: ln(1 + zgPG) = p R0 R0 r. (31) For emission from the physical surface of a maximally compact body in PG, r=R0 , hence ln(1 + zgPG) = p R0. (32) Solving for R0 , R0=1 pln(1 + zgPG). (33) Distance in Terms of Redshift and Flux Substituting Eq. (33) into the luminositydistance relation gives D∼ln (1 + zgPG) 2p√πf . (34) Thus, in PG, the distance to a remote compact object can be determined directly from its gravitational redshift and apparent ux without appealing to standard candles or cosmological distance ladders. The absolute luminosity scales with the radius of the TAL, which is itself xed by the PG redshift. This relation has major cosmological ramications. 7 5 Minimum Mass for a True Black Hole in PG In prevailing gravitational theories, particularly General Relativity, a black hole is dened as a compact object whose gravitational eld prevents the escape of any electromagnetic radiation. This condition is formalized by the existence of an event horizon, beyond which all light paths are causally disconnected from distant observers. The dening physical assumption is therefore absolute light trapping, independent of wavelength or photon energy. In the Push Gravity (PG) framework, the same operational criterion is adopted: a black hole is understood as an object from which no electromagnetic radiation can escape. However, because PG predicts a nite and continuous gravitational redshift rather than a divergent horizon, this denition raises a critical question that is usually implicit rather than explicit in standard treatments: given that electromagnetic radiation spans a nite range of wavelengths, does a nite upper limit to gravitational redshift exist, beyond which no observable radiation of any wavelength can reach a distant observer? In PG, gravitational redshift increases monotonically with compactness but remains nite for any nite mass. Consequently, a true black hole, dened as an object from which no light of any wavelength escapes, can exist only if the gravitational redshift exceeds a maximum physically meaningful value. A natural upper bound on wavelength is obtained by considering the minimum conceivable photon frequency. Following the PG framework, we adopt a conservative lower bound of νmin ∼1 Hz , corresponding to a maximum wavelength λmax =c νmin ≈3×108m. (35) Gravitational redshifts in astronomy are inferred from spectral lines, which typically lie in the optical band. A representative emitted wavelength may therefore be taken as λemit ≈5×10−7m. (36) The maximum gravitational redshift consistent with these bounds is then dened by the wavelength ratio 1 + zgmax =λmax λemit ≈6×1014. (37) For maximally compact objects with total absorptivity AR= 1 , the PG massradius relation yields the eective mass required to produce a given gravitational redshift. Solving Eqs.. 17 and 33 for the limiting case with zgmax gives Mmin =c4 Gg0 [ln(1 + zgmax)]2. (38) Substituting the numerical values yields Mmin ≈1.05 ×1038 kg ≈5.29 ×107M. (39) This result implies the existence of a nite minimum mass for a true black hole in PG. Objects below this threshold, regardless of compactness, must necessarily emit radiation at suciently long wavelengths and therefore cannot be completely dark. Because the mass scale depends only logarithmically on the choice of emitted wavelength, the existence of this threshold is robust against reasonable variations in spectral assumptions. The PG framework therefore predicts that stellar-mass and intermediate-mass black-hole candidates are not strictly light-trapping objects, but instead extremely compact bodies with large yet nite gravitational redshifts. Only objects exceeding the above mass threshold qualify as true black holes in the strict physical sense. Horizon-scale imaging of Sagittarius A* and M87* by the Event Horizon Telescope (Akiyama, 2019, 2022) therefore probes the compactness of these objects, but does not by itself establish the existence of an event horizon in the general-relativistic sense. Within PG, such observations are compatible with extremely compact, high-redshift objects below or near the true black-hole mass threshold. This prediction diers fundamentally from the general-relativistic notion of black holes and provides a clear observational and conceptual distinction between the two frameworks. The adopted upper bound on wavelength is not arbitrary, but corresponds to an objective physical limit discussed and developed in the main work Danilatos (2025b). This wavelength is associated with the minimum physical quantum, termed the planckion, which acts as the push particle mediating the fth force eld identied as the Planck eld. Such radiation is expected to be presently undetectable and lies well beyond the infrared and microwave ranges associated with the cosmic microwave background (CMB). A key implication of this result is that the CMB need not be directly associated with true black holes, nor uniquely with an early hot Big Bang phase. Instead, within the PG framework and under the caveat of Section 6.8, the CMB may arise predominantly from cumulative gravitational and other redshift processes operating throughout an eternal universe, as discussed further at the conclusion of this article. 8 Note: For nding the above Mmin outcome, the value g0= 1.331942797 ×109m s−2 applied is the latest theoretically derived estimate within the PG framework (Danilatos, 2025b). Existing terrestrial gravity measurements do not contradict this lower bound, in that no evidence has been found for a smaller eective value. Should future developments of PG establish a larger value of g0 , the corresponding gravitational redshifts would increase accordingly, thereby reinforcingrather than weakeningthe principal conclusion of this work: that gravitational redshift can attain very high values within the PG framework. At the same time, an increase in g0 would reduce the minimum mass required for the formation of a true black hole, relative to the value derived above. This dependence has direct implications for the population, distribution, and observational interpretation of compact objects throughout the universe. 5.1 Observational Implications for LIGO and the Event Horizon Telescope The existence of a nite minimum mass for a true black hole in PG has direct and testable observational consequences for both gravitational-wave and horizon-scale imaging experiments, most notably those conducted by the LIGO/Virgo/KAGRA collaborations and by the Event Horizon Telescope (EHT). Gravitational-wave observations. LIGO and Virgo have detected numerous compact-object mergers, many of which are interpreted within General Relativity as stellar-mass black hole binaries. Within the PG framework, objects with masses below the true black-hole threshold derived above are not strictly lighttrapping entities, but rather extremely compact massive bodies with large yet nite gravitational redshifts. Consequently, the post-merger remnants inferred from gravitational-wave data need not correspond to classical GR black holes with event horizons (Abbott, 2016, 2022). In PG, ringdown signals conventionally attributed to horizon-bound quasinormal modes may instead arise from the total absorption layer (TAL). Systematic deviations from GR predictions in the late-time ringdown spectrum, damping rates, or mode structure would therefore be expected. Precision tests of the no-hair theorem and searches for post-merger echoes provide a natural observational arena in which PG predictions may be distinguished from GR. Event Horizon Telescope imaging. EHT observations of Sagittarius A* and M87* are commonly interpreted as direct images of black hole shadows formed by photon capture at the event horizon. In PG, however, no true horizon exists for objects below the minimum mass threshold. Instead, the observed dark regions correspond to extremely high but nite gravitational redshift within the TAL, which suppresses outgoing radiation without requiring complete causal disconnection (Akiyama, 2019, 2022). This distinction implies that the apparent shadow size, brightness prole, and polarization structure inferred from horizon-scale observations may dier from GR expectations. In the PG framework, the dominant emission arises from the Total Absorption Layer (TAL) located at the compact radius R0 , which may lie well exterior to the GR photon-capture region and the nominal shadow boundary. Radiation from regions interior to the TAL is assumed to be observationally irrelevant at the present stage, as the interior is dominated by inactive (black) mass. Consequently, PG predicts that the observed emission morphology reects the physical radius R0 rather than a mathematical event horizon. Future multi-frequency and polarizationresolved EHT observations may therefore discriminate between GR-based shadow interpretations and the PG prediction of emission governed by a mass-dependent TAL. More details about TAL are provided in a following Section 7.6 and Fig. 2 as part of an introduction to the main work on PG. Discriminating signatures. A combined analysis of LIGO/Virgo/KAGRA and EHT data oers a powerful means to test PG. Objects inferred to be stellar-mass black holes from gravitational waves but lacking a true light-trapping mass would constitute direct evidence against classical horizons. Conversely, conrmation that only supermassive objects exceeding the PG minimum mass behave as fully dark sources would strongly support the PG interpretation. Thus, PG not only oers a revised theoretical denition of black holes, but also makes concrete, falsiable predictions accessible to current and near-future observational facilities. 9 Critical understanding: Converting the classical potential energy to a mass equivalent via E=mc2 applies only when A R= 1 . This means that the exact Newtonian derivation of the gravitational redshift in Section 2.3 necessitates that the photon be treated (considered) as a highly compact body itself. Otherwise, we must introduce appropriate adjustments. There is an in depth investigation in the main work: A theoretical and computational analysis has been implemented in Section  16 Two-sphere variation of mass and force  of version v27. See, in particular, subsection  16.3.1 Energy considerations . Furthermore, we quote from page 163  ...However, if we use extremely dense bodies, then our potential energy expended transforms almost entirely to kinetic mass. Understood that the processes described are reversible. This understanding is compatible with particle physics conrming the conversion of mass to energy, because we may assume that the particles involved are extremely dense, as we have already found for the electron and positron. Hence, the equivalence Eq. 345 blends harmoniously with E=mc2 that was used to derive it.  We have subsequently derived our own Ee=mec2 equation independently under PG. 7.6 Mass Distribution in Absorption Layers The eective (gravitational) mass of a body arises from the absorption of gravions and is therefore not uniformly distributed throughout its interior. Instead, it decreases monotonically from the outer surface toward the center. For low-density bodies, such as planets, the variation is negligible; for stars it becomes noticeable; and for white dwarfs, neutron stars, and black-hole analogues it becomes signicant to dominant. A qualitative representation of this behavior is shown schematically in Fig. 2. Within PG, the internal structure of compact objects diers fundamentally from the picture assumed in conventional physics. Even ordinary bodies contain a small fraction of passive (black) mass. This fraction increases with both size and real density: it is larger in the Sun than in the Earth, larger still in white dwarfs, and dominant in neutron stars and black-hole candidates. The variable shading in Fig. 2 conveys this idea (not to scale), with darker interior regions representing the increasing black-mass fraction. These conceptual diagrams assume average interior densities; however, in practice the real density may vary strongly with radius. PG theory shows that the actual density prole aects all other parameters, and therefore the schematic representation for the Sun should be regarded only as indicative. With accurate data, PG allows the construction of self-consistent internal proles for the Sun, white dwarfs, neutron stars, and any intermediate bodies. The mass-distribution layers depicted in the gure are quantitatively computable from the PG equations. To characterize the depth over which gravions are absorbed, we introduce the total absorption layer (TAL) of a sphere. The TAL is the eective thickness within which the incident gravions are absorbed, thereby establishing the maximum possible surface acceleration of the object. Whether this maximum is actually achieved depends on the relation between the radius R and the TAL: • For planets and most stars: TAL > R , • For compact bodies (white dwarfs, neutron stars): TAL < R , • For black-hole analogues: TAL R . In the Newtonian regime (low density), TAL R , so the gravion absorption eectively samples the entire body; conversely, in extreme-density objects the eective mass is concentrated in a thin outer shell resembling (but being) the Schwarzschild surface. Further details are provided in the main work Although this discussion focuses on gravitational push particles, PG introduces analogous push particles for the electric eld and, more generally, for all fundamental interactions. A unied push-eld framework is under development. To maintain focus on cosmological applications in this paper, we defer treatment of the combined multi-eld interactions. The description above represents an initial conceptualization of interior structure within PG. It is expected to evolve as the theory is expanded, particularly once the classication of electric, nuclear, and other push particles is rened, together with corresponding decompositions of real mass into eective and black components. Future high-accuracy revisions of surface gravity for various celestial bodies will also require updates to the internal PG models. Within this framework, the limiting gravitational acceleration g0 plays a key role in stellar evolution. The transition of a main-sequence star to a white dwarf must occur once the internal pressure approaches the maximum gravionic pressure, p0g=J0 c=g2 0 π2G, (59) a quantity that will be explicitly known once J0 or g0 is measured or derived theoretically. For a rst theoretical value g0= 1.33 ×109m s−2 , we obtain p0g= 2.70 ×1027 Pa, (60) 16 Sun TAL1>>R white dwarf TAL2 neutron star TAL3 black hole TAL4 event horizon astrophysical jet astrophysical jet Figure 2: Diagrammatic representation of the Sun, white dwarf, neutron star, and black hole, illustrating the progressive concentration of eective mass within the Total Absorption Layer (TAL). Increasing compactness corresponds to a thinner TAL and a larger fraction of interior black (passive) mass. 17 well above estimates of the central pressure of the Sun, p≈3×1013 →3.5×1016 Pa. (61) For white dwarfs, such as Sirius B, the central pressure is estimated to be 106 times that of the Sun, giving pdwarf ≈1.8×1020 →2.1×1023 Pa, (62) which is again far below p0g . Thus PG imposes no conict with established astrophysical thresholds for the transition from main-sequence stars to white dwarfs, and onward to more compact states. If the qualitative structure suggested by Fig. 2 is broadly correct, it challenges existing methods for determining mass, radius, and distance of compact objects. For main-sequence stars, where the contraction factor q (see main PG report) is expected to be close to unity, corrections to standard astrophysical measurements may be small. However, for non-main-sequence and compact objects (white dwarfs, neutron stars, black-hole candidates), substantial discrepancies between conventional and PG-derived values may arise. The Chandrasekhar curve, for example, may require modication within PG rather than serving as a ground to reject PG; the same generally applies for established wisdom about the actual existence of the universe, i.e. a universe theorized on probably incorrect principles. PG is being extended into a quantum push eld theory (QPFT), which will allow a comprehensive re-evaluation of nuclear physics, particle structure, and force-eld interactions. This development may ultimately lead to a revised cosmological framework grounded in PG principles. 8 Discussion and conclusions The analysis presented in this work demonstrates that the observed redshift--distance relation, traditionally interpreted as evidence for universal expansion, may alternatively arise from a systematic selection eect coupled to gravitational redshift within the PG framework. Specically, the combined correlation between detection distance, minimum observable mass, compactness, and PG gravitational redshift can generate an apparent Hubble-like law without invoking metric expansion of space. This proposal does not challenge the empirical success of observational cosmology, but rather the physical interpretation of one of its foundational observables. The increasing tensions revealed by recent JWST observations, together with the long-standing Hubble tension, indicate that a reassessment of implicit assumptions is timely. In this context, PG oers a concrete and falsiable hypothesis for a systematic bias that has not been previously incorporated into standard cosmological analyses. If the redshift--distance relation at large distances is dominated by the gravitational redshift of increasingly massive and compact systems, then the inferred expansion of the universeand by extension the Big Bang paradigmmay represent an artifact of interpretation rather than a physical reality. In such a scenario, the Cosmic Microwave Background (CMB) would also warrant reinterpretation, potentially as the integrated, highly redshifted radiation from a vast population of unresolved compact sources, rather than as a relic of an early hot phase. A central strength of the PG framework is that it makes distinct, testable predictions. When galaxies are binned by intrinsic luminosity or eective mass, the redshift--distance correlation should weaken and exhibit increased scatter, reecting the dependence of gravitational redshift on compactness rather than distance. Classical tests such as the Tolman surface-brightness relation must be re-examined, since in PG the observed dimming arises from intrinsic redshift eects rather than spacetime stretching. High-redshift galaxy spectra should display signatures indicative of emission from deep gravitational potentials, and accretion-disk inferences based on GR should yield systematically altered ISCO radii when reinterpreted under PG. PG does not deny the existence of Doppler shifts, blueshifts, or conventional low-redshift gravitational redshifts. All well-established local and lowz phenomena remain essentially intact. The claim advanced here is narrower and more precise: the largest observed redshifts, currently attributed to cosmic expansion, may instead be dominated by gravitational redshift associated with total absorption layer (TAL) structures of massive compact bodies. This distinction is essential and avoids conict with rmly established observations at smaller redshifts. The present exposition has focused primarily on the gravitational eld, characterized by the parameters (g0, G) , but PG further encompasses corresponding push-eld formulations for electric, nuclear, and Planckscale interactions. In extremely compact objects, the TAL is expected to host a layered atmosphere of push particles mediating multiple elds. A complete treatment of these interactions lies beyond the scope of this paper, which is intentionally restricted to cosmological implications. A unied development toward a quantum push eld theory (QPFT) is ongoing. 18 It is therefore imperative to emphasize that the arguments presented here should be interpreted as an entry point rather than a closed framework. A rigorous reassessment of astronomical distance scales, luminosities, masses, and radii under PG requires a systematic remapping of existing data across the observable universe. Such an undertaking necessarily depends on the deeper theoretical foundations of PG, including the distinction between eective gravitational mass and real mass, the structure of absorption layers, and the role of black matter. For these reasons, readers seeking a comprehensive understanding of the physical basis underlying the present cosmological reinterpretation are strongly encouraged to consult the main PG work, currently available in preprint form and under continued development ( (Danilatos, 2025b)). A broader qualitative discussion of cosmological implications may also be found in earlier work addressing the question of whether the Big Bang itself represents an observational artifact. In conclusion, the PG framework oers a coherent and physically motivated alternative interpretation of large cosmological redshifts within a static, at universe. Whether this interpretation ultimately supplants or complements the expanding-universe paradigm is an empirical question. What is clear, however, is that PG introduces new degrees of freedom, new selection eects, and new testable predictions that merit serious examination by the cosmological community. 8.1 A Gravitational Selection Bias as an Alternative to Expansion Under PG, the observable galaxy population at increasing distance is ltered by a Malmquist-type bias of a new kind: weaker or less massive systems fall below the detection threshold, leaving only those with the largest gravitational redshifts. This mechanism provides a purely gravitational explanation for the empirical redshiftdistance relation usually interpreted as evidence of universal expansion. The possibility that such a bias exists has gained additional relevance due to tensions revealed by JWST observations, notably the appearance of massive, luminous highz galaxies at far earlier epochs than permitted by the Λ CDM framework. While the expanding-universe paradigm remains the consensus, the Hubble tension and JWST earlygalaxy crisis strongly suggest that unrecognized systematics may still be present. The PG-based bias proposed here is both concrete and falsiable, and we urge the community to perform the tests outlined below. 8.2 Testable Predictions The predictions listed below apply specically to regimes in which the PG gravitational redshift component satises the dominance condition of the caveat in Sec. 6.8, i.e., where non-PG redshift contributions are subdominant. In such regimes, the observed redshift reects primarily the compactness and TAL structure of massive bodies rather than recessional motion or spacetime expansion. The predictions therefore do not claim to replace all known redshift mechanisms, but instead isolate the parameter space in which PG eects are expected to be observationally decisive. The PG interpretation leads to several specic predictions that dier sharply from those of an expanding universe: 1. Intra-sample scatter. When galaxies are sorted by intrinsic luminosity or mass, the redshiftdistance correlation should weaken, as gravitational redshift depends primarily on compactness rather than distance. 2. Surface brightness evolution. The Tolman surface-brightness test, with its characteristic 1/(1+z)4 dependence, should be reinterpreted: in PG the dimming arises from the intrinsic redshift of compact sources, not from spacetime stretching, implying a dierent functional dependence. 3. Spectral signatures of deep potentials. Highz galaxy spectra should display characteristics of emission emerging from an extreme gravitational environment, not young stellar populations in an expanding universe. 4. Accretion-disk radii and ISCO behaviour. If GR is replaced by PG, the inferred ISCO (innermost stable circular orbit) radius must change. This point is particularly relevant in light of precision tests of strong-eld gravity using gravitational-wave observations of compact binary mergers (Abbott, 2016, 2022), where horizon-scale assumptions enter indirectly through waveform modeling. The same data may correspond to substantially larger eective radii, consistent with PG compact objects rather than GR black holes. These predictions allow PG to be tested without ambiguity. 19 8.3 Mass, Radius, and the Underestimation Problem Sections 3 and 7.6 showed that the mass inferred under GR corresponds only to the eective mass Me in PG, which is a subset of the total real mass (hyle). The proportion of eective to real mass (being the contraction factor , q ) depends sensitively on compactness and the structure of the TAL. As a result, conventional methods systematically underestimate the true radii and gravitational parameters of extremely massive systems. Related concerns have been raised in the broader context of horizonless or non-standard compact objects, where observational degeneracies can mask substantial deviations from general-relativistic expectations (Cardoso & Pani, 2019). This provides a natural explanation for why the largest observed redshifts may be dominated by PG gravitational eects rather than by recessional velocity. The most distant JWST galaxies may therefore be compact PG objects with extraordinary TAL structure and not necessarily early-universe systems. 8.4 Reappraising the Big Bang and Expansion If large redshifts arise primarily from PG gravity, several pillars of the expanding-universe model must be reconsidered: 1. Photometric and spectroscopic mass estimates require correction under PG, especially for systems outside the main sequence such as white dwarfs, neutron stars, and black holes. 2. Tired-light mechanisms may regain relevance, not as a complete alternative, but as part of a more complex redshift budget in dusty or dense environments ( ? Kokorev et al. , 2023; Gottumukkala et al. , 2024; Giulietti et al. , 2024). 3. Gravitational redshift bias increasingly dominates the highz population, while low-mass galaxies fall below detection thresholds. 4. The Cosmic Microwave Background (CMB) may need reinterpretation. If the universe is not expanding, the CMB could arise from the integrated quasi-thermal emission of extremely distant, highly compact PG bodies whose TAL redshifts shift their output into the microwave band. This concept aligns with suggestions by Lovyagin et al. (2022) that static models can account for CMB-like features. The philosophical implications are also noteworthy: a static, eternal, at universe may be physically simpler and avoids several conceptual paradoxes (like singularities, notional Schwarzschild radius, etc.), inherent in Big Bang cosmology. 8.5 Addressing Standard Objections Push Gravity (PG) does not deny the existence of Doppler shifts, blueshifts, or conventional low-level gravitational redshifts. All lowz phenomena remain essentially unchanged and are interpreted in the standard manner. The claim of PG is narrower and more specic: the large and extreme redshifts conventionally interpreted as evidence for cosmic expansion may instead arise from gravitational redshift generated by massive compact PG objects. Several common objections to static-universe or non-expansion models are often raised. The key point is that none of these objections directly invalidate PG, because PG introduces a distinct physical mechanismgravitational redshift produced by extended TAL structuresthat can reproduce many observational signatures normally attributed to expansion. The most frequently cited objections to non-expanding cosmologies fall into several well-dened categories: Supernova time dilation. PG does not dispute the observed time dilation of Type Ia supernova light curves. Rather, PG asserts that the highz component of cosmological redshift may be gravitational, with standard Doppler contributions still operating at ordinary distances. The separation of these components requires systematic reassessment with PG luminosity and massradius relations. Uniform redshift across spectral lines. Critiques that gravitational redshift would produce inconsistent line shifts assume GR-like compactness relations. In PG, light originating from the TAL of a maximally compact object emerges from a nearly uniform gravitational potential, ensuring consistent shifts across all spectral linesmatching observations of distant galaxies. 20 CMB isotropy and spectrum. CMB properties do not exclude PG. Under PG, radiation from a vast population of extremely compact, extremely distant TAL-dominated objects can produce a uniform, thermalized background without invoking a hot Big Bang. This alternative interpretation requires the full PG framework (mass activation, TAL structure, push-particle media) and is developed in the main work. Elemental abundances and large-scale structure. PG modies the underlying massradiusdensity relations of astrophysical systems. As a result, both primordial nucleosynthesis constraints and structure formation scenarios require re-evaluation. These issues do not undermine PG; rather, they represent directions for future detailed work once the expanded QPFT formalism is fully developed. For completeness, and to avoid ambiguity regarding parameter choices, we summarize here the characteristic eld parameters used in PG. The present exposition focuses on the gravitational eld, characterized by the pair (g0, G) with values (1.33×109,6.67×10−11) , in SI units. In the broader theory developed in the main work, each physical force eld is mediated by its own class of push particles, described by analogous pairs: • Electric eld: (g02 = 5.56 ×1051, G2= 8.25 ×1025) • Nuclear eld: (g04 = 5.56 ×1051, G4= 8.25 ×1027) • Planck (new) eld: (g05 = 5.56 ×1051, G5= 2.79 ×1032) The TAL of a maximally compact body acts as a layered atmosphere containing the push particles for all force elds, each contributing to a corresponding eective mass distribution. This layered structure cannot be fully elaborated here; its derivation belongs to the ongoing development of Quantum Push Field Theory (QPFT). For a complete understanding of the cosmological implications, the reader must consult the main PG monograph (Danilatos, 2025b), where these mechanisms, eld hierarchies, and governing equations are developed in detail. A broader qualitative discussion of cosmology from the PG perspective, including early formulations of the static-universe argument, can be found in the earlier preprint Is the Big Bang an Artifact? (Danilatos, 2024). 8.6 A Path Forward The conclusions of this work can be summarized as follows: 1. PG provides a quantitative mechanism for generating very large gravitational redshifts from compact objects with radii far larger than GR permits. 2. A natural selection bias emerges: at greater distances only the most massive PG objects remain visible, producing an apparent Hubble law without expansion. 3. The Big Bang, cosmic expansion, and associated cosmological constructs may therefore be artifacts of misinterpreting gravitational redshift. 4. JWST observationswhich strongly contradict Λ CDM early-galaxy formation timelinesare consistent with PG expectations. 5. 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