Gravitational flux from cosmic expansion drives galactic dynamics

Gravitational Flux from Cosmic Expansion Drives Galactic Dynamics Arto Annila∗ Department of Physics, University of Helsinki, Helsinki, Finland † (Dated: November 27, 2025) Rather than postulating dark matter or modified gravity, we attribute the acceleration beyond the local field, seen in galaxy rotation curves and velocity dispersions, to gravitational flux from cosmic expansion. This effect, of order 10-10 ms-2, follows without free parameters from applying Gauss’s flux theorem to all receding galaxies, reproducing the generalized Tully-Fisher and Faber-Jackson relations. Although isotropic on large scales, the enormous efflux of space cannot be ruled out by the shell theorem—formulated for stationary rather than dispersing matter—nor dismissed with distance, since the quadratic rise in galaxy number outweighs the inverse falloff of their potentials. From this perspective, space is not mere abstract geometry but a dynamic relativistic substance: a spin-2 boson, paired-photon vacuum with undulating energy density consistent with general covariance and tests of relativity. Accordingly, bodies move neither inward by inexplicable attraction nor outward by unexplained expansion, but by coupling, via mass, to space in flux. The Type Ia supernova data are then consistent with space expanding through the influx of quanta released from matter in astrophysical processes, rather than implying a dark-energy-driven metric acceleration. Structures emerge on ever larger scales because the virial radii of efflux–influx balance lengthen as spatial density thins from the early universe to the present sparseness, giving rise to the observed cosmic gravitational redshift. I. INTRODUCTION The conundrum of why stars do not spiral out of galaxies, despite their velocities too high to be bound by visible mass, echoes the one-time puzzle of why electrons in their curved paths do not radiatively spiral into the nucleus. Back then, Bohr proposed that atoms are stable because the angular momentum L=mevr =nh/2πof an electron of mass me, orbiting with velocity vat a distance rfrom the nucleus, is quantized in multiples nof Planck’s constant h, reduced by the 2πcircumference factor. However, the Bohr model did not actually explain atomic stability by associating the standing electron wave with a quantized physical substance. In turn, galactic stability is ascribed to dark matter that tops up visible matter to balance the angular momentum L=mvr =mr2dφ/dt =Ut, with the gravitational potential energy Uover the orbital period t. Then, in stable orbit, a star of mass m, with velocity vat a distance rfrom the galactic center, sweeps out equal areas r2dφ in equal times dt, by Kepler’s second law. However, despite matching observations, the dark matter hypothesis does not explain galactic dynamics by associating the missing mass with a specific physical substance. Although the ultimate nature of matter and space lies beyond effective theories, their parameters are often taken to represent real substances. Yet, after extensive studies and surveys, dark matter remains elusive. The gravity of the problem cautions against dismissing paradigm shifts lightly — could the dark matter parameter in the metric model of spacetime, in fact, represent the acceleration arising from the flux of spatial physical substance? In analogy with hydrodynamics, the acceleration due to flux does not cancel out: bodies are drawn inward as the spatial substance escapes between them to sparser surroundings. Conversely, bodies are driven apart as the spatial substance enters between them from denser sources. Inertia, too, suggests that bodies are coupled to a spatial substance. Thus, despite isotropic cosmic expansion, the acceleration from flux cannot be ruled out by the shell theorem formulated for stationary rather than dispersing matter, nor dismissed with distance, since the quadratic increase in galaxy number outweighs the inverse falloff of their gravitational potential. To account for the effect of expansion on galactic dynamics, we apply Gauss’s theorem ΦR=RaR·dSR=−4πGM to the whole universe of mass M, treating space itself as a relativistic physical substance with density-dependent wave speed c. This spatial substance expands through a spherical surface SR= 4πR2at radius R=ct, confining causal influence within cosmic age t≈13.8 billion years, not at the comoving radius derived from metric expansion through a model-dependent scale factor. As the universe ages, the spatial substance expands from the denser past to the sparser present along the gradient aR=−∇ϕin the gravitational potential ϕ=−GM/R =−c2of the undulating substance with characteristic wave propagation. ∗Contact author: [email protected] †https://www.mv.helsinki.fi/home/aannila/arto 2 By Birkhoff’s theorem, the detailed dynamics of expansion is smoothed out on large scales, leaving an asymptotically flat universal field aR=GM/R2=c/t ≈7.0×10−10 ms−2— of the same order as the threshold acceleration ∼10−10 ms−2where galaxy rotation curves and velocity dispersions begin to deviate from local Newtonian dynamics [1–9]. The Machian definition GM/c2R= 1 of the gravitational constant G[10–13], essentially the mass–energy equivalence for the whole universe Mc2=GM2/R, yields M=c2R/G ≈1.7×1053 kg. Then, the corresponding estimate for the energy density in matter ρMc2≈0.6×10−9Jm−3is naturally in balance with the spatial energy density, consistent with observations of a spatially flat universe [14], though distinct from the much smaller baryonic matter density ρb derived from the metric model. In the following sections, we first argue that cosmic expansion sets space in flux, giving rise to a field that permeates the universe. Next, we provide a physical basis for this flux in the form of a transparent, quantized, relativistic, and weakly interacting spatial substance, where photons are paired in opposing phases, consistent with terrestrial measurements and astronomical observations. Then, we show that galactic dynamics results from the efflux of space into sparser surroundings, while expansion itself results from the influx of quanta released from matter through astrophysical processes. Leaving no need for dark matter or dark energy, we conclude that galaxy rotation curves, velocity dispersions, large-scale structure formation, and Type Ia supernova data are more naturally understood as manifestations of space in flux than as evidence of a dark sector. II. THE UNIVERSAL GRAVITATIONAL FLUX As proposed by Mach and formalized by Sciama [10], the gravitational potential ϕof all receding matter gives rise to inertia. The change ∂v/∂t in the velocity of a body relative to the relativistic spatial substance, characterized by wave speed c, induces a field of −(ϕ/c2)∂v/∂t. This all-permeating effect of distant receding matter arises from the geometric structure of the universe: while the gravitational potential of each galaxy falls as 1/r, the number of galaxies rises as r2with distance. Consequently, the most distant galaxies, such as those imaged by the James Webb Space Telescope, contribute the most to ϕ, rendering inertia insensitive to local variations [10]. We are not the first to construct cosmology from Mach’s principle to address dark matter and dark energy problems [15, 16]; however, we describe the influence of distant matter via a tangible spatial substance. All ordinary matter, dispersing from the dense origin of the universe at t= 0 to its sparse present state at t=R/c, generates a gradient −∇ϕ=aR. According to Gauss’s theorem for gravitational flux, this gradient drives space into flux ΦR=ZaR·dSR=−4πG ZρMdV =−4πGM (1) through the surface SRat radius R=ct. The total mass M=RρMdV sums all sources within the expanding volume V. Rather than the critical density ρc= 3H2/8πG derived from the first Friedmann equation for metric expansion, the mass density here is given by ρM= 1/4πGt2≈6.3×10−27 kgm−3, decreasing over cosmic time tthrough transformations of matter into spatial substance, as it is consistent with Poisson’s equation for gravity, ∇2ϕ= 4πGρM= 1/t2, the differential form of Gauss’s theorem. The spatial substance is characteristed by the wave speed c≈3.0×108ms−1that increases as the density ρ= ρMc2≈6×10−10 Jm−3decreases in balance with the decreasing mass density ρM[14]. This dynamic balance requires spatial continuity, given by ∂ρ/∂t+∇·(ρv) = σ, where σdenotes the rate of matter-to-space transformations through astrophysical processes [17–19]. In integral form, this becomes RVσdV =d/dtRVρdV +R∂V ρv·dS, which is the Reynolds transport theorem generalized with a source term. For an isotropically expanding universe with radial velocity v=cˆr, the surface term reduces to the outward flux across a spherical boundary of S= 4πR2. During the diluting expansion, the gravitational flux evolves as dΦR dt =−4πd dt ZGρMdV =−4πd dtGM =−4πc3,(2) where the balance condition Mc2=GM2/R, analogous to the virial theorem applied to the universe [11–13], rearranges through R=ct to c2R=c3t=GM, and thus differentiates to c3. This volumetric change through transformations of matter into space in the least time naturally results in an isotropic expansion that conserves total momentum dp/dt = 0. The total power of transformations P=Z4πR2dR c2dρM/dt =Z4πc2t2cdt c2(d/dt)(1/4πGt2) = c5/G (3) is equal to the Planck luminosity LP=c5/G ≈3.6×1052 W [20]. 3 The seemingly classical equations do not reduce to Newtonian gravity, where the mass is conserved. While consistent with mass-energy equivalence, the gravitational flux does not have a one-to-one correspondence in general relativity because spacetime does not fully geometrize the spatial substance—its flow along density gradients, its emergence from matter, its evolution in energetic balance with decreasing matter, and its quantized character. Gravitational flux is analogous to electromagnetic flux. Sharing the same undulating spatial substance, gravitation and electromagnetism propagate with the same wave speed c2=GM/R = 1/εoµo, determined by the gravitational potential and the vacuum permittivity εoand permeability µo[21–23]. Continuity in the gravitational potential manifests itself as inertia, just as continuity in the electromagnetic potential manifests itself as displacement current and inductance. As anticipated by Faraday and Einstein [24, 25], gravitation is integral to space wherever density exists, whereas electromagnetism is configurational to space where phase coherence persists. The two remain uncoupled because electromagnetic components are transverse to the null geodesic — the least-time path of a photon. The notion of space as a substance endowed with physical properties once initiated a paradigm shift from actionat-a-distance to causal interactions propagating at finite speed [21, 25]. Building on this view, gravity is no longer an inexplicable Aristotelian attraction; instead, bodies move because they couple, via mass, to an all-pervading spatial substance that flows toward thermodynamic balance along paths of least action. III. THE PAIRED-PHOTON VACUUM To ground the physics of gravitation in a spatial substance, we revive aether, however, as a transparent, relativistic, quantized, and locally Lorentz-invariant quintessence comprising quanta of light. Since the photon has never been observed to divide or decay, it stands as the indivisible and indestructible building block of both vacuum and particles [26]. This atomistic premise could be falsified, but to the best of our knowledge, all evidence remains consistent with it. Elementary particle reactions, including annihilation and pair production, continue to be consistent with the tenet that both space and matter comprise photons. The Michelson–Morley experiment disproved a light-carrying medium, not the light-comprising substance we propose: rays of photons, real rather than virtual, paired with opposite phases (Fig. 1) [18, 27, 28]. This neutral spin-2 composite shares the properties attributed to the graviton. As constituents of the vacuum, photons invariably propagate at the characteristic wave speed c=λ/τ, defined by the wavelength λper period τ. Consequently, light traverses a fixed distance Lin equal time both parallel (t∥= 2L/c) and perpendicular (t⊥= 2L/c) to Earth’s velocity v[23], consistent with relativity. Put simply, the paired-photon vacuum is Lorentz invariant, consistent with the null result of the Michelson–Morley experiment. FIG. 1. Two copropagating wavelets with opposing electromagnetic components (colored dark and light) illustrate a pair of photons out-of-phase, forming a massless, spin-2 composite particle without a net electromagnetic field. The very existence of gravitational waves suggests that space is a physical substance with density variations propagating at the characteristic wave speed c. Then, the chirps detected at the Laser Interferometer Gravitational Wave Observatory (LIGO) are better understood as changes in vacuum wavelength rather than interferometer arm length — a hypothesis that once troubled Lorentz himself [29]. Furthermore, stellar aberration θ= arctan(cy/n ÷cx/n) = arctan(cy÷cx), in Cartesian components, resulting from Earth’s motion with velocity v=cx, is inherently independent of the refractive index n, not because space lacks substance. Similarly, the Sagnac time difference, ∆t= 2(v/n ÷c/n)(L/c), is fully consistent with a dynamic, relativistic, paired-photon substance. Following Fresnel’s reasoning, the Fizeau experiment is understood to show photons propagating at a lower wave speed, c′=c/[n−(n2−1)v/c]≈c/n + (1 −1/n2)v, due to the overdensity (n2−1) in the vacuum that permeates the water flowing at a velocity v/c ≪1. In short, although these experiments and their reiterations ruled out the luminiferous aether, they did not rule out the possibility that the vacuum itself is composed of photons. 4 The paired-photon vacuum also makes sense of astronomical observations by relating a local potential GMo/r to the universal potential c2=GM/R through n2=c2/c′2= (1 −GMo/c2r)−1≈1 + GMo/c2r, as observed in the perihelion precession, geodetic precession, frame dragging, escape velocities, gravitational lensing, redshift, time delay, gravitational waves, decay times, and clock rates [27, 30–33]. The dissipation rate of photons, or time dilation t′=γt, likewise depends on gravity and velocity vthrough n2=c2/c′2=t′2/t2= (1−GMo/c2r)−1= (1−v2/c2)−1, as demonstrated by the Pound–Rebka, Vessot–Levine, Rossi–Hall, and Hafele–Keating experiments. In turn, the geodesic surface of the oblate Earth, with radius roand spinning at velocity ωro=v≪c, shows that the gravitational and kinematic effects balance as GMo(1/ro−1/r′ o) = v2. Analogous to gravity in general relativity, the paired-photon vacuum can be geometrized, constrained by the intrinsic properties of the photon. The photon is massless because it cannot couple to the vacuum it constitutes, which defines the photon’s path through the null geodesic condition gµν dxµ dλ dxν dλ = 0,(4) encoded in the metric gµν, where xµ(λ) are coordinates along the geodesic with the affine parameter λpreserving the proportionality of intervals. The finite wave speed csets the causal structure, given by the null spacetime interval ds2=gµνdxµdxν= 0. The full geodesic equation, accounting for both curvature and torsion of the photon path, d2xµ dλ2+ Γµ νρ dxν dλ dxρ dλ −1 2Tµ νρ dxν dλ dxρ dλ = 0 ⇒d2xµ dλ2+ Γµ νρkνkρ−1 2kµSνρkνkρ= 0,(5) with kµ≡dxµ/dλ, geometrizes the vacuum with a generalized connection ˜ Γµ νρ = Γµ νρ −1/ 2Tµ νρ, where the symmetric part Γµ νρ accounts for variations in vacuum density via the metric gµν, while the antisymmetric part Tµ νρ =kµSνρ encodes the vacuum phase through Sνρ =−Sρν, akin to the electromagnetic tensor Fνρ. In the proposed paired-photon vacuum, there is no free test photon moving through an external medium; rather, every photon is an integral part of the paired-photon medium, a non-trivial vacuum state. Consequently, torsion aligns with the direction of photon propagation and encodes the transverse phase correlations of this self-sustaining structure. The relation Tµ νρ =kµSνρ thus naturally describes a photon as part of the background photon sea. Because the phase (polarization) is transverse to the propagation direction, the electromagnetic field remains uncoupled from gravitation, i.e., the density of the paired-photon substance. Although geometrization of gravity via the Einstein field equations recast instantaneous action as motion in curved spacetime, it also redirected attention from explaining gravitation itself to modeling its effects. Accordingly, Friedmann introduced the scale factor a(t) to account for early cosmological observations with the Hubble parameter H≡˙a/a. Later, dark matter and dark energy parameters were added to fit further data, yet without explaining the cause of expansion. IV. GALACTIC DYNAMICS Galaxies are so extended that, far from their dense centers, the efflux of space drawn along with expansion reveals itself in stellar velocity dispersions and circular velocities. Similarly, galaxy clusters are so outspread that the efflux is apparent in their velocity dispersions. On even larger scales, beyond the radii of flux balance, far-flung galaxies are flown farther apart by the enormous influx emerging from matter-to-space transformations throughout the universe. Rotation curves, velocity dispersions, and recession all point to expansion as the common cause of radial and circular accelerations aR=c2/R =u2/r = 2πv2/r ≈10−10 ms−2, on top of local acceleration ao=GMo/r2. Consequently, the mass versus the radial u=√aRrand orbital v=paRr/2πvelocity lines run parallel in the log-log plots, offset by a factor of √2π≈2.5 [34], and the single-parameter relations a=ao+aR=u2/r for velocity dispersions and a=ao+aR/2π=v2/r for rotation curves fit well, almost as if Newtonian dynamics were modified [9, 35, 36]. To focus on the dynamics of a galaxy, a group, or a cluster, we single out a local flux Φofrom the universal flux (Eq. 1) ΦR= Φo+ ΦR−=Z(ao+aR−)·dSr+ZaR−·(dSR−dSr) =−4πGMo−4πG(M−Mo) (6) 5 by partitioning aRinto a=ao+aR−, threading through the local surface, Sr= 4πr2, enclosing the local baryonic mass, Mo, within the radius, r, and the remaining universal field, aR−, threading through SR−Sr. Assuming symmetric mass distributions locally (by the shell theorem) and globally (by the cosmological principle), aoand aR−are radial and hence parallel, allowing their magnitudes to be directly compared. The source of the local field, ao=GMo/r2, is Mo, and the sources of aR−=G(M−Mo)/R2are all other ordinary masses, M−Mo. When considering a galaxy, a group of galaxies, or even a cluster of galaxies, Mo≪M, and hence aR−≈aR. A. Radial acceleration When the local ρMoexceeds the universal ρMdensity, efflux dominates, and the relative strengths of the acceleration components a≈ao+aR=ao1 + aR ao(7) define three regimes. In dense systems where aR/ao<1, as in large elliptical galaxies, local acceleration rules [37]. Systems where aR/ao≈1, such as rich clusters, show more complex behavior. In sparse systems where aR/ao≫1, the universal acceleration governs; dwarf galaxies, poor clusters, and peripheral objects display in their velocity dispersions essentially only aR[34, 36]. To derive the full velocity dispersion, Eq. 7 is multiplied by the flux relation σ2r∝GMo, through the spherical surface enclosing mass Mo, yielding the generalized Faber–Jackson relation σ4∝aGMo[36, 38, 39], appropriate for the system in global dynamical balance with the whole universe rather than in isolation from it (Fig. 2). The acceleration due to the efflux of space is easily misread through the dynamical mass balance σ2∝G(Mo+ MDM)/r, as if there were dark matter (DM) within the radius of interest ralongside baryonic matter. The smaller the baryonic mass Mo, the greater this misinterpretation, particularly evident in dwarf galaxies [40]. Conversely, the low velocity dispersions seen in globular clusters of ultra-diffuse galaxies do not imply a lack of dark matter [41, 42], but rather reflect minimal efflux from their own low densities, while their peculiar velocities reveal the efflux from their hosting system. Likewise, dwarf satellites show low velocity dispersion and high orbital velocities. B. Circular acceleration Similarly to radial acceleration, a star orbiting in a spiral galaxy experiences total acceleration a=v2 r≈ao+aR 2π=ao1+ 1 2π aR ao=GMo r21+ 1 2π Mr2 MoR2,(8) arising from two contributions: (i) the local field ao=GMo/r2, due to the baryonic mass Mowithin the orbital circumference 2πr, (ii) the universal field aR/2π=GM/2πR2, scaled down by the 2πcircumference factor because the field acts over the full cycle rather than over the linear unit radius, due to the efflux of space drawn along with all receding mass M−Mo≈M[18, 43]. Near the galactic center, the local field ao≫aR/2πexceeds the universal field, so the gravitational flux Φo≈ −4πGMoscales directly with the enclosed mass. In hydrodynamic terms, the efflux of space, perceived as gravitational attraction, is intense due to the steep density gradient between the local ρMoand the surrounding cosmic ρMdensity. At larger radii, where aR/2π≈ao, the universal field becomes discernible on top of the local field [44]. Further out, stars and gas clouds experience essentially only aR/2π≫ao. To derive the full rotation curve, Eq. 8 is multiplied by the flux relation v2r=GMothrough the spherical surface enclosing mass Mo, yielding the generalized Tully–Fisher relation v4=aGMo[36, 39, 45], characteristic of orbital systems in dynamical balance with the universal gravitational field rather than isolated from it (Fig. 2). Similarly to the circular velocities of distant stars, the velocities of satellite galaxies, v4≈aRGMo/2π, remain flat because a≈aR/2π > aois constant, not because v2(r) = G(Mo+MDM(r))/r would be flat, as if there were a dark matter halo MDM(r)∝r⇒ρDM ∝r−2. At even greater distances, the efflux fades as the local overdensity δρ≡(1 −ρM/ρMo) tends to zero, and the velocity v4=aGMo=δρ(ao+aR/2π)GMo(9) decreases, as if the dark-matter halo had steepened [46, 47]. The cubic fall-off of the overdensity δρtoward the flux balance rfb = (Mo/M)1/3Rtraces observations. Milky Way satellite galaxies lie within rfb ≈1.4×106ly, given a baryonic mass MMW ≈1.0×1011M⊙, and clusters of MCL ≈1.0×1014M⊙span rfb ≈14 ×106ly. 6 FIG. 2. Velocity dispersion σand circular velocity vas functions of radial distance r, shown on linear (left) and logarithmic (right) scales, from the center of an elliptical galaxy (black dotted lines) and a spiral galaxy (black solid lines). Their baryonic masses, Mo= 1011M⊙, are distributed according to Hernquist (re= 10,000 ly) and S´ersic (re= 20,000 ly, n= 2) profiles. Velocity dispersions are computed using the generalized Faber–Jackson relation, σ4=δρ(ao+aR)GMo, assuming isotropic stellar motion along the line of sight. Circular velocities are computed using the generalized Tully–Fisher relation, v4=δρ(ao+aR/2π)GMo, assuming circular orbits (Eq. 8). As long as the local density exceeds the universal density δρ≡(1 −ρM/ρMo)>0, the universal acceleration aR=c/t arises from the efflux of space into the expanding universe. For comparison, the Newtonian acceleration ao=v2/r =GMo(r)/r2is also plotted (gray dotted and solid lines). The Colab notebook GalaxyDynamiX is available to vary the parameters. Although reminiscent of MOdified Newtonian Dynamics (MOND), the acceleration relations in Eqs. 7 and 8 do not modify Newton’s law. In MOND, a cosmic-scale threshold acceleration, on the order of 10−10 ms−2, is used as a parameter to model aRof the efflux as if gravity itself were modified. Consequently, this approach fails particularly for dwarf spheroidals, galaxy clusters, and certain irregular or gas-rich systems. Since the fluxes of space along the local and universal density gradients manifest in detailed dynamics, the precise form of the MOND interpolation function, f(ao/aR)ao=a, to account for the mass discrepancy v2/v2 b= 1 + aR/2πaobetween the observed velocity vand the baryonic expectation vb, is not the main issue [34, 36, 44]. C. Recession Beyond the radius, where the local ρMo(r) falls below the universal ρM(r, t) density, the influx of space from astrophysical processes throughout the universe supersedes the local efflux, and the Hubble flow carries bodies apart. As described by Hubble’s law, the radial velocity u=√aRr=cpr/R follows from aR=c/t =c2/R, causing the most distant galaxies to recede at speeds approaching c. The differential form of Gauss’s flux theorem, Poisson’s equation for gravity, ∇2ϕ=∇·aR= 4πGρM=c2 R2=1 t2,(10) gives the decelerating rate of expansion dH/dt =−1/t2with H= 1/t, as the matter density ρMdeclines. Accordingly, the flux density 4πGρMdecreases as its sources Mtransform into spatial substance (Eq. 2). It is worth stressing that R=ct is not a parameter but the extent of spatial substance, determined by its density-dependent wave speed c, and by cosmic time t, summing the photon periods since the onset of expansion. Thus, R=ct should not be mistaken for a statement of linear expansion; rather, the expansion is decelerating because astrophysical processes transform matter into spatial substance. 7 Solving ρMo=ρMdefines the radius of flux balance, rfb =Mo M1 /3 R=Mo 4πρM1 /3 =GMot21 /3,(11) which lengthens as the universe ages (Fig. 3). This scale-free growth corresponds to the power-law autocorrelation of galaxies and voids [48, 49]. The cosmic web becomes coarser not because dark matter concentrates, but because space rarefies over time. Consequently, structures form earlier and on larger scales than predicted by ΛCDM [50, 51]. According to Eq. 11, Milky Way-like galaxies, with r= 150 ×103ly and Mo= 1011M⊙, could have emerged as early as t≈300 ×106years (Fig. 3). Earlier objects were more compact. In turn, galaxy groups began to form around one billion years and clusters around three billion years. The KBC Void, the Local Hole, is naturally the least dense, being among the oldest regions in the universe. FIG. 3. The age tof the universe as a function of decreasing density ρ(Eq. 10) outlines the characteristic gravitational timescale of structure formation, from the early supranuclear densities comparable to stellar-mass black hole densities to the present-day densities of superclusters. The metric expansion fitted to the Type Ia supernova data with dark energy implies an accelerated expansion. In contrast, the decelerating physical expansion naturally aligns with the data without free parameters because light is understood to shift toward red as it travels from the dense past to the sparse present [18, 31, 32]. In other words, in addition to climbing out of local gravitational wells, those of a star, galaxy, and cluster, a photon also climbs the broader gravitational potential of the aging universe. The observed cosmological redshift is therefore not fundamentally different from local gravitational shifts. Accordingly, this physical cosmology, where matter transforms into space resulting in an isotropic expansion, is consistent with observations interpreted through cosmic-scale averaging, unlike timescape cosmology [52, 53] or backreaction due to local inhomogeneities [54, 55], and stands in contrast to the flawed tired-light hypothesis. Inferring from the force of expansion F=c4/G, per SR, the negative pressure −p=F/SR=ρMc2≈10−9Jm−3(Eq. 10) arises from baryonic matter transforming into space rather than from dark energy. 8 V. DISCUSSION Despite extensive searches, dark matter and dark energy remain unsubstantiated, yet are presumed to account for 95% of the universe’s energy content to reconcile cosmological models with observations — a discrepancy that may signal a fundamental misunderstanding of gravitation. Recognizing that perceptions are theory-laden [56], we ask: Could gravitational attraction and cosmic expansion be two sides of the same phenomenon? Frequency shifts only show that distant galaxies recede and nearby ones approach, but not why. A common thread is the characteristic acceleration, on the order of 10−10 ms−2, consistently inferred from galaxy rotation curves, velocity dispersions, and recession velocities — though in opposite directions. Its magnitude, notably close to c/t, points to a universal field aR=c/t =c2/R =GM/R2, related to all ordinary matter Mdispersing throughout the universe, expanding its radius R=ct at speed cover time t≈13.8×109years. By contrast, assuming metric expansion, the calculated acceleration of approximately 0.2c/t due to distant matter falls short by a factor of five [57]. By Poisson’s equation (Eq. 10), the decelerating expansion −dH/dt = 1/t2= 4πGρMis related to the decreasing density of matter ρM, suggesting that space emerges from matter, rather than galaxies drifting apart without cause. After all, the amount of matter consumed by stars, supernovae, and active galactic nuclei is not negligible. Extrapolating from dense origins to heat death ρM(t→ ∞)→0, the transformation of matter into space naturally entails Mc2=GM2/R and defines the matter density ρMequal to the critical density ρc≡1/4πGt2, thus addressing the Hubble tension and rendering the cosmological fine-tuning problem of flatness null and void. From this perspective, the relation ρ= Λc4/8πG between the dark energy density and the cosmological constant Λ models the balance ρ=ρMc2=c4/4πGR2≈0.6×10−9Jm−3between the spatial energy density and the matter density within the causal bounds of the universe 4πR2. At first glance, the unifying view of gravitational attraction and cosmic expansion as a spatial substance in flux, carrying bodies both inward and outward, may seem radical. However, historically, the notion that space embodies gravity is not new [25, 58, 59]. The novelty here is that photons make the medium, characterized by wave speed c, rather than move through some pre-existing medium at speed c. This transparent, relativistic vacuum, comprising light quanta paired out of phase [18], is consistent with the classical experiments, such as the Michelson-Morley null result, and modern ones, such as the dynamic Casimir effect [60], as well as with theoretical foundations: Bose-Einstein statistics, Maxwell’s equations, Lorenz gauge, and graviton properties. Conversely, eventual empirical evidence contradicting this physical plenum, for example, if a photon were observed to split, would falsify the proposed explanation for galaxy rotation, velocity dispersion, and cosmic expansion. From a hydrodynamic perspective, space in flux behaves like any other substance flowing along geodesics toward thermodynamic balance, where forces even out. As the universe flattens toward a state of least curvature, bodies shape into spheroids, settle into planes [38, 39], and galaxies align [61]. Satellite galaxies are not missing around their hosts; instead, universal acceleration, acting as a central force, has zeroed them in on stable orbits. As the expanding space thins, efflux and influx balance ever farther out, and hence ever larger structures stretch across widening voids. Although perturbations to the Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) metric reproduce the peaks in the angular power spectrum of the cosmic microwave background (CMB), they cannot account for large-scale structure formation without invoking dark matter. Since a series of peaks can arise from general principles, not solely from acoustic oscillations [62], the need for dark matter and dark energy parameters suggests that a stretching metric may not faithfully model the physics of expansion. Furthermore, in the FLRW metric, the angular diameter distance is non-monotonic with redshift, in contrast to the intuitive expectation that the farther an object is, the smaller it appears [32]. The even dispersion of distant galaxies and the uniformity of CMB naturally follow from matter transforming into space in the least time [17, 18], rather than from impromptu cosmic inflation. Consistent with Gauss’s flux theorem, Newton’s second law F=dp/dt states that the greater the force, the faster the change: massive stars burn brightest but fade fastest; early-type galaxies decline in number density with redshift faster than late-type galaxies. In essence, the higher the local density, the faster the rate of matter-to-space transformations, i.e., the faster expansion. Thus, regardless of initial irregularities, the least-time principle drives the universe toward isotropy. Unlike dark matter, the universal field of all ordinary matter is inseparable from the matter itself. Thus, abundance matching, which correlates galaxy luminosities with dark-matter halos, is neither theoretically motivated nor empirically substantiated [63, 64]. Furthermore, while dark matter struggles with the cusp-core problem, the universal gravitation of all ordinary matter is naturally flat, featureless, and far-extending, lending itself to single-parameter modeling (MOND). Despite the arguments presented, the explanation of galaxy rotation and velocity dispersion through gravitational flux from cosmic expansion may be dismissed on the grounds that lensing by ordinary matter appears too little by a large margin. However, it is worth recalling that the magnitude of deflection θ, for a known lens mass M⊙, is derived solely from the angular difference between the light rays that graze the eclipsed Sun and those from the night sky. 9 Although it may seem trivial, the parallel displacement of the two rays, nearly equal in magnitude to the deflection itself [65], has been neglected in determining θ[31]. Since the deflected photon also gets delayed, one might argue that the Shapiro time delay ∆t, for a radio signal grazing the solar limb ro, provides an exact calibration between the lensing power and the solar mass free from dark matter. In fact, the round-trip delay 2∆t≈200 µs [66, 67] corresponds by roθ≈c∆tto a deflection θabout five times greater than θGR = 4GM⊙/c2ro[31]. Accordingly, it is no coincidence that dark matter is estimated to be roughly five times more abundant than ordinary matter. Given this discrepancy between gravitational bending and time delay, lensed images of background galaxies do not, contrary to common belief, substantiate dark matter; even the gravitational lensing of the Bullet Cluster, often cited as decisive evidence, can be interpreted through the least-time paths of light without dark matter [18, 31]. In conclusion, the flux of space offers a natural explanation for the phenomena attributed to dark matter and dark energy. 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