The Present Accretion Principle: Temporal Becoming as the Driver of Cosmic Expansion

The Present Accretion Principle: Temporal Becoming as the Driver of Cosmic Expansion Eton J. Ziner-Cohen October 2025 Abstract I propose that cosmic expansion and the passage of time are two aspects of a single process: the continual actualization of physical reality. When new events become actual, spacetime must geometrically enlarge to accommodate them. This Present Accretion Principle (PAP) links the Hubble expansion to the global rate of entropy production, providing a unified physical and ontological explanation for the arrow of time and for the universe’s accelerating growth. In its equilibrium limit, PAP reproduces general relativity; small, smooth deformations away from equilibrium generate testable percent-level departures from ΛCDM in late-time observables. Keywords: cosmology; thermodynamics; spacetime; emergence; arrow of time 1 Introduction — The Problem of Time and Cosmic Expansion The universe expands. Observationally this is beyond dispute; conceptually it remains obscure. Within the standard ΛCDM model, acceleration is attributed to a cosmological constant or to dark energy—terms that describe the phenomenon but do not explain why spatial volume should increase, nor why it increases irreversibly in the same direction as the thermodynamic arrow of time. General relativity tells how curvature responds to energy–momentum but remains silent on the ontological status of time. Its manifold is a fixed four-dimensional entity; every event is equally real; “change” is only apparent. Our lived sense of the present—of the continual emergence of new events—finds no expression in this picture. Conversely, process-based or phenomenological accounts of time treat becoming as primitive but leave geometry undefined. The aim here is to close that gap. The hypothesis advanced is that these two puzzles—the physical cause of cosmic expansion and the metaphysical problem of temporal becoming—are facets of a single principle. The universe expands because new actuality continually enters into being. All realized events persist; the present marks the frontier where potential becomes actual; spatial expansion is the metric consequence of this accretion of actuality. Formally, dVH dt=λΦdNact dt,(1) where VH is the Hubble-scale volume, Nact counts realized degrees of freedom, and λ and Φ are a characteristic volume scale and monotone mapping. When the rate of becoming vanishes, the universe attains holographic equilibrium—the de Sitter limit in which no further expansion occurs. This relation extends earlier ideas that treat cosmic growth as informational or thermodynamic in nature: Padmanabhan’s “emergence of space” [ 1 ], causal-set growth [ 2 ], and thermodynamic/entropic derivations of gravity and cosmic acceleration [ 3 – 6 ]. It leads to a direct, testable 1 consequence: the Hubble rate should correlate with the global rate of entropy production. A confirmed correlation would physically link the cosmological, thermodynamic, and experiential arrows of time. 2 The Present Accretion Principle: Formal Definition and Relation to Existing Frameworks The Present Accretion Principle (PAP) treats temporal becoming as a physical process: an ontological accretion whose geometric counterpart is the increase of spacetime volume. 2.1 Formal Statement Let VH ( t ) be the proper Hubble volume 4 πc3/ 3 H3 , and Nact ( t ) a coarse-grained measure of actualized degrees of freedom proportional to total entropy Stot. Then dVH dt=λΦdNact dt,(2) with λ∼L3 pand Φ monotone. The simplest linear case, dVH dt=λdNact dt,(3) expresses a direct proportionality between volumetric expansion and the rate of realization. When ˙ Nact →0, expansion halts at holographic equipartition. 2.2 Thermodynamic and Holographic Connections If Nact ∝Stot, then dVH dt∝dStot dt,(4) so expansion mirrors entropy production. Vanishing ˙ Stot yields the static de Sitter limit. Padmanabhan’s emergent-space law [1, 7] dVH dt=L2 p(Nsur −Nbulk),(5) appears as the equilibrium limit of PAP: the difference between horizon and bulk degrees of freedom equals the difference between realized and unrealized actuality. Expansion ceases when they coincide. Possible Microphysical Origin of the Present Accretion Relation The proportionality between volumetric expansion and entropy production need not be merely phenomenological. If the cosmic horizon obeys the holographic bound S = A/ 4 Gℏ , then each increment of realized information ∆ S corresponds to an increase of horizon area ∆ A . Interpreting this as the continual activation of Planck-scale degrees of freedom implies ˙ A∝˙ S , and therefore ˙ VH∝˙ Stot once the local curvature is integrated over the horizon scale. In this reading, spacetime volume accretes because information is being realized. 2.3 Relation to Causal-Set Growth In causal-set theory [ 2 ] spacetime grows element by element. PAP provides the continuum analogue: each increment of time corresponds to an increment of actuality, producing continuous increase in four-volume. The mapping Nact ↔n ( t ) connects microscopic element birth to macroscopic expansion. 2 2.4 Entropy, Irreversibility, and the Arrow of Time Equation (4) equates spatial growth with entropy increase. Irreversible processes—stellar evolution, black-hole accretion, structure formation—raise Stot , and hence Nact . Expansion persists only while such processes continue. The thermodynamic, cosmological, and experiential arrows of time are thus one and the same. Dark energy becomes a kinematic trace of temporality’s asymmetry. When the production of new degrees of freedom ceases, expansion freezes into equilibrium. The universe’s geometry records, in its growth, the conversion of potentiality into actuality. 3 Mathematical Formulation: From PAP to Modified FRW Dynamics We work in a spatially flat FLRW background with scale factor a ( t ) and Hubble parameter H= ˙a/a. Standard components obey H2=8πG 3ρ, ˙ H=−4πGρ+p c2,˙ρ+ 3Hρ+p c2= 0.(6) PAP adds a closure relation tying geometry to becoming. 3.1 Horizon-Volume Realization (PAP-H) Let RH = c/H and VH = 4π 3R3 H . Define Nact ( t ) as the number of actualized degrees of freedom. Postulate dVH dt=λΦ˙ Nact.(7) For the linear case Φ(x)=x, d dt4πc3 3H3=λ˙ Nact ⇒˙ H=−λ c3 4πL3 p H4˙ Nact,(8) where factors of Lp ensure dimensional consistency in SI units; in Planck units ( c = G = ℏ = kB = 1) Eq. (8) is exact. Here and henceforth we assume Φ( x )is smooth and strictly monotonic on the relevant domain, precluding pathological or non-invertible forms. Combining (6) and (8) yields a modified acceleration equation in which geometry depends explicitly on the rate of actualization. This can be recast as an effective fluid with density ρPAP and pressure pPAP: ˙ H=−4πGhρ+p c2+ρPAP +pPAP c2i,(9) with ρPAP +pPAP c2=λ c3 16π2G L3 p H4˙ Nact.(10) Acceleration arises when ˙ Nact >0; general relativity is recovered as ˙ Nact →0. 3.2 Comoving-Volume Realization (PAP-C) For data analysis it is convenient to relate expansion directly to the comoving volume: d(a3) dt= 3a3H=βΨ˙ Nact,(11) with Ψ′>0 and βhaving dimensions of time. Taking Ψ(x) = xgives H(t) = β 3a3˙ Nact(t).(12) 3 Substitution into (6) defines an effective dark-energy density ρeff (t) = β2 72πG ˙ N2 act a6−ρm−ρr,(13) and an effective equation-of-state parameter weff (z)=−1 + 1 3H2 dH d ln(1 + z).(14) Variations in ˙ Nact thus generate observable departures from w=−1. 3.3 Microphysical Driver A natural proxy is total entropy: Nact =Stot kB ,˙ Nact =˙ Stot kB , Stot =SBH +S⋆+Sgas +· · · .(15) At late times SBH dominates; empirical histories of ˙ Stot ( z ) allow direct tests of Eqs. (11) and (12) . 3.4 Asymptotics and Consistency De Sitter limit: ˙ Nact →0 implies ˙ H→0, H→H∞. Early times: Large ˙ Nact enhances |˙ H| or H ; constraints from BBN and CMB bound λ and β . Covariance: defining Nact =Rs uµdΣµkeeps the formulation coordinate-independent. 3.5 Minimal Parametric Form For empirical fits, adopt ˙ Nact(z) = ˙ N0 (1+z)α 1 + 1+z z∗γ,(16) peaking near z∗≃1–3. Equation (12) gives a smooth deformation of ΛCDM: H2(z)=H2 ΛCDM(z)1+δPAP(z;α, γ, z∗, η),(17) with η∝β2˙ N2 0 . Early-universe behavior remains standard; late-time percent-level deviations are observable via BAO, supernovae, and the ISW effect. 4 Phenomenology and Predictions The Present Accretion Principle reframes cosmic acceleration as a manifestation of irreversibility. Once ˙ Nact ( z ) or its thermodynamic analogue ˙ Stot ( z ) is specified, observable consequences follow. In observational terms, ˙ Nact represents the global rate of realization—the cumulative effect of local irreversible processes such as stellar fusion, black-hole accretion, and cosmogenic particle production, coarse-grained across the cosmic horizon (see Fig. 2). Hubble-rate curvature. Integrating the deformation yields H2(z)=H2 0Ωm(1+z)3+ Ωr(1+z)4+ ΩPAP f(z),(18) where f ( z ) traces the cumulative history of ˙ Nact . The model predicts percent-level deviations from ΛCDM, testable by BAO and Type Ia supernovae. 4 Figure 1: Illustrative PAP deviation in the Hubble rate. Percentage difference between the toy PAP prediction and ΛCDM for 0 ≤z≤ 3. We use the driver described in the Minimal Parametric Form subsection with ( α, γ, z∗ ) = (2 , 4 , 2) and a small deformation parameter ϵ = 5 × 10 −4 , normalized so the ratio is unity at z = 0. The curve demonstrates the order-ofmagnitude effect without fitting data. Potentiality Actualization Spatial Expansion entropy increase →metric growth Figure 2: Conceptual schematic of the Present Accretion Principle. Potentiality transitions to actuality through irreversible processes that increase entropy; geometry expands to accommodate the realized states. Integrated Sachs–Wolfe effect. A time-varying weff ( z ) modifies the late-time potential, producing an ISW cross-correlation between CMB anisotropies and large-scale structure proportional to the entropy-production rate. Structure growth. The linear-growth equation f′+f2+ 2 + ˙ H H2!f=3 2Ωm(z) (19) gives a growth index γ ( z ) ≈ 0 . 55 + 0 . 02[1 + weff ( z )]. This predicts mild redshift dependence measurable via fσ8(z). Entropy–expansion correlation. Equation (4) predicts d VH/ d t∝ d Stot/ d t . Empirical entropy-production histories derived from stellar and black-hole accretion can directly test this proportionality. Future equilibrium. As ˙ Nact → 0, H→H∞ . The apparent fine-tuning of dark energy then reflects our transient position within the decline of cosmic irreversibility. 5 4.1 Energy Conditions and Stability Because ρPAP +pPAP c2∝H4˙ Nact,(20) the weak and null energy conditions hold for ˙ Nact > 0. No new degrees of freedom appear; the modification alters only background dynamics. Linear perturbations remain stable for all monotone Φ. 4.2 Quantitative Viability A single dimensionless parameter η∼λ˙ N0/H3 0 reproduces observed acceleration for η≃ 10 −2 – 10 −3 . This preserves early-universe physics and satisfies Planck and BBN limits. Future surveys (DESI, Euclid, LSST) can test the predicted curvature in H(z) and the ISW amplitude [8]. 5 Discussion and Foundational Implications While the formalism can stand as a dynamical modification of FRW cosmology, its deeper import is conceptual: expansion as the geometric record of becoming. The universe’s growth is the spacetime imprint of reality’s continuous self-actualization. 5.1 Spacetime as Accreting Totality General relativity depicts a static four-manifold. PAP instead views spacetime as accreting: its volume increases as new events become actual. The past endures; the present is the moving boundary where potential crosses into actuality. Expansion conserves being by enlarging the manifold to contain all that has occurred. 5.2 Entropy and the Unified Arrow of Time Equation (4) unites three arrows long treated separately—thermodynamic, cosmological, and experiential—into one expression of irreversibility. Entropy measures realized microstates; spatial expansion preserves them; consciousness registers their continual increase. The relation dVH/dt∝dStot/dtmakes this identity quantitative. 5.3 Relation to Earlier Frameworks PAP intersects three traditions: thermodynamic gravity [ 3 , 4 , 9 ], causal-set cosmology [ 2 ], and process philosophy (Whitehead, Bergson, Hartshorne). It translates metaphysical insight into testable physics. 5.4 Metastable Equilibrium and Renewal As irreversible processes wane ( ˙ Nact → 0), the universe approaches holographic equipartition: d VH/ d t→ 0, H→H∞ . This de Sitter limit represents a metastable equilibrium of actuality—a pause, not an end. No new states are being actualized, yet all realized states persist. The manifold ceases to accrete because potentiality is momentarily exhausted. Quantum mechanics forbids absolute stillness. A de Sitter vacuum possesses finite temperature TdS = H∞/ 2 π , so fluctuations or phase transitions can reopen potentiality ( ˙ Nact > 0), reigniting expansion and initiating a new epoch of becoming. Cosmic history thus unfolds as cycles of equilibrium and renewal, each preserving continuity with what preceded it. 6 Framework Core Principle Distinction under PAP Jacobson (1995) Einstein equations as an equation of state from local horizon thermodynamics (near-equilibrium heat flow). Expansion reflects the global rate of actualization, not solely local equilibrium; GR recovered as ˙ Nact →0. Padmanabhan (2012) Expansion as relaxation toward holographic equipartition between surface and bulk degrees of freedom. Equipartition is the endpoint; the driver is continual increase in realized degrees of freedom. Causal-set growth Discrete element “birth” stochastically grows spacetime. PAP provides the continuum analogue: volumetric accretion proportional to the realizedinformation flux. Table 1: Table 1. Comparison of approaches to cosmic expansion. PAP reframes expansion as ontological accretion. Existing frameworks emerge as limits or complementary views: local-equilibrium (Jacobson), equipartition dynamics (Padmanabhan), and discrete growth (causal sets). Yet even equilibrium does not sever actuality from possibility. If no potential for becoming remained, persistence itself would lose definition. In quantum terms that minimal openness resides in vacuum fluctuations; ontologically it is the breath that prevents being from collapsing into nothing. Completion is never absolute—the act of becoming slows, but the possibility of becoming endures, allowing being itself to remain. 5.5 Limitations and Open Questions The Present Accretion Principle remains at a phenomenological stage. Open issues include specifying the microphysical channel by which irreversible processes register as horizon-scale actualization, clarifying whether ˙ Nact can be derived from known non-equilibrium quantumgravity formalisms, and testing whether entropy-production proxies can be reliably measured at cosmological scales. Future work should examine whether the PAP relation can emerge from holographic information flux or from stochastic causal-set growth, providing a concrete bridge between process ontology and covariant dynamics. These questions define the frontier on which PAP may either integrate with or revise established cosmological theory. 6 Conclusion and Outlook The Present Accretion Principle (PAP) unifies cosmology, thermodynamics, and ontology through the assertion that space expands in proportion to the rate of actualization. Expansion is therefore not an incidental consequence of hidden energy but the geometric expression of time’s asymmetry. Coupling d VH/ d t to d Nact/ d t turns the mystery of cosmic acceleration into the physics of irreversibility. The universe expands while actuality increases; when irreversible processes fade, holographic equipartition is reached and expansion stabilizes in a de Sitter-like equilibrium—a balance between being and the faint remainder of becoming. Formally, PAP recovers general relativity in the limit ˙ Nact → 0 and mimics ΛCDM for small, smooth variations in the becoming rate. Empirically, it predicts a measurable correlation between the Hubble rate and global entropy production. Conceptually, it reinterprets dark energy as the residual impetus of realization itself. Future research will refine, derive, and test the principle: (i) phenomenological refinement 7 of ˙ Stot ( z ) from stellar and black-hole data; (ii) theoretical embedding from microscopic or holographic non-equilibrium dynamics; and (iii) conceptual extension clarifying how equilibrium and recurrence express the interplay of being and possibility. References [1] T. Padmanabhan. Emergence and expansion of cosmic space as due to the quest for holographic equipartition. arXiv:1206.4916, 2012. [2] David P Rideout and Rafael D Sorkin. Classical sequential growth dynamics for causal sets. Phys. Rev. D, 61:024002, 1999. [3] Ted Jacobson. Thermodynamics of spacetime: The einstein equation of state. Phys. Rev. Lett., 75:1260–1263, 1995. [4] Erik Verlinde. 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