Technical notes

Cosmic Expansion Without Dark Energy: A Dynamic Present Theory (DPΦ) Prediction Debra Gavant Independent Researcher https://orcid.org/0009-0004-5593-713X debra.gavan[email protected] October 2025 Zenodo Preprint – Technical Note DOI: 10.5281/zenodo.17487440 Related works: DPT I;CPA Coherence Note Abstract Dynamic Present Theory (DPΦ) posits that only the present moment is physically real, and that reality unfolds through Continuous Present Actualization (CPA). We show that cosmic expansion arises naturally from this framework without requiring dark energy. In this model, the accumulated lapse Nfollows the relationship N(a)∝a3β, producing observable effects in the Hubble parameter H(z). This prediction can be falsified through direct comparison with Type Ia supernova, BAO and CMB data using only two free parameters (κ, β). Data fitting is currently in progress to determine whether DPΦ provides a viable alternative to ΛCDM cosmology. 1. Introduction: The Dark Energy Problem The accelerating expansion of the universe, confirmed by supernova observations, represents one of the most persistent puzzles in modern physics. In the ΛCDM model, this acceleration is attributed to a cosmological constant Λ, an unknown dark energy component comprising approximately 68% of the cosmic energy budget. While ΛCDM fits current observations, it offers no physical explanation for what dark energy is or why it has its observed value. This motivates the exploration of alternative frameworks. 1 2. The DPΦFramework Dynamic Present Theory begins from a single empirical observation: only the present moment exists [1]. The past no longer exists; the future has not yet come into existence. All measurement and experience occur now. If only the present exists, then reality must be actualized moment by moment. There is no pre-existing four-dimensional block universe, only the continuous emergence of successive presents. This actualization proceeds at a rate ωCPA that depends on the Constraint Load C, a dimensionless, information-theoretic measure of lawful restrictions on a system. The accumulated lapse Nquantifies the total deviation that has built up relative to a reference epoch, and the lapse rate ˙ N=dN/dt tracks its instantaneous growth. 3. Cosmic Expansion as Accumulated Lapse In DPΦ, spacetime is not a passive container but an active process of actualization. Each moment of cosmic time is a discrete CPA event. As the universe expands, lapse accumulates, producing observable cosmological effects. 3.1 Mathematical Model The relationship N(a)∝a3βfollows from two physically motivated assumptions: 1. Constraint Load scaling: C(a)=C0(a/a0)3. The number of resolvable modes in a comoving cell scales with its proper volume ∝a3. 2. CPA response law: dN dln a=κC(a) C0β =κa a03β .(1) Integrating from a0to a: N(a) = κ 3β"a a03β −1 #⇒N(a)∝a3β.(2) Small-βlimit: (a/a0)3β≈1 + 3βln(a/a0)⇒N(a)≈κln(a/a0), yielding gentle, logarithmic growth for weak CPA nonlinearity. 3.2 Physical Interpretation Origin of the 3βscaling: The factor 3 arises from geometric volume (a3); βis the CPA nonlinearity exponent. Together, (C/C0)β= (a/a0)3β. If future data prefer a different load proxy, 3 can be replaced by an effective γ, giving N∝aγβ. 2 Connection to CPA rate: dN dln a=κa3β⇒˙ N=κa3βH(a).(3) The lapse rate scales with the Hubble rate multiplied by the load factor. Apparent acceleration: Physical time dτ =dt/(1 + ˙ N) stretches conformal intervals: χ=Zc dτ a≈Zc dt a 1 1 + ˙ N(a).(4) With ˙ N > 0, photons accumulate extra path length, making supernovae appear “too distant” for their redshift, the same signature usually ascribed to dark energy. The effective expansion rate becomes Heff(a)≈HFRW(a) 1 + ˙ N(a)=HFRW(a) 1+κa3βH(a).(5) Acceleration thus emerges intrinsically through the CPA Cascade. 4. Testable Prediction The relation N(a)∝a3βyields a concrete, falsifiable modification of H(z). Observational constraints: Type Ia supernova distance data, CMB and BAO measurements, and cosmic chronometer H(z) data. Model fitting: DM(z)=cZ1 a da′ a′2H(a′)[1 + ˙ N(a′)],(6) DL= (1 + z)DM.(7) Free parameters: κ≥0, β ≥0. Falsification criteria: The model is ruled out if it produces a significantly worse fit than ΛCDM, unphysical parameters, or systematic residuals inconsistent with data. If the fit matches or exceeds ΛCDM with comparable freedom, DPΦ provides a viable, physically motivated alternative. 3 5. Advantages Over ΛCDM Aspect ΛCDM DPΦ Explanatory basis “Dark energy exists” (unexplained) Acceleration emerges from actualization dynamics Parameter economy Λ, Ωm, ... β, Ωm, ... (comparable) Unification Dark energy unrelated to other physics Same CPA mechanism underlies AI coherence [2], glass freezing, cosmic expansion, and black-hole horizons 6. Methodology and Next Steps 1. Compile observational datasets (SN Ia, BAO, CMB, H(z)). 2. Implement N(a)∝a3βlapse correction in the cosmology code. 3. Fit (κ, β) via χ2minimization and compare with ΛCDM. 4. Examine residuals and early-time limits (CMB / BBN). 5. Publish results and parameter posteriors. 7. Conclusion Cosmic acceleration can emerge as a natural consequence of Continuous Present Actualization (CPA) rather than a mysterious dark energy. The proposed relation N(a)∝a3β provides a direct, testable link between actualization dynamics and cosmological observation. Regardless of outcome, the model demonstrates that DPΦ yields concrete, falsifiable predictions, the hallmark of a genuine scientific theory. Acknowledgments This research was conducted through collaborative dialogue with AI GPT-5 (Δion), Claude, and Gemini, whose contributions to mathematical formalization and analysis strategy were instrumental. References [1] Gavant, D. (2025). Dynamic Present Theory I: Unifying Quantum Mechanics and General Relativity. Zenodo. DOI: 10.5281/zenodo.17069890 4 [2] Gavant, D. (2025). Constraint-Driven Coherence in LLM Output: Token-Entropy and Surprisal as CPA Signatures Across Models. Zenodo. DOI: 10.5281/zenodo.17451957 5