A Bayesian Evidence Test of a Unified Photonic-Condensation Dark Sector (PCH) Against ΛCDM

A Bayesian Evidence Test of a Unified Photonic-Condensation Dark Sector (PCH) Against ΛCDM S. Mehmet Türkoğlu Independent researcher (Türkiye) Date: 2026-02-09 **Subtitle:** Planck 2018 bandpower surrogate likelihood + DESI 2024 BAO + Pantheon+ (MU_SH0ES) Abstract We present a Bayesian model comparison between a baseline flat ΛCDM cosmology and an effective-fluid realization of the Photonic Condensation Hypothesis (PCH), in which the dark sector is treated as a single quantum medium whose condensed (clumping) regime can behave as dark matter while its pressure-like regime can drive late-time acceleration. We implement PCH as a three-parameter redshift-dependent effective equation of state w(a) = -1 + α(1-a) + β a(1-a) - γ(1-a)^2 and perform nested-sampling inference using a joint dataset consisting of a Planck 2018 TT/TE/EE *bandpower surrogate likelihood*, DESI 2024 BAO distance constraints, and Pantheon+ supernovae (MU_SH0ES). Despite three additional degrees of freedom, the evidence favors PCH over ΛCDM for this setup (Δ ln Z ≈ 3.24 ± 0.72, Bayes factor ≈ 25.4). The PCH posterior exhibits a strong internal coupling among (α, β, γ), in particular a near-linear α–β degeneracy (corr ≈ -0.952), suggesting the data constrain the PCH sector predominantly through a collective mode rather than independent parameters. We emphasize that the Planck component is approximate and that definitive conclusions require validation with official likelihoods and broader datasets. **Keywords:** cosmology; dark matter; dark energy; Bayesian evidence; nested sampling; Planck; DESI; supernovae; unified dark sector; photonic condensation 1. Motivation The standard cosmological model (flat ΛCDM) successfully fits a broad range of observations, yet the physical nature of its dominant components—cold dark matter (CDM) and dark energy (Λ)—remains unknown. Motivated by the possibility that these “two unknowns” could be different macroscopic phases of a single underlying quantum medium, PCH proposes that: - a **condensed / clumping regime** behaves effectively as **dark matter** (structure formation), - a **pressure / wave-support regime** behaves effectively as **dark energy** (accelerated expansion). This paper tests a concrete *effective* implementation of that idea against ΛCDM in a Bayesian evidence framework. 2. Effective PCH model used here 2.1 Unified dark sector as an effective fluid We model the PCH dark sector as a single fluid with a scale-factor dependent effective equation of state: \[ w(a) \equiv -1 + \alpha(1-a) + \beta\,a(1-a) - \gamma(1-a)^2 . \] This form ensures \(w\to -1\) as \(a\to 1\) while allowing controlled deviations at earlier times. In this phenomenological mapping: - **α** controls the leading pressure-like deviation, - **β** controls an intermediate-time condensation/clumping response, - **γ** provides a curvature/restoring term stabilizing the transition behavior. 2.2 Toy wave-dynamics illustration (visual intuition) Separately from the cosmological fit, we show illustrative 2D wave-dynamics frames (nonlinear Schrödinger / Gross–Pitaevskii-like evolution with a gravity-like attraction, gating, and damping). The intensity \(|\psi|^2\) exhibits: - multi-core clumping (dark-matter-like morphology), - interference / pressure-support structures (dark-energy-like response). These images are *illustrative* (not a direct cosmological likelihood fit), but help communicate how a single wave medium can display both clustering and pressure behavior. 3. Data and likelihoods We analyze: 1. **Planck 2018 TT/TE/EE bandpowers (surrogate likelihood).** Implemented as a diagonal-error χ² in bandpower space with a calibration nuisance parameter \(A_{\rm PLK}\) (Gaussian prior) and a prior on optical depth τ. **Important:** this is **not** the official Planck likelihood and does not capture full covariances/nuisance modeling. 2. **DESI 2024 BAO.** BAO distances with published covariance. 3. **Pantheon+ supernovae (MU_SH0ES).** Distance moduli with covariance matrix. 4. Inference method We perform Bayesian inference with nested sampling (UltraNest), obtaining posterior samples and the Bayesian evidence \(Z\) for each model. Model comparison uses: \[ \Delta \ln Z = \ln Z_{\rm PCH} - \ln Z_{\Lambda{\rm CDM}} . \] 4.1 Priors and physicality cuts (as implemented) For ΛCDM we sample: - \(H_0 \in [55, 85]\), - \(\omega_b \equiv \Omega_b h^2 \in [0.020, 0.024]\), - \(\omega_c \equiv \Omega_c h^2 \in [0.090, 0.140]\), - \(\log_{10} A_s \in [-9.5, -8.5]\), - \(n_s \in [0.90, 1.05]\), with Gaussian priors on \(A_{\rm PLK} = 1.000 \pm 0.0025\) and \(\tau = 0.0544 \pm 0.0073\). For PCH we add uniform priors: - \(\alpha,\beta,\gamma \in [-3,3]\). We reject samples that violate basic physicality requirements (e.g., negative dark-sector energy density at early times). In particular, we enforce a conservative early-time bound \(\Omega_{\rm fld}(z\!=\!3000) < 0.03\) as a proxy for “no excessive early dark energy.” 5. Results 5.1 Bayesian evidence - \(\ln Z_{\Lambda{\rm CDM}} =\) -4439.16 ± 0.44 - \(\ln Z_{\rm PCH} =\) -4435.92 ± 0.57 Thus: \[ \Delta \ln Z = 3.24 ± 0.72, \] corresponding to a Bayes factor \(\exp(\Delta \ln Z)\approx\) 25.4 in favor of PCH for this dataset. At maximum likelihood, the best-fit improvement is \(\Delta\chi^2 \approx\) -17.2 (negative favors PCH; see convention), indicating that PCH can reach a better fit even before the evidence accounts for additional parameter volume. 5.2 Derived parameter shifts: \(H_0\), \(\Omega_m\), \(\sigma_8\), \(S_8\) From equal-weight posterior samples (with \(\sigma_8\) and \(S_8\equiv\sigma_8\sqrt{\Omega_m/0.3}\) computed per sample), we obtain median ±68% credible intervals: Parameter ΛCDM PCH \(H_0\) [km s⁻¹ Mpc⁻¹] 67.74^{+0.61}_{-0.61} 64.60^{+1.84}_{-1.44} \(\Omega_m\) 0.308^{+0.008}_{-0.008} 0.334^{+0.016}_{-0.019} \(\sigma_8\) 0.801^{+0.005}_{-0.005} 0.803^{+0.005}_{-0.006} \(S_8\) 0.811^{+0.015}_{-0.014} 0.847^{+0.024}_{-0.028} **Figure 1** visualizes the posterior shifts in \(H_0\) and \(S_8\). 5.3 The “Perfect Trio”: strong internal coupling among (α, β, γ) Although α, β, and γ are individually broad, their *joint* posterior is highly structured: - corr(α,β) = -0.952 (strong anticorrelation), - corr(α,γ) = 0.836, - corr(β,γ) = -0.641. A simple linear fit gives: \[ β ≈ -1.03 α + 0.52 . \] This indicates that current data constrain the PCH sector mainly along a **collective mode** (a low-dimensional manifold in parameter space), which is qualitatively consistent with (but does not by itself prove) the idea that “clumping” and “pressure” responses are not independent knobs. **Figure 2** shows the α–β degeneracy. 6. Discussion: interpretation without overclaiming The most scientifically interesting outcome is **not** that individual (α,β,γ) are “measured,” but that they are **tightly coupled** in the posterior while PCH remains competitive (and Bayes-favored) despite added flexibility. However, caution is essential: - The Planck component here is a **surrogate** likelihood; official Planck analyses include full covariances and many nuisance parameters. - A strong posterior degeneracy can reflect **parameterization**, **limited data sensitivity**, or **prior geometry**, not necessarily a physical conservation law. - PCH shifts \(H_0\) downward and \(S_8\) upward relative to the ΛCDM posterior *in this setup*; whether this helps or worsens known “tensions” depends on external datasets not included here. Therefore, these results should be seen as a **promising stress-test signal**: “this effective PCH implementation is not immediately ruled out and may be favored on this dataset,” motivating stricter tests. 7. Robustness tests needed next To upgrade these findings into a strong scientific claim: 1. Replace the Planck surrogate with **official likelihoods** (Cobaya/MontePython pipeline). 2. Match sampler settings and enforce stricter convergence (more live points, smaller \(d\ln Z\)). 3. Add external data (ACT/SPT, CMB lensing, weak lensing, RSD, BBN). 4. Perform **prior-sensitivity** and reparameterization checks. 5. Cross-validate with an independent sampler (dynesty/PolyChord) and posterior predictive checks. 8. Outlook: testable signatures A unified dark sector should link expansion history to growth. Discriminants may include: - high-redshift structure formation (JWST-era galaxy abundance; qualitative motivation), - CMB lensing and small-scale anisotropies, - full-shape clustering and redshift-space distortions, - potential wave/soliton-like features in halo statistics. 9. Conclusion On a Planck bandpower surrogate + DESI BAO + Pantheon+ dataset, an effective-fluid PCH model is Bayes-favored over ΛCDM with Δ ln Z = 3.24 ± 0.72. The key internal feature is the strong α–β–γ coupling, suggesting the dark-sector extension is effectively constrained through a collective degree of freedom. This is **scientifically interesting** as a path toward testing “one medium, two behaviors.” It is **not yet definitive** until validated with full likelihoods and broader datasets. Figures **Figure 1.** Posterior distributions for \(H_0\) and \(S_8\) in ΛCDM and PCH. **Figure 2.** Strong α–β degeneracy in the PCH posterior. **Figure 3.** Toy wave-dynamics frames (|\(\psi\)|²) illustrating multi-core clumping and pressure-support structures in a single wave medium (illustrative only). References (indicative) - Planck Collaboration (2018), *Planck 2018 results. VI. Cosmological parameters*. - DESI Collaboration (2024), BAO distance measuremen