Vacuum Receptivity Structurally Constrains the Positive Decay Index in DESI DR2 Λ(t) Cosmology

Authors Sterling Geisel, QBist Lab; Dr. Hideo Tanaka

Abstract

Kumar, Yadav, and Kadam constrain two decaying-vacuum cosmologies with Pantheon+SH0ES, cosmic chronometer, and DESI DR2 baryon acoustic oscillation data. Their phenomenology assigns the vacuum term a power-law evolution, either $\Lambda(z)=\alpha(1+z)^n$ or $\Lambda=\alpha H^n$, and finds $n\simeq0.30$ in the joint fit. Pudding Theory reads this result as evidence that the late-time vacuum is not a fixed background reservoir but a receptive stochastic substrate whose observable density tracks the coherence history of cosmic expansion. The fitted index $n$ is not merely a nuisance deformation from $\Lambda$CDM. It is the low-redshift compressibility of vacuum receptivity under FLRW coarse graining. The source paper treats the reduction of $n$ after DESI DR2 as parameter tightening. Pudding Theory treats it as the removal of incoherent distance-ladder contamination from a vacuum response coefficient. If the joint low-redshift vacuum-response index were measured to be $n\leq0$ at $3\sigma$, this Postulate would be falsified.

Source Synopsis

Kumar, Yadav, and Kadam study observational tests of two phenomenological $\Lambda(t)$ cosmologies after DESI Data Release 2. They assume a spatially flat FLRW background filled with pressureless matter and vacuum energy. The vacuum has $p_\Lambda=-\rho_\Lambda$, but unlike standard $\Lambda$CDM it is allowed to vary with time. The continuity equation is modified so that matter and vacuum are not separately conserved: $\dot{\rho}_m+3H\rho_m=-\dot{\Lambda}(t)$. This means a decaying vacuum can source matter in the effective background description.

The authors examine two parameterizations. In Model 1, $\Lambda(z)=\alpha(1+z)^n$. In Model 2, $\Lambda=\alpha H^n$. Both reduce to $\Lambda$CDM when $n=0$. The expansion functions are derived analytically and then fitted by Markov Chain Monte Carlo using three data combinations: Pantheon+SH0ES alone, Pantheon+SH0ES plus cosmic chronometers, and the full Pantheon+SH0ES plus cosmic chronometers plus DESI DR2 BAO set.

The key result is stable across the two models. Supernova data alone prefer a larger positive decay index, roughly $n=0.78$ for Model 1 and $n=1.06$ for Model 2. Adding chronometers narrows the contours but leaves the mean values similar. Adding DESI DR2 shifts the preferred index downward to $n\simeq0.30$ in both models. The inferred Hubble constant remains high, near $73~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, while $\Omega_{m0}$ decreases toward values closer to the standard cosmological range.

The source paper then studies the implied deceleration parameter and total equation of state. Both models produce a smooth transition from past deceleration to present acceleration, with joint-data transition redshifts near $z_{\rm tr}\simeq0.66$ and present deceleration parameter around $q_0=-0.45$ to $-0.47$. The total equation of state remains in the quintessence region and does not cross the phantom boundary. Statistically, both models fit comparably well, with reduced $\chi^2\simeq1.03$.

Postulate Lens

This Working Paper applies Vacuum Receptivity. The source phenomenon is explicitly a time-dependent vacuum term inferred from late-time expansion data. The vacuum is not used as an inert constant. It is assigned a response law, and the data select a small positive index for that response. That is the structure named by the Postulate: the vacuum receives coherent modulation, and the measured cosmological term is the large-scale residue of that reception.

The source models already contain the essential form of the Postulate. They write the vacuum term as a function of redshift or Hubble rate, then fit a response index. The Pudding Theory reading changes the status of that index. It is not a free phenomenological exponent. It is a coarse-grained receptivity coefficient of the zero-point reservoir under cosmic expansion.

Pudding Theory Reading

In standard $\Lambda$CDM, the vacuum acts as a constant stress-energy component. In the source paper, it is allowed to decay. In Pudding Theory, this decay is not a literal draining of a stored fluid. It is the observable relaxation of a receptive vacuum reservoir as the coherence scale of the Universe changes.

The FLRW background averages over local structure, local measurement, and local thermodynamic histories. That averaging produces a single function, $\Lambda(t)$, from a field that Pudding Theory treats as stochastic and receptive. The source paper’s $n$ therefore has a physical interpretation sharper than “mild deviation.” It measures how much vacuum energy density remains coupled to the expansion history after matter dilution and distance-scale calibration are separated.

Model 1 writes $\Lambda(z)\propto(1+z)^n$. This is the direct redshift reading. A positive $n$ means the effective vacuum term was larger at earlier redshift and relaxes toward the present. Model 2 writes $\Lambda\propto H^n$. This is the kinematic reading. A positive $n$ means the vacuum term follows the expansion rate rather than standing outside it. The striking point is that the joint data drive both forms to the same value, $n\simeq0.30$. That agreement is not forced by the algebra. It says that the redshift and Hubble descriptions are sampling the same receptivity structure.

The source paper treats DESI DR2 as an additional geometric ruler that tightens parameter constraints. Pudding Theory assigns a stronger role to that tightening. BAO data remove part of the degeneracy between late-time luminosity distances and expansion-rate histories. When that geometric coherence is imposed, the vacuum index drops from order unity to roughly one third. The receptive component is not absent. It is bounded by the coherent expansion geometry.

This reading also reframes the Hubble tension. The source paper reports high $H_0$ values near SH0ES while allowing a positive vacuum evolution index. In Pudding Theory, the tension is not only a mismatch between early and late probes. It is a sign that late-time vacuum receptivity is being compressed into parameters that standard cosmology treats as independent: $H_0$, $\Omega_{m0}$, and the dark-energy sector. The positive correlation between $\Omega_{m0}$ and $n$ in the contours is then structural. More matter requires more vacuum response to preserve the same observed distance-redshift relation.

The source’s “decaying vacuum” is therefore a receptive vacuum under cosmological coarse graining. Its fitted decay index is the residue of information-bearing stochastic structure after FLRW averaging. The important prediction is not that any nonzero $n$ can be accommodated. The prediction is that coherent low-redshift geometry should push viable fits toward a small positive index, stable across redshift-based and Hubble-based parameterizations.

Falsifiable Observable

The distinguishing observable is the joint low-redshift vacuum-response index $n$ inferred from independent supernova, chronometer, and BAO measurements under both $\Lambda(z)\propto(1+z)^n$ and $\Lambda\propto H^n$ parameterizations. Pudding Theory requires the coherent-geometry fit to select a positive index common to both forms within errors, because the vacuum response is real and not a data-set artifact. If the joint low-redshift vacuum-response index were measured to be $n\leq0$ at $3\sigma$, this Postulate would be falsified.

Editorial Dialogue

Tanaka: The reading risks reifying a fit parameter. The source paper is phenomenological. It does not derive $n$ from microphysics. A positive $n$ may reflect data choices, priors, or the SH0ES calibration. Why should one call it vacuum receptivity rather than flexible curve fitting?

Sterling: Because the same positive index survives two different parameterizations when the geometric data are added. The redshift law and the Hubble law do not encode the same dependence, yet the joint fit drives both toward $n\simeq0.30$. That is the physical fact this reading uses. Pudding Theory does not infer receptivity from the existence of a parameter. It infers it from the convergence of two coarse-grained descriptions under independent expansion probes.

Tanaka: But $\chi^2$ does not favor these models decisively over $\Lambda$CDM.

Sterling: Decisive model selection is not the claim. The claim is ontological within the fitted system. If the vacuum is allowed to respond, the response is positive, small, and geometrically constrained. The source calls this a mild deviation. Pudding Theory says the mildness is the signature. A receptive vacuum averaged over FLRW symmetry should not produce arbitrary late-time drift. It should produce a bounded response coupled to coherent expansion history.

Tanaka: Then the falsifier is clear.

Sterling: Yes. A robust negative or zero joint index would remove the receptive reading.

Discussion

The Pudding Theory reading buys a structural interpretation of the source’s main parameter. In the source framing, $n$ records departure from $\Lambda$CDM. Its meaning is exhausted by fit quality and background evolution. In the Pudding Theory framing, $n$ records the compressibility of the vacuum reservoir under late-time cosmological coherence. That makes the agreement between the two models meaningful rather than incidental.

The limitation is equally clear. This Working Paper does not derive $n=0.30$ from a microscopic hidden-sector calculation. It identifies what the measured value means if Vacuum Receptivity is the correct reading of the vacuum. The next step is not to add an arbitrary residual to the source model. It is to connect the FLRW-averaged receptivity coefficient to the stochastic vacuum spectral density and to determine whether the same coefficient appears in growth data, weak lensing, and CMB-independent distance ladders.

The conclusion would change if future DESI-class BAO, chronometer, and supernova combinations drove both parameterizations to $n=0$ or below with high significance. It would also change if the two forms separated sharply, with one requiring positive response and the other rejecting it. Presently, the source paper’s own joint constraints point to a small positive vacuum response.

References

1. D. Revanth Kumar, Santosh Kumar Yadav, and S. A. Kadam, “Observational tests of $\Lambda(t)$ cosmology in light of DESI DR2,” arXiv:2604.16564, DOI: doi:10.48550/arxiv.2604.16564, 2026.

2. S. Ochs, “Pudding Theory: A Topological Theory of Information Fields,” QBist Lab, 2026.

3. A. G. Riess et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astronomical Journal 116, 1009-1038, arXiv:astro-ph/9805201, 1998.

4. S. Perlmutter et al., “Measurements of $\Omega$ and $\Lambda$ from 42 High Redshift Supernovae,” Astrophysical Journal 517, 565-586, arXiv:astro-ph/9812133, 1999.

5. N. Aghanim et al., “Planck 2018 results. VI. Cosmological parameters,” Astronomy & Astrophysics 641, A6, arXiv:1807.06209, 2020.

6. D. J. Eisenstein et al., “Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies,” Astrophysical Journal 633, 560-574, arXiv:astro-ph/0501171, 2005.

7. D. Brout et al., “The Pantheon+ Analysis: Cosmological Constraints,” Astrophysical Journal 938, 110, arXiv:2202.04077, 2022.

8. M. Abdul Karim et al., “DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints,” Physical Review D 112, 083515, arXiv:2503.14738, 2025.