CMB Peaks & BAO Simulation
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Zenodo Open Access
P7A Simulation Code
DOI: 10.5281/zenodo.19124365
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Big Flare-Up Theory — Paper 7A — Simulation Evidence

CMB Acoustic Peaks and BAO
Generated Without a Big Bang

The standard model attributes the acoustic peak structure of the CMB and the Baryon Acoustic Oscillation scale to a singular plasma event at recombination, frozen in the early universe. This simulation shows the same structure emerging from an ongoing steady-state mechanism operating in the living, infinite, eternal universe — with no primordial initial condition.
Sharma, V. S. (2026). A Steady-State Reinterpretation of the CMB Acoustic Peak Pattern and the BAO Feature in the BFUT Framework. Zenodo. Companion to Paper 7: Dynamic Thermal Equilibrium as an Alternative Origin for the CMB Temperature.
What the Standard Model Claims

Before recombination, photons and baryons formed a tightly coupled plasma. Sound waves propagated through this plasma, driven by the competition between radiation pressure and gravity. At recombination, the photons decoupled and these sound waves were frozen — preserved as the acoustic peak pattern we observe today in the CMB angular power spectrum, and as the preferred clustering scale of approximately 490 million light years known as the Baryon Acoustic Oscillation.

Both signatures are treated as fossil evidence of a one-time event. The standard model asserts they could only have been produced this way.

The BFUT challenge is precise and limited. This paper does not deny that the observations are real. It denies that they uniquely require a singular Big Bang origin. The mechanism producing acoustic oscillations — Thomson scattering coupling of photons and baryons against diffusion-like damping — operates continuously wherever ionised plasma exists. It is not unique to the pre-recombination era. And the BAO scale of approximately 490 million light years is not a raw observation: it is a number derived by assuming the very expansion history it is cited to support.

The BFUT Mechanism

The Big Flare-Up Theory proposes that ongoing astrophysical processes — expanding HII shells around star-forming regions, AGN-driven cavities in cluster plasmas, supernova superbubbles, ripple-like pressure disturbances in intracluster media — continuously inject shell-like and ripple-like acoustic power into the baryon-photon system. This ongoing injection is balanced by scale-dependent damping. The result is a steady-state power spectrum at every scale.

The master equation governing this balance is:

dP(k,t)/dt = I(k,t) − D(k,t) × P(k,t)

In statistical steady state this gives P(k) = I(k) / D(k), where I(k) is the ongoing injection power at wavenumber k from shell-like source populations, and D(k) = D₀ + D₂k² is the effective damping law with the k² term physically motivated by the Silk-like diffusion coefficient D_diff = c/(3 n_e σ_T).

Shell geometry alone generates oscillatory Fourier structure: a shell of radius R produces a power contribution proportional to [sin(kR)/(kR)]². This is not a property of a Big Bang. It is a property of any shell-like structure in three-dimensional space.

The Simulation

To test whether this mechanism is computationally viable — not merely a theoretical analogy — a numerical simulation programme was conducted across six progressively refined versions. The simulation implements the master equation through discrete time-stepping toward steady state. Shell source populations are modelled as Gaussian-weighted distributions of shell radii using compensated finite-thickness sinc-squared kernels. The real-space correlation function is obtained by numerical Fourier transform. The angular power spectrum is obtained by a Limber-like projection.

The question asked of each simulation version was simple: does the mechanism produce recognisable CMB-like acoustic peaks and a BAO-like real-space correlation bump? And does the result improve systematically as the physics becomes more realistic?

Progression of Results
VersionPeaksPeak Positions (ℓ)BAO-like bumpStatus
v21~210~50 MpcFirst directional signal
v3-lite2~210, ~387~80.6 MpcFirst encouraging result
v4-fast2222, 415~100 MpcClear convergence
v5-fast3222, 414, 602~120 Mpc✓ First major breakthrough
v6-fast3218, 411, 595~135 Mpc✓ Strong proof-of-principle

The monotonic improvement is the scientific result. Every refinement of the physics — larger source scale, increased compensation offset, broader projection depth, two-band source mixture — moved the simulation closer to the observed values. This is the signature of a mechanism that is physically real rather than a curve-fitting exercise. A model that improves consistently under more realistic physics is making a genuine scientific claim.

Best Run Parameters (v6-fast Benchmark)
ParameterValuePhysical meaning
Source band 1R* = 300 Mpc, σ = 16 Mpc, weight 0.70Dominant shell scale and spread
Source band 2R* = 420 Mpc, σ = 30 Mpc, weight 0.30Secondary shell population
Compensation offset ΔR42 MpcFinite shell thickness correction
Compensation strength β0.98Inner shell subtraction weight
Shell thickness σ_shell10 MpcPhysical shell wall width
Damping D₂1.5Silk-type diffusion coefficient
Damping D₄0Higher-order suppression (unused)
Projection centre χ*16,500 MpcEffective comoving depth
Projection width σ_χ2,600 MpcDepth window width

Run the Simulation

Press Run to execute the v6-fast benchmark in your browser. The simulation computes the steady-state power spectrum P(k), the real-space correlation function ξ(r), and the angular power spectrum C using the master equation and v6 parameters. No Big Bang. No recombination. No primordial initial condition.

Computing steady-state power spectrum...
What This Simulation Does and Does Not Claim

This simulation does not claim: a Planck-precision fit to the observed CMB power spectrum, exact reproduction of peak height ratios, derivation of the polarisation spectrum (TE/EE/BB), or a mode-by-mode replacement of the standard Boltzmann code. The current optical depth of the intergalactic medium is orders of magnitude lower than the pre-recombination plasma, and no claim is made that present-day coupling reproduces the full recombination-era transfer function quantitatively.

This simulation does establish: that the steady-state shell/ripple mechanism is numerically generative. It produces three acoustic-like peaks at approximately correct angular positions and a BAO-like correlation feature at approximately the correct scale — from ongoing physics, without any primordial initial condition. This is sufficient to falsify the uniqueness claim: the observed signatures cannot be cited as exclusive evidence of a singular recombination event if the same qualitative structure emerges from ongoing physics.

The Falsifiable Prediction

The BFUT interpretation makes a concrete prediction that distinguishes it from the standard account. If the structured component of the CMB anisotropy is generated and sustained by ongoing astrophysical processes, then after foreground cleaning and subtraction of standard secondary anisotropy contributions, a real residual cross-correlation should remain between selected CMB anisotropy components and independent tracers of cosmic star-formation activity.

This prediction does not yet have a closed-form amplitude estimate — that requires a full BFUT transfer-function treatment. But a robust null result at sufficient sensitivity, after careful control of foreground leakage and known secondary effects (ISW, SZ, gravitational lensing), would count against this prediction. The CMB-S4 experiment has the sensitivity to test it.

Scope and Next Steps

The current simulation programme establishes proof-of-principle computational viability. The next stage is a full BFUT transfer-function treatment: deriving the CMB angular power spectrum from the steady-state mechanism with the same rigour as the standard Boltzmann-code approach. That treatment will address peak height ratios, polarisation spectra, and a precision BAO amplitude prediction. Simulation code for the v6-fast benchmark is openly available for download and verification.