Elastic Bounce Cosmology (EBC): A Phenomenological Framework for Quasi-Cyclic Cosmic Expansion with a Dynamic Spatial Restoring Force and its Linear Perturbation Theory

We present Elastic Bounce Cosmology (EBC), a phenomenological framework in which the cosmic scale factor is governed by modified Friedmann equations incorporating a dynamic, scale-factor-dependent effective cosmological term. The central hypothesis is that space possesses an intrinsic elastic property — a geometric restoring force that drives oscillatory expansion and contraction without singularity. The cosmological constant is replaced by a single dynamical term Λ_EBC(a) = Λ₀(a_*/a − a/a_*), where a_* is the equilibrium scale factor. A non-singular minimum scale factor a_min > 0 is a postulate of the framework rather than a derived result: in the physical radiation-filled background it is not a dynamical zero of the modified Friedmann equation but is fixed externally through the BBN-lithium constraint on the bounce temperature (Section 3.1), and a first-principles treatment of the bounce phase remains open. The elastic restoring force instead governs the large-scale turnaround near the equilibrium scale a_*, driving the cyclic expansion and contraction without a cosmological constant. This version (v6.0) develops the linear perturbation theory of the elastic sector. A single shear-rigidity coupling — induced by the clock field rather than added by hand — heals the scalar gradient instability of the pure domain-wall fluid within a well-defined stability window, while leaving the tensor sector exactly luminal and ghost-free; a structural classification theorem fixes the admissible Lagrangian class to quadratic order in the perturbations. Carried into observables, the parameter-free w₀ = −2/3 exacts a structural price: the same background suppresses the late-time structure-growth amplitude (with S₈ ≈ 0.76, a mild but systematic deficit) and forces a low matter density ω_m = 0.119 that is inconsistent with the CMB shape under the ΛCDM reference inference (see Section 9.5 for the model-dependence of this comparison). These two effects share the single root w₀ = −2/3 ⇒ H₀ ≈ 61 and cannot be removed by any admissible model reserve without forfeiting the parameter-free prediction; they are reported openly as the structure-growth and CMB shadow of the analytic result. EBC rests on a covariant footing: the elastic component is derived from a material-field Lagrangian density, which automatically guarantees energy-momentum conservation ∇_μ T^μν_el = 0 via diffeomorphism invariance. The relation to established solid dark energy models (Bucher & Spergel 1999, Battye et al.) is established: EBC contains a frustrated domain-wall network as the leading-order limit, with the elastic restoring force as a structural extension. Postulate P3 (external reference time) is reformulated as a covariant clock field generating a preferred cosmological foliation, removing the metaphysical content of earlier formulations. A key analytic result follows directly from this approach: the effective dark-energy equation of state in the current observational regime (a ≪ a_*) is w_EBC(a) = −1 + (1 + x²) / [3(1 − x²)], x = a/a_*, yielding w₀ ≈ −2/3 in the limit a₀ ≪ a_* without tuning of model parameters. This prediction is nearly constant (w varies by less than 1% across all observable redshifts; effective w_a ≈ −0.01). The DESI DR2 BAO data (2025), combined with the CMB and Type Ia supernovae, instead favour an evolving equation of state — in the w₀w_aCDM parametrisation w₀ ≈ −0.42, w_a ≈ −1.75 (DESI+CMB) — and disfavour a constant w at the 2.4–4σ level. EBC does not reproduce this evolution. Because EBC is not a member of the w₀w_a family, the model-independent comparison is the direct fit of H_EBC(z) to the compressed BAO distances (Section 8.1), which disfavours EBC against ΛCDM. The constant w₀ = −2/3 is thus a sharp, falsifiable prediction that the current DESI DR2 data disfavour. The framework offers conceptual reinterpretations of several open problems in ΛCDM: dark energy as a geometric property of space, the lithium-7 problem via selective nuclear photodisintegration at the bounce, the JWST high-redshift black hole population as inherited compact relics from prior cycles, the horizon and flatness problems through bounce geometry without an inflaton field, and baryogenesis distributed across multiple cycles. A joint analysis of DESI DR2 BAO, Pantheon+ supernovae and the CMB acoustic scale θ_* disfavors EBC against ΛCDM at Δχ² ≈ 95, with the deficit dominated by the supernova Hubble-diagram shape; the Hubble tension is not alleviated at the background level. At the background level EBC is therefore a falsifiable but currently disfavored alternative; its value lies in the conceptual unification of several open problems, in the linear perturbation theory and structural classification theorem developed here, and in one sharp surviving prediction — the jerk parameter j₀: EBC predicts j₀ ≈ 0.30 versus j₀ = 1 in ΛCDM, a Δj₀ ≈ 0.7 separation accessible to Rubin LSST and DESI Year 5. A full CMB acoustic-peak treatment, a free-x₀ marginalisation, and a coupled multi-component (Boltzmann-code) analysis remain open for future work. Version history v2 (2026): Initial public release (later German translation added).v4 (2026): Major revision — phenomenological bounce term removed from the Friedmann equations, first physical bounce characterized as radiation-dominated, corrected j₀/w_a/q₀ predictions, new derivation appendix and DESI Y1 + Pantheon+ + CMB joint fit (German translation added). Intermediate versions v3/v3.x and v5/v5.x were developed internally but never published. v6 (2026): Comprehensive revision extending the background model to its full linear perturbation theory and phenomenology.- New: perturbation analysis (tensor/vector/scalar sectors) and two structural theorems fixing w₀ = −2/3 as a theorem-derived, parameter-free prediction rather than an assumption.- New: phenomenological consequences — structure growth (fσ₈, S₈), CMB consistency, and the ω_m "trilemma" reported openly as the structural price of w₀ = −2/3.- Updated: data migrated from DESI DR1 to DESI DR2; the framework is now characterized as falsifiable and currently disfavoured at the background level, with j₀ ≈ 0.30 as the decisive test.- New: full reproducibility appendix — a bundle of self-checking Python scripts (assert-gated) reproducing every quantitative result, figure, and key symbolic derivation in the paper.- Available in English and German.