DESI DR1 ShapeFit+BAO growth ratios: a compressed-likelihood constraint on the GCV growth-response amplitude (epsilon)

We construct a one-parameter (ε) compressed-likelihood constraint on a late-time growth-response deformation motivated by the GCV UV-mapping programme.

Data. We use the public DESI DR1 ShapeFit+BAO six-bin growth-ratio compression
A_obs(z) at effective redshifts
z_eff = 0.295, 0.510, 0.706, 0.930, 1.317, 1.491,
as reported in the DESI DR1 full-shape (ShapeFit) analysis.

Model. The background expansion is fixed to the GR-exact ΛCDM branch (no refit of geometry or dark-energy parameters). Growth is modified only through
A(z) = (fσ₈)_th / (fσ₈)_ref = 1 + ε g(z),
where g(z) is a fixed response shape calibrated in the GCV UV mapping. Two template choices are tested.

Likelihood. We build a standalone one-dimensional likelihood for ε using the published asymmetric 68% uncertainties per bin. No public bin-to-bin covariance is available for this ratio product, so the likelihood is treated as diagonal across redshift bins.

Outputs. We report best-fit values and 68% constraints on ε for both response templates, profile-likelihood Δχ² relative to ε = 0, and robustness checks. The inferred ε values are compared to UV-mapped benchmark targets (PB1, PB2).

Scope. This is a growth-only consistency/stress test on a fixed GR-exact background. It does not reproduce the DESI internal pipeline, does not use measurement-level full-shape likelihood inputs, and does not infer the numerical value of Λ_eff.

Project overview and related material:
https://github.com/gcv-framework/gcv-vacuum-energy

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