Assess alternative scale-dependent MG parameterizations for tighter constraints

Determine whether alternative functional forms for the scale dependence of the modified-gravity functions μ(a,k) and Σ(a,k), beyond the ratio-of-polynomials form specified in Eqs. (3.6)–(3.7) with parameters λ, c1, and c2, can yield improved constraints when analyzed with the current cosmological datasets used in this work.

Background

In Section 3.2.2 the authors extend the μ–Σ modified gravity parameterization to include scale dependence using rational functions in k with parameters λ, c1, and c2 (Eqs. 3.6–3.7). They test two representative choices for λ and find that, while μ0 and Σ0 remain well constrained and consistent with GR, the additional scale parameters are difficult to constrain with current data.

They note that binned parameterizations in redshift and scale (Section 3.3) appear to provide tighter constraints on scale-dependent effects than the specific functional form adopted in Section 3.2.2. This motivates the explicit open question of whether alternative functional parameterizations of scale dependence could perform better with the same data.