As is well known, measurements of the Sunyaev-Zeldovich effect can be combined with observations of the X-ray surface brightness of galaxy clusters to estimate the angular diameter distance to these structures. In this paper, we show that this technique depends on the fine structure constant, α. Therefore, if α is a time-dependent quantity, e.g., α = α₀(z), where is a function of redshift, we argue that current data do not provide the real angular diameter distance, D_A(z), to the cluster, but instead D_A^data(z) = (z)² D_A(z). We use this result to derive constraints on a possible variation of α for a class of dilaton runaway models considering a sample of 25 measurements of D_A^data(z) in redshift range 0.023 < z < 0.784 and estimates of D_A(z) from current type Ia supernovae observations. We find no significant indication of variation of α with the present data.

In order to probe a possible time variation of the fine-structure constant ( $$\alpha $$α ), we propose a new method based on Strong Gravitational Lensing and Type Ia Supernovae observations. By considering a class of runaway dilaton models, where $$\frac{\Delta \alpha }{\alpha }= - \gamma \ln {(1+z)}$$Δ α α = - γ ln ( 1 + z ) , we obtain constraints on $$\frac{\Delta \alpha }{\alpha }$$Δ α α at the level $$\gamma \sim 10^{-2}$$γ ∼ 10 - 2 ( $$\gamma $$γ captures the physical properties of the model). Since the data set covers the redshift range $$0.075 \le z \le 2.2649$$0.075 ≤ z ≤ 2.2649 , the constraints derived here provide independent bounds on a possible time variation of $$\alpha $$α at low, intermediate and high redshifts.

In this work, we constrain the Hubble constant parameter, H ₀, using a combination of the Pantheon sample and galaxy clusters (GC) measurements from minimal cosmological assumptions. Assuming the validity of the cosmic distance duality relation, an estimator is created for H ₀ that only depends on simple geometrical distances, which is evaluated from Pantheon and a GC angular diameter distance sample afterward. The statistical and systematic errors in GC measurements are summed in quadrature in our analysis. We find H ₀ = 67.22 ± 6.07 km s^-1 Mpc^-1 in 1σ confidence level (C.L.). This measurement presents an error of around 9%, showing that future and better GC measurements can shed light on the current Hubble tension.

A new method based on large scale structure observations is proposed to probe a possible temporal variation of the fine-structure constant ( $$\alpha $$α ). Our analyses are based on time-delay of Strong Gravitational Lensing and Type Ia Supernovae observations. By considering the runaway dilaton scenario, where the cosmological temporal evolution of the fine-structure constant is given by $$\frac{\Delta \alpha }{\alpha } \approx -\gamma \ln {(1+z)}$$Δ α α ≈ - γ ln ( 1 + z ) , we obtain limits on the physical properties parameter of the model ( $$\gamma $$γ ) at the level $$10^{-2}$$10 - 2 ( $$1\sigma $$1 σ ). Although our limits are less restrictive than those obtained by quasar spectroscopy, the approach presented here provides new bounds on the possibility of $$\frac{\Delta \alpha }{\alpha } \ne 0$$Δ α α ≠ 0 at a different range of redshifts.