A trium test on beyond $\Lambda$CDM triggering parameters

We performed a Bayesian study on three beyond LCDM phenomenological triggering parameters, the growth index $\gamma$, the dark energy equation of state parameter $w$ and the lensing deviation from the GR prediction parameter $\Sigma$, using the latest cosmological geometric, growth and lensing probes, all in a consistent implementation within the modified gravity cosmological solver code MGCLASS. We find, when we combined all our probes, i.e. the cosmic microwave background (CMB), the baryonic acoustic oscilation (BAO), the growth measurements $f\sigma_8$ and the 3$\times$2pt joint analysis of weak lensing and galaxy clustering in photometric redshift surveys, assuming flat space, constraints compatible with general relativity and $\Lambda$CDM for $\omega = -1.025\pm0.045$, and $\Sigma = 0.992\pm0.022$ at the 68\% level, while $\gamma = 0.633\pm0.044$ is still within $\sim 2 \sigma$ from the $\Lambda$CDM value of $\gamma \sim 0.55$, and that when $\Sigma$ is considered as constant; while $\gamma_\ell = -0.025 \pm0.045$ when the lensing parameter is parameterised as function of a lensing index, introduced for the first time in this work, as $\Sigma(z)=\Omega_m(z)^{\gamma_\ell}$.Comment: Matches the accepted version after a proof reading and minor change