Gravitational redshift profiles in the $f(R)$ and symmetron models

Aims. We investigate the gravitational redshift in clusters of galaxies in the symmetron and Hu-Sawicky $f(R)$ models. The characteristic feature of both models is the screening mechanism that hides the fifth force in dense environments recovering general relativity. Methods. We use $N$-body simulations that were run using the code \texttt{Isis}, which includes scalar fields, to analyse the deviation of observables in modified gravity models with respect to $Λ$CDM. Results. We find that due to the presence of the screening, the deviation is highly dependent on the halo mass. For instance, the $f(R)$ parameters $|f_{R0}|=10^{-5}$, $n=1$ cause an enhancement of the gravitational signal by up to 50% for halos with masses between $10^{13}\,M_\odot h^{-1}$ and $10^{14}\,M_\odot h^{-1}$. The characteristic mass range where the fifth force is most active varies with the model parameters. The usual assumption is that the presence of a fifth force leads to a deeper potential well and thus, a stronger gravitational redshift. However, we find that in cases in which only the central regions of the halos are screened, there could also be a weaker gravitational redshift.

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