“…For more details on the implementation of the scalar fields and other technicalities we refer to . For this purpose, we focus on simple observables such as the matter power spectrum, halo mass function, density profiles, and velocity profiles to investigate modified gravity signatures that were previously studied in Li et al (2012bLi et al ( , 2013, Hammami et al (2015), Schmidt et al (2009), Gronke et al (2015, Lombriser et al (2012Lombriser et al ( , 2014, Winther et al (2012), Terukina & Yamamoto (2012), Shi et al (2015), Pujol et al (2014), Hellwing et al (2013), He et al (2013He et al ( , 2015, Schmidt (2010), Brax et al (2013), Tessore et al (2015), Gronke et al (2015) that can also be observed (Berti et al 2015;Zivick et al 2015;Mak et al 2012;Cai et al 2015;Song et al 2015;Wilcox et al 2015;Jain & Khoury 2010;Schmidt 2010;Hellwing et al 2014). This paper is organized as follows: in Sect.…”