Spherical collapse in DHOST theories fails for the beyond-Horndeski parameter β1 above about 10^-7 because the scalar-field gradient becomes imaginary, and the halo mass function is suppressed relative to ΛCDM.
One can map the DHOST action to the α-basis representation of the EFT of dark energy following [44] and [17]
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Spherical collapse in DHOST theories and EFT of dark energy
Spherical collapse in DHOST theories fails for the beyond-Horndeski parameter β1 above about 10^-7 because the scalar-field gradient becomes imaginary, and the halo mass function is suppressed relative to ΛCDM.