CMB constraints on DHOST theories

We put constraints on the degenerate higher-order scalar-tensor (DHOST) theories using Planck 2018 likelihoods. In our previous paper, we developed a Boltzmann solver incorporating effective field theory parameterised by six time-dependent functions, $\alpha_i$ $(i={\rm B},{\rm K},{\rm T},{\rm M},{\rm H})$ and $\beta_1$, which can describe DHOST theories. Using Markov-Chain Monte-Carlo method with solver, find viable parameter region of model parameters characterising other standard cosmological parameters. First, consider simple $\alpha_{\rm K} = \Omega_{\rm DE}(t)/\Omega_{\rm DE}(t_0)$, B}=\alpha_{\rm T}=\alpha_{\rm M}=\alpha_{\rm H}=0$ $\beta_1=\beta_{1,0}\Omega_{\rm DE}(t_0)$ in $\Lambda$CDM background where $t_0$ is present time obtain $\beta_{1,0}=0.032_{-0.016}^{+0.013}$ (68\% c.l.). Next, focus another given $\mathcal{L}_{\rm DHOST} X + c_3X\Box\phi/\Lambda^3+ (M_{\rm pl}^2/2+c_4X^2/\Lambda^6)R 48c_4^2X^2/(M_{\rm pl}^2\Lambda^{12}+2c_4\Lambda^6X^2)\phi^\mu\phi_{\mu\rho}\phi^{\rho\nu}\phi_\nu$ $X:=\partial_\mu\phi\partial^{\mu}\phi$ two positive constant parameters, $c_3$ $c_4$. this model, consistently treat perturbations, $c_3 1.59^{+0.26}_{-0.28}$ upper bound $c_4$, $c_4<0.0088$