CMB constraints on DHOST theories

Understand

We put constraints on the degenerate higher-order scalar-tensor (DHOST) theories using the Planck 2018 likelihoods.

• In our previous paper, we developed a Boltzmann solver incorporating the effective field theory parameterised by the six time-dependent functions, $\alpha_i$ $(i={\rm B},{\rm K},{\rm T},{\rm M},{\rm H})$ and $\beta_1$, which can describe the DHOST theories.
• Using the Markov-Chain Monte-Carlo method with our Boltzmann solver, we find the viable parameter region of the model parameters characterising the DHOST theories and the other standard cosmological parameters.
• First, we consider a simple model with $\alpha_{\rm K} = \Omega_{\rm DE}(t)/\Omega_{\rm DE}(t_0)$, $\alpha_{\rm B}=\alpha_{\rm T}=\alpha_{\rm M}=\alpha_{\rm H}=0$ and $\beta_1=\beta_{1,0}\Omega_{\rm DE}(t)/\Omega_{\rm DE}(t_0)$ in the $\Lambda$CDM background where $t_0$ is the present time and obtain $\beta_{1,0}=0.032_{-0.016}^{+0.013}$ (68\% c.l.).