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.). Next, we focus on another theory given by $\mathcal{ L}_{ \rm DHOST} = X + c_3X\Box\phi/\Lambda^3+ (M_{ \rm pl}^2/2+c_4X^2/\Lambda^6)R + 48c_4^2X^2/(M_{ \rm pl}^2\Lambda^{ 12}+2c_4\Lambda^6X^2)\phi^\mu\phi_{ \mu\rho}\phi^{ \rho\nu}\phi_\nu$ with $X:=\partial_\mu\phi\partial^{ \mu}\phi$ and two positive constant parameters, $c_3$ and $c_4$. In this model, we consistently treat the background and the perturbations, and obtain $c_3 = 1.59^{ +0.26}_{ -0.28}$ and the upper bound on $c_4$, $c_4<0.0088$ (68\% c.l.).
Categories: astro-ph.CO gr-qc