CMB constraints on DHOST theories

Abstract

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, ${\alpha }_i$ $(i=\mathrm{B},\mathrm{K},\mathrm{T},\mathrm{M},\mathrm{H})$ 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 ${\alpha }_{\mathrm{K}}={\Omega }_{\mathrm{DE}}(t)/{\Omega }_{\mathrm{DE}}(t_0)$, ${\alpha }_{\mathrm{B}}={\alpha }_{\mathrm{T}}={\alpha }_{\mathrm{M}}={\alpha }_{\mathrm{H}}=0$ and ${\beta }_1={\beta }_{1,0}{\Omega }_{\mathrm{DE}}(t)/{\Omega }_{\mathrm{DE}}(t_0)$ 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 ${\mathcal{L}}_{\mathrm{DHOST}}=X+c_{3}X\square \varphi /{\Lambda }^3+(M_{\mathrm{pl}}^2/2+c_4{X}^2/{\Lambda }^6)R+48c_4^2{X}^2/(M_{\mathrm{pl}}^2{\Lambda }^{12}+2c_4{\Lambda }^6{X}^2){\varphi }^{\mu }{\varphi }_{\mu \rho }{\varphi }^{\rho \nu }{\varphi }_{\nu }$ with $X:={\partial }_{\mu }\varphi {\partial }^{\mu }\varphi$ and two positive constant parameters, $c_3$ and $c_4$. In this model, we consistently treat the background and the perturbations, and obtain $c_3=1.59_{-0.28}^{+0.26}$ and the upper bound on $c_4$, $c_4<0.0088$ (68\% c.l.).

arXiv comment10 pages, 4 figures, 1 table; v2 : typos corrected

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