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We present a new class of nonsingular bounce cosmology free from instabilities, using a single scalar field coupled to gravity within the framework of the Degenerate Higher-Order Scalar-Tensor (DHOST) theories. In this type of scenarios, the gradient instability that widely exists in nonsingular bounce cosmologies in the framework of scalar-tensor and Horndeski/Galileon theories is removed by the effects of new operators introduced by the DHOST, due to the modification that they later bring about to the dispersion relation of perturbations. Hence, our results demonstrate that there is indeed a loophole for this type of bounce scenarios to be free from pathologies when primordial perturbations evolve through the bounce phase, and thus the theoretical {it no-go} theorem for nonsingular bounce cosmology of Horndeski/Galileon theories can be delicately evaded in DHOST extensions.
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We improve the DHOST Genesis proposed in cite{Ilyas:2020zcb}, such that the near scale invariant scalar power spectrum can be generated from the model itself, without involking extra mechanism like a string gas. Besides, the superluminality problem of scalar perturbation plagued in cite{Ilyas:2020zcb} can be rescued by choosing proper DHOST action.
We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices, and the tensor to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be acquired by introducing a matter contraction phase before the Ekpyrotic phase or invoking a thermal gas as the source. The DHOST bounce scenario with cosmological perturbations generated by thermal fluctuations proves to be the most efficient one, and the corresponding predictions are in perfect agreement with observational bounds. Especially the tensor-to-scalar ratio is many orders of magnitude within the allowed region since it is suppressed by the Hubble parameter at the beginning of the bounce phase.
In quadratic-order degenerate higher-order scalar-tensor (DHOST) theories compatible with gravitational-wave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by $dot{phi}/H^p={rm constant}$, where $dot{phi}$ is the time derivative of a scalar field $phi$, $H$ is the Hubble expansion rate, and $p$ is a constant. While the tracker is present up to the cubic-order Horndeski Lagrangian $L=c_2X-c_3X^{(p-1)/(2p)} square phi$, where $c_2, c_3$ are constants and $X$ is the kinetic energy of $phi$, the DHOST interaction breaks this structure for $p eq 1$. Even in the latter case, however, there exists an approximate tracker solution in the early cosmological epoch with the nearly constant field equation of state $w_{phi}=-1-2pdot{H}/(3H^2)$. The scaling solution, which corresponds to $p=1$, is the unique case in which all the terms in the field density $rho_{phi}$ and the pressure $P_{phi}$ obey the scaling relation $rho_{phi} propto P_{phi} propto H^2$. Extending the analysis to the coupled DHOST theories with the field-dependent coupling $Q(phi)$ between the scalar field and matter, we show that the scaling solution exists for $Q(phi)=1/(mu_1 phi+mu_2)$, where $mu_1$ and $mu_2$ are constants. For the constant $Q$, i.e., $mu_1=0$, we derive fixed points of the dynamical system by using the general Lagrangian with scaling solutions. This result can be applied to the model construction of late-time cosmic acceleration preceded by the scaling $phi$-matter-dominated epoch.
In this article, we present an emergent universe scenario that can be derived from DHOST cosmology. The universe starts asymptotically Minkowski in the far past just like the regular Galileon Genesis, but evolves to a radiation dominated period at the late stage, and therefore, the universe has a graceful exit which is absent in the regular Galileon Genesis. We analyze the behavior of cosmological perturbations and show that both the scalar and tensor modes are free from the gradient instability problem. We further analyze the primordial scalar spectrum generated in various situations and discuss whether a scale invariance can be achieved.
We study the screening mechanism in the most general scalar-tensor theories that leave gravitational waves unaffected and are thus compatible with recent LIGO/Virgo observations. Using the effective field theory of dark energy approach, we consider the general action for perturbations beyond linear order, focussing on the quasi-static limit. When restricting to the subclass of theories that satisfy the gravitational wave constraints, the fully nonlinear effective Lagrangian contains only three independent parameters. One of these, $beta_1$, is uniquely present in degenerate higher-order theories. We compute the two gravitational potentials for a spherically symmetric matter source and we find that for $beta_1 ge 0$ they decrease as the inverse of the distance, as in standard gravity, while the case $beta_1 < 0$ is ruled out. For $beta_1 > 0$, the two potentials differ and their gravitational constants are not the same on the inside and outside of the body. Generically, the bound on anomalous light bending in the Solar System constrains $beta_1 lesssim 10^{-5}$. Standard gravity can be recovered outside the body by tuning the parameters of the model, in which case $beta_1 lesssim 10^{-2}$ from the Hulse-Taylor pulsar.
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