The most promising alternative that can solve the initial singularity problem, one of the biggest problem in modern physics is a non-singular bouncing scenario, where the universe is supposed to undergo a smooth transition from the initial contracting phase to the currently expanding phase. In the non-singular bouncing scenario the Hubble parameter has to grow during the bounce period, which within the framework of General Relativity is possible only if there exists an exotic matter component that does not respect the Null Energy Condition (NEC). Here the problem is that it is challenging to realize the NEC violation without pathologies such as ghost and gradient instabilities and superluminality.
An important yet unresolved issue is superluminality, which is another undesirable feature of low energy effective field theory, since it indicates that such a theory can not be UV-completed in a Lorentz-covariant way. Beyond-Horndeski theories admit non-singular bouncing scenario without ghost and gradient instabilities and superluminality and with conventional asymptotics. However, superluminality issue reappears once we add to the theory an extra scalar field minimally coupled to gravity which has the luminal sound speed.
In our work, we have, for the first time, constructed a bouncing cosmology based on the Degenerate Higher-Order Scalar-Tensor (DHOST) theory, which exhibits neither ghost instability nor gradient instability, nor superluminality, nor strong gravity in the past and future. The model includes a scalar field with sound speed equal to the speed of light, and this scalar field generates nearly scale-invariant scalar perturbations consistent with observational data during the contracting phase.
The following figure shows the squared propagation speed of scalar perturbations in our model as a function of time.
The inset shows squared propagation speed in the vicinity of cosmic bounce. In this work, the Planck units was used, where the speed of light c, the Planck constant h and the reduced Planck mass Mpl are all set to 1.
Our research, which for the first time constructed a cosmological bounce model consistent with observational data without any instabilities or superluminality based on the DHOST theory, is expected to contribute to solving the long-standing unresolved problem of the initial singularity of the universe.
The result was published in the "Journal of High Energy Physics" [05, 005 (2025)] under the title of "Fully viable DHOST bounce with extra scalar" (https://doi.org/10.1007/JHEP05(2025)005).
