Bifurcated symmetry breaking in scalar-tensor gravity (2112.02835v2)

Abstract: We present models that simultaneously predict presence of dark energy and cold dark matter along with slow-roll inflation. The dark energy density is found to be of order $({\rm a \;few \;meV})^4$, and the mass of dark matter constituent is $\approx 1\,$ meV. These numbers are given in terms of the present value of Hubble constant $H_0$ and the Plank energy $1/\sqrt{16 \pi G_N}$: they are $(H_0 M_{\rm P})^2$ for the energy density and $(H_0 M_{\rm P})^{1/2}$ for the dark matter constituent mass. The basic framework is a multi-scalar tensor gravity with non-trivial conformal coupling to the Ricci scalar curvature in the lagrangian density. The key for a right amount of dark energy is to incorporate in a novel way the spatially homogeneous kinetic contribution of Nambu-Goldstone modes in a spontaneously broken multi-scalar field sector. Proposed theories are made consistent with general relativity tests at small cosmological distances, yet are different from general relativity at cosmological scales. Dark matter is generated as spatially inhomogeneous component of the scalar system, with roughly comparable amount to the dark energy. In some presented models a cosmological bifurcation of symmetry breaking of scalar sector is triggered by the spontaneous breaking of electroweak SU(2) $\times $ U(1) gauge symmetry, hence the separation occurring simultaneously at the electroweak phase transition. The best experimental method to test presented models is to search for the fifth-force type of scalar exchange interaction with a force range, $O(10^{-2})$ cm, whose coupling to matter is basically of gravitational strength.