Inflation in symmergent metric-Palatini gravity

In this paper, we study the cosmological inflation phenomenon in symmergent gravity theory. Symmergent gravity is a novel framework which merges gravity and the standard model (SM) so that the gravity emerges from the matter loops and restores the broken gauge symmetries along the way. Symmergent gravity is capable of inducing the gravitational constant G and the quadratic curvature coefficient cO from the loop corrections of the matter sector in a flat space-time. In the event that all the matter fields, including the beyond the standard model (BSM) sector, are mass degenerate, the vacuum energy can be expressed in terms of G and cO. The parameter which measures the deviation from the mass degeneracy is dubbed alpha. The parameters, cO and alpha, of symmergent gravity convey the information about the fermion and boson balance in the matter (SM+BSM) sector in number and in mass, respectively. In our analysis, we have investigated the space of the symmergent parameters cO and alpha wherein they produce results that comply with the inflationary observables ns, r, and dns/d ln k. We have shown that the vacuum energy together with the quadratic curvature term arising in the symmergent gravity prescription are capable of inflating the universe provided that the quadratic curvature coefficient cO is negative (which corresponds to fermion dominance in number in the matter sector) and the deviation from the mass degeneracy in the matter sector is minute for both boson mass dominance and fermion mass dominance cases.