Cosmological Solutions and Qualitative Analysis in the Generalized Scalar-Tensor Theory of Gravity with the Higgs Potential

The paper considers Higgs inflation in the Jordan and Einstein pictures. In Jordan’s picture, the dynamic equations are presented in terms of the Higgs field and a superpotential. In the approximation of small field values and in the slow-rolling mode, examples of solutions are found, and verifiability by cosmological parameters is analyzed. Dynamic equations are also obtained in the Einstein picture, and a nonsingular solution is found for a weak Higgs field, whose cosmological parameters slightly differ from the observed data. To analyze the cosmological dynamics, the set of equations in Einstein’s picture is reduced to the form of an autonomous set of equations. Singular points of the dynamical system are found, and a phase portrait near these points is presented for different values of the nonminimal interaction parameter \(\xi\). The case of large values of \(\xi\) is also considered.