Abstract

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.

中文翻译：

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具有希格斯势的广义标量张量引力理论的宇宙学解和定性分析

摘要

该论文考虑了乔丹和爱因斯坦图片中的希格斯暴胀。在乔丹的图片中，动力学方程是用希格斯场和超势来表示的。在小场值的近似和慢滚动模式中，找到了解的示例，并分析了宇宙学参数的可验证性。爱因斯坦图片中也得到了动力学方程，并找到了弱希格斯场的非奇异解，其宇宙学参数与观测数据略有不同。为了分析宇宙动力学，爱因斯坦图像中的方程组被简化为自治方程组的形式。找到动力系统的奇异点，并针对不同的非最小相互作用参数值呈现这些点附近的相图\(\xi\)。还考虑了\(\xi\)较大值的情况。