Abstract Assuming that a scalar field controls the inflationary era, we examine the combined effects of string and f ( R ) gravity corrections on the inflationary dynamics of canonical scalar field inflation, imposing the constraint that the speed of the primordial gravitational waves is equal to that of light’s. Particularly, we study the inflationary dynamics of an Einstein-Gauss–Bonnet gravity in the presence of α R 2 corrections, where α is a free coupling parameter. As it was the case in the pure Einstein-Gauss–Bonnet gravity, the realization that the gravitational waves propagate through spacetime with the velocity of light, imposes the constraint that the Gauss–Bonnet coupling function ξ ( ϕ ) obeys the differential equation ξ = H ξ , where H is the Hubble rate. Subsequently, a relation for the time derivative of the scalar field is extracted which implies that the scalar functions of the model, which are the Gauss–Bonnet coupling and the scalar potential, are interconnected and simply designating one of them specifies the other immediately. In this framework, it is useful to freely designate ξ ( ϕ ) and extract the corresponding scalar potential from the equations of motion but the opposite is still feasible. We demonstrate that the model can produce a viable inflationary phenomenology and for a wide range of the free parameters. Also, a mentionable issue is that when the coupling parameter α of the R 2 correction term is α 1 0 − 3 in Planck Units, the R 2 term is practically negligible and one obtains the same equations of motion as in the pure Einstein-Gauss–Bonnet theory, however the dynamics still change, since now the time derivative of ∂ f ∂ R is nonzero. We study in detail the dynamics of inflation assuming that the slow-roll conditions hold true and also we briefly address the constant-roll case dynamics, and by using several illustrative examples, we compare the dynamics of the pure and R 2 -corrected Einstein-Gauss–Bonnet gravity. Finally the ghosts issue is briefly addressed.

中文翻译：

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使用字符串和 R2 校正的规范标量场膨胀

摘要 假设一个标量场控制了暴胀时代，我们研究了弦和 f ( R ) 重力修正对正则标量场暴胀的暴胀动力学的综合影响，施加了原始引力波的速度等于光的。特别是，我们研究了存在 α R 2 修正的爱因斯坦-高斯-博内引力的膨胀动力学，其中 α 是一个自由耦合参数。与纯爱因斯坦-高斯-博内引力的情况一样，引力波以光速在时空中传播的认识强加了高斯-博内耦合函数 ξ ( ϕ ) 服从微分方程 ξ = H ξ ，其中 H 是哈勃速率。随后，提取了标量场的时间导数的关系，这意味着模型的标量函数，即 Gauss-Bonnet 耦合和标量势是相互关联的，只需指定其中一个即可立即指定另一个。在这个框架中，自由指定 ξ ( ϕ ) 并从运动方程中提取相应的标量势是有用的，但相反的方法仍然可行。我们证明该模型可以产生可行的暴胀现象学和广泛的自由参数。此外，一个值得一提的问题是，当 R 2 校正项的耦合参数 α 在普朗克单位中为 α 1 0 − 3 时，R 2 项实际上可以忽略不计，并且可以获得与纯爱因斯坦-高斯中相同的运动方程– Bonnet 理论，但动态仍在变化，因为现在∂ f ∂ R 的时间导数非零。我们在假设慢滚条件成立的情况下详细研究了暴胀的动力学，并且我们还简要讨论了恒滚情况动力学，并通过使用几个说明性示例，我们比较了纯爱因斯坦和 R 2 校正爱因斯坦的动力学-高斯-博内引力。最后简要介绍了幽灵问题。