实现宇宙暴涨的方法多种多样，最简单的方法是通过引入最小耦合的正则标量场来实现暴涨。现在唯一被实验探测到的标量场为希格斯(Higgs)标量场，但是，用希格斯标量场驱动暴涨所得到的原初引力波信号较大，而这与观测相矛盾。为了能让希格斯暴涨模型与观测相符，寻找压低原初引力波信号的模型至关重要。通过引入引力的高阶修正项——Gauss-Bonnet项，我们发现只要Gauss-Bonnet项的耦合函数与势函数为倒数关系，则对任意的暴涨势函数(包括希格斯暴涨)，原初引力波信号可以被压的任意低。不仅如此，Gauss-Bonnet项还能让暴涨模型轻松地满足沼泽地判据。Gauss-Bonnet暴涨模型属于最一般的标量-张量理论——Horndeski理论的一部分。本文对Horndeski理论也作了粗略的介绍。2017年，人们首次测量到引力波速度，引力波速度与光速的相对偏差量级为10⁻¹⁵。利用引力波速度观测结果，我们对Horndeski理论的模型参数给出了简单的限制。 暴涨模型虽然能给出曲率扰动和引力波扰动的功率谱；但是，一般情况下，人们并不直接将功率谱的表达式与观测数据相比较；而是将功率谱参数化，将其中最重要的两个参数——曲率扰动谱指数(简称谱指数)和引力波扰动幅度与标量扰动幅度的比值(简称张标比)，与观测数据进行比较。人们发现，存在多个暴涨模型给出相同谱指数和张标比的现象，即暴涨吸引子现象(inflationary attractors)，比如，非最小耦合希格斯暴涨模型、R²暴涨模型、α=1的E-model以及耦合函数取Ω(φ)=1+ζf(φ)势函数取V=λf(φ)²的标量张量理论模型都给出n〓-1=2／N， r=12／N²的理论预言。我们的研究指出这种吸引子现象并不是特例，任给一个势函数(对应一对谱指数和张标比)，通过简单的方法，我们能找到相对应的吸引子作用量。作为例子，我们给出了E-model、T-model和山顶势函所对应的吸引子作用量。 除了慢滚暴涨模型外，常滚暴涨模型也有很多人研究。相比慢滚暴涨，常滚暴涨模型有它特有的特点，比如扰动出视界后可能仍然增长，可以用于产生原初黑洞。常滚暴涨模型就是假设其中一个慢滚参数η〓为常数的暴涨模型。η〓>0的正则常滚暴涨模型可以分为三种情况：(1)哈勃参数为指数函数的幂次暴涨(power-law inflation)，(2)哈勃参数为双曲余弦函数的双曲余弦常滚暴涨，(3)哈勃参数为双曲正弦函数的双曲正弦常滚暴涨；η〓<0的正则常滚暴涨模型可以分为两种情况：(1)哈勃参数为余弦函数的余弦常滚暴涨，(2)哈勃参数为正弦函数的正弦常滚暴涨。在复数域下，余弦(正弦)常滚暴涨模型可以归到双曲余弦(正弦)常滚暴涨模型中。不同的常滚暴涨模型，有不同的优缺点。双曲余弦常滚暴涨模型能给出与观测相吻合的理论预言，但是暴涨不能自然结束。当η〓>3／2时，该模型预言的扰动出视界后仍然会增长，此时我们应该在暴涨结束时计算扰动谱的值，而不是在出视界时刻计算扰动谱；当η〓<3／2时，扰动出视界后保持不变。双曲正弦常滚暴涨模型虽然可以自然结束暴涨，并且给出的扰动出视界后保持不变；但是给出的理论预言只能与观测在2σ置信范围内吻合，而且该模型要求慢滚参数满足η〓<1。 在忽略慢滚参数ε〓时，分别满足η〓和η〓=3-η〓为常数的两个常滚暴涨模型给出相同的谱指数和张标比公式，它们似乎满足某种对偶关系；但是，当考虑ε〓的影响时，这两个暴涨模型不仅给出的谱指数公式不相同，并且背景演化方式和扰动的演化都完全不一样，因此，实际上，它们之间没有对偶关系。我们也给出观测对它们的限制。η〓<<1的常滚暴涨模型只能与观测在2σ置信区间内相吻合；〓≈3的常滚暴涨模型却可以与观测在1σ置信区间内相吻合。 在本文的最后，我们研究了Gauss-Bonnet项在常滚暴涨模型中的作用。当常滚参数较小时， Gauss-Bonnet项仍然可以起到压低张标比的作用；但是，当常滚参数比较大时，上述压低作用失效。 关键词：慢滚暴涨、常滚暴涨、Gauss-Bonnet暴涨、暴涨吸引子

 There are many ways to realize inflation, the simplest one is by using the scalar field with slow-roll conditions. If we use Higgs filed, which is the only detected scalar field presently, to achieve inflation, the prediction of large primordial gravitational waves is inconsistent with the observations. In order to unify the Higgs inflation model with the observations, it is very important to find a mechanism which can reduce the amplitude of primordial gravitational waves. With the help of the Gauss-Bonnet term which is a higher-order correction term of gravity, we find that the gravitational wave signals can be reduced as small as we want, for any inflationary model including the Higgs inflation, as long as the coupling function of the Gauss-Bonnet term is reciprocal to the potential. Moreover, the Gauss-Bonnet term can help inflationary models satisfy the swampland criteria easily. The Gauss-Bonnet term is also a part of Horndeski theory which is the most general scalar-tensor theory. We also give a brief introduction to Horndeski theory. In 2017, the speed of the gravitational waves was first measured, the relative deviation between the speed of gravitational waves and the speed of light was about 10⁻¹⁵. With the help of the speed of the gravitational waves, we also give constraints on the parameters of the Horndeski theory. Although the power spectra of the curvature perturbation and the tensor perturbation can be calculated for a given inflationary model, in general, people do not compare the power spectra itself with the observations, instead, they parameterize the power spectra and use two of the most important parameters, the curvature power spectrum index named scalar index and the ratio of the amplitude of the primordial gravitational waves to the amplitude of curvature perturbation named tensor to scalar ratio, to compare with the observations. It has been found that there exists a phenomenon of inflationary attractors, that many inflationary models can give the same scalar index and tensor to scalar ratio. For example, the non-minimally coupled Higgs inflation model, R² inflation model, E-model with α = 1 and the scalar-tensor inflationary models with the coupling function Ω（φ) = 1 + ξf(φ) and the potential V = λf(φ)² all give the same prediction with n〓 -1=2/N and r = 12/N². Our study points out that this phenomenon is not a special case. For a given potential which gives a particular scalar index and tensor to scalar ratio, we can find the corresponding attractor action through a sample method. As an example, we have given the attractor actions corresponding to E-model, T-model and Hilltop inflation. In addition to the slow-roll inflationary models, the constant-roll inflationary models have also been studied by many people. The constant-roll inflations have their own characteristics, such as the curvature perturbation may grow on the super-horizon scales, and they can be used to generate the primordial black hole. The constant-roll inflation is the model where one of the slow-roll parameters is a constant. The constant-roll inflationary model with η〓 > 0 has three cases: (1) the power-law inflation with the Hubble parameter being the exponential function, (2) the hyperbolic-cosine constant-roll inflation with the Hubble parameter being the hyperbolic cosine function and (3) the hyperbolic-sine constant-roll inflation with the Hubble parameter being the hyperbolic sine function. The constant-roll inflationary model with η〓 < 0 has two cases: (1) the cosine constant-roll inflation with the Hubble parameter being the cosine function, (2) the sine constant-roll inflation with the Hubble parameter being the sine function. For the complex scalar field, the cosine (sine) constant-roll inflationary model can be thought as the hyperbolic cosine (sine) constant-roll inflationary model. Different constant-roll inflationary models have their own advantages and disadvantages. The hyperbolic cosine constant-roll inflationary model can give predictions that are consistent with the observations, but it cannot exit inflation graceful. If η〓 > 3/2, the curvature perturbations grow on the sup-horizon scales, as a result, we should evaluate the scalar power spectrum at the end of the inflation instead of the horizon cross. If η〓< 3/2, the curvature perturbations keep to be a constant on sup-horizon scales. For the hyperbolic sine constant-roll inflation, it can exit inflation graceful, and the curvature perturbations keep to be a constant on sup-horizon scales, but the predictions are only consistent with the observations at the 2σ confidence level. Moreover, this model requires the slow-roll parameters satisfy η〓< 1. Neglecting the contribution from the slow-roll parameter ε〓, two constant-roll inflationary models with η〓 and 〓 = 3 -η〓 being constant, respectively, give the same scalar index and the tensor to scalar ratio, so it seems that there exists a duality between them. However, if we consider the effect of ε〓 , not only the scalar indices, but also the evolutions of the background and the perturbation are all different. Actually, we conclude that there is no duality between them. The constant-roll inflationary models with η〓<< 1 are consistent with the observations at the 2σconfidence level, and the constant-roll inflationary models with 〓≈3 are consistent with the observations at the la confidence level. At the end of this thesis, we study the role of the Gauss-Bonnet term in the constant-roll inflation. The Gauss-Bonnet term can also reduce the tensor-to scalar ratio if the constant parameter is small enough, but if the constant parameter is not small, the reduction mechanism is not efficient. Key words: slow-roll inflation, constant-roll inflation, Gauss-Bonnet inflation, inflationary attractors