论文标题
在宇宙发展过程中，$ e $ - 折数的型号独立界限
Model independent bounds for the number of $e$-folds during the evolution of the universe
论文作者
论文摘要
我们提出了一个简单的程序，以获得有关宇宙学兴趣数量的通用界限，例如在通货膨胀，再加热和辐射期间的$ e $ folds数量以及加热温度。主要的假设是代表宇宙进化的每个时期中的每个时期，是由于一种物质即时变化为下一个物质，描述了宇宙的新时代。此假设通常用于获得简单宇宙学模型的弗里德曼方程解决方案的解决方案，以在宇宙学量中找到与模型无关的界限。特别是，我们发现$ - \ frac {1} {1} {3} <ω__{re} <\ frac {1} {1} {3} $绑定的$ n_k \ \ frac {1} {1} {1} {3} $作为上限非常有力，在膨胀期间$ e $ - $ e $ - 在$ e $ - $ e $ - $ e} $ e} $ a} $ω_{reω{recy}时也非常强大。 $ω__{re} $是加热过程中状态参数的有效方程。这些是任何单场通货膨胀模型都应满足的独立结果。例如，我们用基本的$α$吸引子模型说明了两种方法，并展示了它们如何相互补充。
We present a simple procedure to obtain universal bounds for quantities of cosmological interest, such as the number of $e$-folds during inflation, reheating, and radiation, as well as the reheating temperature. The main assumption is to represent each of the various epochs of evolution of the universe as being due to a single substance changing instantaneously into the next, describing a new era of evolution of the universe. This assumption, commonly used to obtain solutions of the Friedmann equations for simple cosmological models, is implemented here to find model-independent bounds on cosmological quantities of interest. In particular, we find that the bound $N_k\approx 56$ for $-\frac{1}{3} < ω_{re} < \frac{1}{3}$ is very robust as an upper bound on the number of $e$-folds during inflation and also as a lower bound when $ω_{re} > \frac{1}{3}$, where $ω_{re}$ is the effective equation of state parameter during reheating. These are model-independent results that any single-field model of inflation should satisfy. As an example, we illustrate the two approaches with the basic $α$ attractor model and show how they complement each other.
