标题： 尺度不变性，新暴胀和衰减的Lambda项 显示英文标题

标题： Scale invariance, new inflation and decaying Lambda terms

摘要： 尺度不变性的实现是在一个引力理论的背景下研究的，其中作用量（在第一类形式中）的形式为$S = \int L_{1} \Phi d^{4}x$+$\int L_{2}\sqrt{-g}d^{4}x$，其中$\Phi$是由自由度构建的密度，即“测度场”，与出现在$L_{1}$、$L_{2}$中的$g_{\mu\nu}$和物质场无关。 如果$L_{1}$包含曲率、标量势$V(\phi)$和$\phi$的动能项，$L_{2}$是另一个势能项，用于$\phi$、$U(\phi)$，那么当在共形爱因斯坦框架（CEF）中分析该理论时，真实真空态具有零能量密度，此时方程采用爱因斯坦形式。 当$V(\phi)$ = $f_{1}e^{\alpha\phi}$且$U(\phi)$ = $f_{2}e^{2\alpha\phi}$时，全局尺度不变性得以实现。在CEF中，标量场势能$V_{eff}(\phi)$除了在零处有一个最小值外，在$\alpha\phi \to\infty$处还有一个平坦区域，具有非零的真空能量，这适用于早期宇宙的新暴胀情景，或者适用于晚期宇宙的缓慢滚动衰减$\Lambda$情景，在这种情况下，真空能量的微小可以被理解为一种跷跷板机制。 显示英文摘要

摘要： Realizations of scale invariance are studied in the context of a gravitational theory where the action (in the first order formalism) is of the form $S = \int L_{1} \Phi d^{4}x$ + $\int L_{2}\sqrt{-g}d^{4}x$ where $\Phi$ is a density built out of degrees of freedom, the "measure fields" independent of $g_{\mu\nu}$ and matter fields appearing in $L_{1}$, $L_{2}$. If $L_{1}$ contains the curvature, scalar potential $V(\phi)$ and kinetic term for $\phi$, $L_{2}$ another potential for $\phi$, $U(\phi)$, then the true vacuum state has zero energy density, when theory is analyzed in the conformal Einstein frame (CEF), where the equations assume the Einstein form. Global Scale invariance is realized when $V(\phi)$ = $f_{1}e^{\alpha\phi}$ and $U(\phi)$ = $f_{2}e^{2\alpha\phi}$. In the CEF the scalar field potential energy $V_{eff}(\phi)$ has in, addition to a minimum at zero, a flat region for $\alpha\phi \to\infty$, with non zero vacuum energy, which is suitable for either a New Inflationary scenario for the Early Universe or for a slowly rolling decaying $\Lambda$-scenario for the late universe, where the smallness of the vacuum energy can be understood as a kind of see-saw mechanism.