来自暴胀极慢滚极限的对数引力
Logarithmic gravity from a very slow roll limit of inflation
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中文总结 AI 辅助
该论文研究暴胀无边界波函数在极慢滚极限下的行为，提出对数引力理论，并证明其概率测度可简化为高斯型，且单圈效应不产生额外共形因子依赖，条件化真空衰变可生成刘维尔指数势。
中文摘要 AI 辅助
我们研究了暴胀无边界波函数在“线性滚动极限”下的行为，其中 $G_N \ o 0$，而哈勃尺度 $H$ 和暴胀子势能的斜率保持固定。尽管在该极限下体引力子涨落被抑制，但量子暴胀子涨落仍然有限。由于再加热发生在固定暴胀子值的表面上，这些涨落转化为再加热度规共形因子的涨落。这些涨落的概率测度大幅简化并变为高斯型，即使对于大的涨落也是如此。在超视界尺度上，由此产生的对数关联理论是 $d$ 维无指数势的刘维尔引力的类比，我们称之为对数引力。二次项和线性项由共形协变散射数据决定；在偶数维中，我们将它们与临界 GJMS 算子和 Branson $Q$-曲率联系起来。根据体幺正性，我们认为单圈效应不会在物理概率测度中产生额外的共形因子依赖性，并且我们在 $2 + 1$ 维中明确验证了这种抵消。对于具有滚动暴胀子的无边界范数，我们证明了非紧致的剩余共形对称性可以通过有限的 Faddeev-Popov 行列式进行规范固定，因此它们不会迫使球面贡献消失。此外，以不存在由气泡成核引起的真空衰变为条件，会在概率测度中产生刘维尔指数势。
英文摘要
We study the inflationary no-boundary wavefunction in a ``linear-roll limit,'' in which $G_N \to 0$ while the Hubble scale $H$ and the slope of the inflaton potential are held fixed. Although bulk graviton fluctuations are suppressed in this limit, quantum inflaton fluctuations remain finite. Because reheating occurs on a surface of fixed inflaton value, these fluctuations become fluctuations of the conformal factor of the reheating metric. The probability measure for these fluctuations simplifies drastically and becomes Gaussian, even for large fluctuations. The resulting log-correlated theory at superhorizon scales is a $d$-dimensional analog of Liouville gravity without the exponential potential, which we call Logarithmic Gravity. The quadratic and linear terms are determined by conformally covariant scattering data; in even dimensions we relate them to the critical GJMS operator and Branson $Q$-curvature. From bulk unitarity, we argue that one-loop effects do not generate additional conformal-factor dependence in the physical probability measure, and we verify the cancellation explicitly in $2 + 1$ dimensions. For the no-boundary norm with a rolling inflaton, we show that the noncompact residual conformal symmetries can be gauge fixed with a finite Faddeev-Popov determinant, so they do not force the sphere contribution to vanish. In addition, conditioning on the absence of vacuum decay by bubble nucleation generates the Liouville exponential potential in the probability measure.
发表机构
- Harvard University（哈佛大学）
- Princeton University（普林斯顿大学）
- Institute for Advanced Study（高等研究院）
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