Investigations of Quantum Effects Related to Black Holes and the Early Universe

该奖项将研究宇宙早期暴胀阶段的黑洞蒸发。一个特别的重点将是确定那个时期的黑洞辐射可能对宇宙背景辐射产生的影响。如果有潜在的可观察到的影响，那么这些可以提供关于暴胀期间原始黑洞存在的信息。霍金最初对黑洞蒸发的计算给出了黑洞在形成后的后期如何蒸发的信息。在一个简单的黑洞形成模型中，将详细研究发生在黑洞形成过程早期和中期的量子效应。这些结果可能会让我们深入了解一个重要的问题，即当黑洞形成时，信息会发生什么变化。模拟黑洞是可以在实验室中研究的系统，可以模拟真实黑洞的一个或多个方面。模拟黑洞是由由铷原子组成的玻色-爱因斯坦凝聚物制成的，这些凝聚物被冷却到非常低的温度。理论计算，本质上与真实黑洞的计算相似，将被用于预测这些模拟黑洞在实验室测量的某些量的值。如果与实验数据一致，那么这将提供证据，证明霍金和其他人对真实黑洞中量子效应的预测是正确的。引力的半经典近似在爱因斯坦的引力理论、广义相对论和完全量子引力理论之间架起了一座桥梁。它已被用于研究早期宇宙中的粒子产生以及黑洞蒸发。半经典近似的有效性将在两种不同的早期宇宙情景下进行研究。一种是简单模型，其中宇宙首先收缩到最小尺寸，然后开始膨胀。另一个是在一个重要的暴胀模型中产生的粒子，这个模型叫做斯塔宾斯基暴胀。粒子的产生发生在暴胀结束后，用物质和辐射填满宇宙。两到三名研究生将参与研究的各个方面。该项目将包括本科生，继续培养本科生和研究生在数值和分析研究技术方面的长期历史，并共同撰写出版物。研究结果将通过出版物和在国家和（或）国际会议上的发言向研究界传播。该研究将涉及黑洞蒸发，玻色-爱因斯坦凝聚物（可以作为黑洞类似物）的可观测效应，以及早期宇宙宇宙学。具体而言，它将研究与暴胀期间原始黑洞蒸发是否会产生可观测效应有关的问题，黑洞形成的信息，模拟黑洞系统中量子效应相关的理论和实验结果之间的对应关系，以及早期宇宙中半经典近似的有效性。对于膨胀期间的黑洞蒸发，一个目标是确定它可能对宇宙背景辐射产生的影响。其他与太初黑洞有关的量子效应也将被研究。黑洞蒸发也将在球对称辐射壳坍缩形成黑洞的情况下进行研究。其目的包括深入了解黑洞如何形成的信息发生了什么，并检查二维引力膨胀理论中类似计算的准确性。可以作为模拟黑洞的玻色-爱因斯坦凝聚体已经在实验室进行了研究。该领域的研究目的是确定玻色-爱因斯坦凝聚体作为模拟黑洞的某些实验结果是否与模拟时空中弯曲空间计算中量子场论的预测在数量上一致。半经典近似已被用于研究早期宇宙中的重要效应，如暴胀后的再加热。这项研究的一个目标是确定半经典近似在某些模型中是否有效，在这些模型中，宇宙收缩到最小尺寸，然后膨胀，以及在后暴胀时代的一个著名的暴胀模型，有时被称为斯塔宾斯基暴胀。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award will study black hole evaporation during an inflationary phase in the very early universe. A particular focus will be to determine possible effects that black hole radiation from that time period could have on the cosmic background radiation. If there are potentially observable effects, then these could provide information about the existence of primordial black holes during inflation. Hawking’s original calculation of black hole evaporation gave information about how black holes evaporate at late times after the black hole forms. A detailed study will be made of quantum effects that occur at early and intermediate times in the black hole formation process in a simple model of black hole formation. The results may provide insight into the important question of what happens to the information when a black hole is created. Analog black holes are systems that can be studied in the laboratory and mimic one or more aspects of real black holes. Analog black holes have been made from Bose-Einstein condensates that consist of Rubidium atoms that have been cooled to very low temperatures. Theoretical calculations, similar in nature to those for real black holes, will be made and used to predict the values for certain quantities for these analog black holes that have been measured in the laboratory. If the agreement is found with the experimental data, then that will provide evidence that predictions made by Hawking and others relating to quantum effects in real black holes are correct. The semiclassical approximation in gravity provides a bridge between Einstein’s theory of gravity, general relativity, and a fully quantum theory of gravity. It has been used to study particle production in the early universe as well as black hole evaporation. The validity of the semiclassical approximation will be investigated for two different early universe scenarios. One is for simple models in which the Universe first contracts to a minimum size and then begins expanding. The other is particle production in an important model of inflation called Starobinsky inflation. The particle production occurs after inflation is over and fills the Universe back up with matter and radiation. Two or three graduate students will participate in various aspects of the research. The project will include undergraduate students, continuing a long history of the training of both undergraduate and graduate students in numerical and analytical research techniques and co-authorship on publications. Results will be disseminated to the research community through publications and presentations at national and/or international meetings. The research will address black hole evaporation, observable effects in Bose-Einstein condensates which can serve as black hole analogs, and early universe cosmology. Specifically, it will investigate questions related to whether observable effects could arise from primordial black hole evaporation during inflation, the information about how a black hole forms, the correspondence between theoretical and experimental results related to quantum effects in analog black hole systems, and the validity of the semi-classical approximation in the early universe. For black hole evaporation during inflation, one goal is to determine the effects it could have on the cosmic background radiation. Other quantum effects related to primordial black holes will also be investigated. Black hole evaporation will also be studied in the case that a spherically symmetric shell of radiation collapses to form a black hole. Objectives include gaining insight into the question of what happens to the information about how a black hole forms and to check the accuracy of similar calculations in two dimensional dilaton theories of gravity. Bose-Einstein condensates that can serve as analog black holes have been studied in the laboratory. The goal of the research in this area is to determine whether certain experimental results for Bose-Einstein condensates which can serve as analog black holes are in quantitative agreement with predictions resulting from quantum field theory in curved space calculations in the analog spacetimes. The semiclassical approximation has been used to study important effects in the early universe such as reheating after inflation. One goal of the research is to determine whether the semiclassical approximation is valid in certain models in which the universe contracts to a minimum size and then expands and in the post-inflation era of a well-known model of inflation, sometimes called Starobinsky inflation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.