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

该奖项将研究宇宙早期膨胀阶段的黑洞蒸发。一个特别的重点将是确定这段时间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效应，那么这些效应可能会提供关于膨胀期间原始黑洞存在的信息。霍金最初对黑洞蒸发的计算提供了有关黑洞形成后的后期黑洞如何蒸发的信息。在一个简单的黑洞形成模型中，将详细研究在黑洞形成过程的早期和中期发生的量子效应。这些结果可能会让我们深入了解一个重要的问题，即当黑洞产生时，信息会发生什么。模拟黑洞是可以在实验室中研究并模拟真实黑洞的一个或多个方面的系统。模拟黑洞是由玻色-爱因斯坦凝聚体制成的，这种凝聚体由冷却到极低温度的Rb原子组成。理论计算本质上类似于真实黑洞的计算，并将用于预测实验室中测量的这些模拟黑洞的某些量的值。如果发现与实验数据一致，那么这将提供证据，证明霍金和其他人关于真实黑洞中量子效应的预测是正确的。引力中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。它已经被用来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个不同的早期宇宙场景中进行研究。一种是简单的模型，在这种模型中，宇宙首先收缩到最小尺寸，然后开始膨胀。另一种是称为斯塔宾斯基膨胀的重要膨胀模型中的粒子生产。粒子的产生发生在膨胀结束后，并用物质和辐射重新填充宇宙。两三名研究生将参与研究的各个方面。该项目将包括本科生，延续了长期以来对本科生和研究生进行的数值和分析研究技术培训以及出版物合作编写的历史。结果将通过出版物和在国家和/或国际会议上的介绍向研究界传播。这项研究将涉及黑洞蒸发、可用作黑洞类比的玻色-爱因斯坦凝聚体中的可观测效应，以及早期宇宙宇宙学。具体地说，它将调查与以下问题有关的问题：在膨胀过程中原始黑洞蒸发是否会产生可观察到的效应；关于黑洞如何形成的信息；与模拟黑洞系统中的量子效应有关的理论和实验结果之间的一致性；以及半经典近似在早期宇宙中的有效性。对于膨胀过程中的黑洞蒸发，一个目标是确定它可能对宇宙背景辐射产生的影响。其他与原始黑洞相关的量子效应也将被研究。在球对称的辐射壳体坍塌形成黑洞的情况下，也将研究黑洞蒸发。目标包括洞察关于黑洞如何形成的信息会发生什么的问题，以及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中进行了研究。这一领域的研究目的是确定可以用作模拟黑洞的玻色-爱因斯坦凝聚体的某些实验结果是否与量子场理论在模拟时空中的弯曲空间计算中得到的预测定量一致。半经典近似已被用来研究早期宇宙中的重要效应，如膨胀后的再加热。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，在众所周知的通货膨胀模型的后通货膨胀时代，有时被称为Starobinsky通货膨胀。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.