{"id":{"repo_id":"tu-berlin","oai_identifier":"oai:depositonce.tu-berlin.de:11303/25150"},"canonical_url":"https://search.dev.ndltd.org/etd/tu-berlin/oai:depositonce.tu-berlin.de:11303/25150","repository":{"repo_id":"tu-berlin","name":"Technische Universität Berlin","base_url":"https://api-depositonce.tu-berlin.de/server/oai/request"},"display":{"title":"New insights into cosmological solutions of the semiclassical Einstein equation","abstract":"In this thesis, we study the semiclassical Einstein equation (SCE) which models the backreaction of a scalar quantum field to the curvature of the underlying space-time. We are especially interested in cosmological solutions providing insight into the effects a quantum field can have on our universe. The main body of this text is divided into five sections. Prior to this main body, we give a comprehensive introduction to quantum field theory on curved space-times and to cosmology. Moreover, we introduce the cosmological SCE and interpret it as an infinite- dimensional dynamical system governing both the metric’s and the field’s degrees of freedom. The first main-part section is devoted to the construction of so-called Minkowski-like vacua. These are certain vacuum states on cosmological space-times and allow to for- mulate a well-posed cosmological model from the SCE. We conclude the section by a numerical approach to the model, evaluating the backreaction in view of several proper- ties observed in our actual universe. A remarkable finding here is that throughout the parameter space, a quantum field’s backreaction is closely reminiscent of Dark Energy- dominated late times. In the second part, we enlarge the class of solutions to the cosmological SCE from the first part. More generally, we develop a systematic approach to obtain new solutions from given ones by introducing certain effective degrees of freedom in terms of functions of time. We show that the latter are governed by an effective third-order equation. Moreover, we prove that under certain conditions on the initial values, our approach yields proper states for the field. The third section further examines the Dark Energy effect of a quantum field. We show that a specific part of the equation, which is dominant throughout a large part of the parameter space, imposes Dark Energy-dominated late times as a generic feature. Also for the regime where the latter is less dominant, we demonstrate that Dark Energy- dominated late times are, under certain assumptions, attractors of the dynamical system of the SCE. The fourth section studies the backreaction of a classical scalar field. The main focus is to develop a systematic approach to the conic-section equations emerging from the backreaction. Note that similar equations emerge from the backreaction of a quantum field with non-vanishing one-point function. On this way, we find a variety of physically interesting features of this backreaction. For instance, we discuss so-called Small Bang solutions, the compatibility of classical fields/one-point functions with (classical) Dark Energy as well as field-driven inflationary early-time phases. The final main-part section characterizes the set of solutions to the SCE in which the universe is exponentially expanding. For these symmetric space-times there is a natu- ral choice of quantum state, the so-called Bunch-Davies state. Exponential phases are expected in our universe’s history both at early and at late time, but the ratio of the corresponding exponential rates is believed to be quite large. We prove that the set of exponential solutions to the SCE is large enough such that the aforementioned ratio can be realized. We conclude with a short discussion and further perspectives.","abstract_html":"In this thesis, we study the semiclassical Einstein equation (SCE) which models the backreaction of a scalar quantum field to the curvature of the underlying space-time. We are especially interested in cosmological solutions providing insight into the effects a quantum field can have on our universe. The main body of this text is divided into five sections. Prior to this main body, we give a comprehensive introduction to quantum field theory on curved space-times and to cosmology. Moreover, we introduce the cosmological SCE and interpret it as an infinite- dimensional dynamical system governing both the metric’s and the field’s degrees of freedom. The first main-part section is devoted to the construction of so-called Minkowski-like vacua. These are certain vacuum states on cosmological space-times and allow to for- mulate a well-posed cosmological model from the SCE. We conclude the section by a numerical approach to the model, evaluating the backreaction in view of several proper- ties observed in our actual universe. A remarkable finding here is that throughout the parameter space, a quantum field’s backreaction is closely reminiscent of Dark Energy- dominated late times. In the second part, we enlarge the class of solutions to the cosmological SCE from the first part. More generally, we develop a systematic approach to obtain new solutions from given ones by introducing certain effective degrees of freedom in terms of functions of time. We show that the latter are governed by an effective third-order equation. Moreover, we prove that under certain conditions on the initial values, our approach yields proper states for the field. The third section further examines the Dark Energy effect of a quantum field. We show that a specific part of the equation, which is dominant throughout a large part of the parameter space, imposes Dark Energy-dominated late times as a generic feature. Also for the regime where the latter is less dominant, we demonstrate that Dark Energy- dominated late times are, under certain assumptions, attractors of the dynamical system of the SCE. The fourth section studies the backreaction of a classical scalar field. The main focus is to develop a systematic approach to the conic-section equations emerging from the backreaction. Note that similar equations emerge from the backreaction of a quantum field with non-vanishing one-point function. On this way, we find a variety of physically interesting features of this backreaction. For instance, we discuss so-called Small Bang solutions, the compatibility of classical fields/one-point functions with (classical) Dark Energy as well as field-driven inflationary early-time phases. The final main-part section characterizes the set of solutions to the SCE in which the universe is exponentially expanding. For these symmetric space-times there is a natu- ral choice of quantum state, the so-called Bunch-Davies state. Exponential phases are expected in our universe’s history both at early and at late time, but the ratio of the corresponding exponential rates is believed to be quite large. We prove that the set of exponential solutions to the SCE is large enough such that the aforementioned ratio can be realized. We conclude with a short discussion and further perspectives.","abstract_has_math":false,"creators":["Rothe, Nicolai"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Gottschalk, Hanno"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025","date_published":"2025","updated_at":"2026-07-27T21:28:47Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":["https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.14279/depositonce-23971"],"render_values":[{"text":"https://doi.org/10.14279/depositonce-23971","href":"https://doi.org/10.14279/depositonce-23971","code":true}]}]},"links":{"outbound_url":"https://depositonce.tu-berlin.de/handle/11303/25150","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gottschalk, Hanno"]},{"key":"dc:creator","label":"Author","values":["Rothe, Nicolai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-07-11T14:49:15Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-07-11T14:49:15Z"]},{"key":"dc:date.issued","label":"Date","values":["2025"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://depositonce.tu-berlin.de/handle/11303/25150","https://doi.org/10.14279/depositonce-23971"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we study the semiclassical Einstein equation (SCE) which models the backreaction of a scalar quantum field to the curvature of the underlying space-time. We are especially interested in cosmological solutions providing insight into the effects a quantum field can have on our universe. The main body of this text is divided into five sections. Prior to this main body, we give a comprehensive introduction to quantum field theory on curved space-times and to cosmology. Moreover, we introduce the cosmological SCE and interpret it as an infinite- dimensional dynamical system governing both the metric’s and the field’s degrees of freedom. The first main-part section is devoted to the construction of so-called Minkowski-like vacua. These are certain vacuum states on cosmological space-times and allow to for- mulate a well-posed cosmological model from the SCE. We conclude the section by a numerical approach to the model, evaluating the backreaction in view of several proper- ties observed in our actual universe. A remarkable finding here is that throughout the parameter space, a quantum field’s backreaction is closely reminiscent of Dark Energy- dominated late times. In the second part, we enlarge the class of solutions to the cosmological SCE from the first part. More generally, we develop a systematic approach to obtain new solutions from given ones by introducing certain effective degrees of freedom in terms of functions of time. We show that the latter are governed by an effective third-order equation. Moreover, we prove that under certain conditions on the initial values, our approach yields proper states for the field. The third section further examines the Dark Energy effect of a quantum field. We show that a specific part of the equation, which is dominant throughout a large part of the parameter space, imposes Dark Energy-dominated late times as a generic feature. Also for the regime where the latter is less dominant, we demonstrate that Dark Energy- dominated late times are, under certain assumptions, attractors of the dynamical system of the SCE. The fourth section studies the backreaction of a classical scalar field. The main focus is to develop a systematic approach to the conic-section equations emerging from the backreaction. Note that similar equations emerge from the backreaction of a quantum field with non-vanishing one-point function. On this way, we find a variety of physically interesting features of this backreaction. For instance, we discuss so-called Small Bang solutions, the compatibility of classical fields/one-point functions with (classical) Dark Energy as well as field-driven inflationary early-time phases. The final main-part section characterizes the set of solutions to the SCE in which the universe is exponentially expanding. For these symmetric space-times there is a natu- ral choice of quantum state, the so-called Bunch-Davies state. Exponential phases are expected in our universe’s history both at early and at late time, but the ratio of the corresponding exponential rates is believed to be quite large. We prove that the set of exponential solutions to the SCE is large enough such that the aforementioned ratio can be realized. We conclude with a short discussion and further perspectives.","In dieser Arbeit untersuchen wir die semiklassische Einstein Gleichung (SCE) als Modell für die Wechselwirkung zwischen einem skalaren Quantenfeld und der Krümmung einer zugrundeliegenden Raumzeit. Dabei interessieren wir uns speziell für kosmologische Lösungen, um den Einfluss eines Quantenfeldes auf unser Universum zu verstehen. Der Hauptteil dieses Textes gliedert sich in fünf Teile. Vor diesem Hauptteil geben wir eine ausführliche Einführung in die Quantenfeldtheorie auf gekrümmten Raumzeiten sowie in die Kosmologie. Danach führen wir die kosmologische SCE ein und interpretieren diese als unendlich-dimensionales dynamisches System für die Freiheitsgrade sowohl der Metrik als auch des Feldes. Im ersten Hauptteil definieren wir die sogenannten Minkowski-artigen Vakua. Diese Zustände erlauben es, die SCE als wohlgestelltes Anfangswertproblem zu betrachten und den Effekt eines Quantenfeldes auf die Raumzeit im Hinblick auf einige physikalische Eigenschaften numerisch zu untersuchen. Bemerkenswert ist hierbei, dass sich das Quantenfeld in ähnlicher Weise wie Dunkle Energie auf die Spät-Zeit-Entwicklung eines Universums auszuwirken scheint. Ausgehend von den Minkowski-artigen Zuständen, vergrößern wir im zweiten Teil die Menge der gefundenen Lösungen der SCE. Allgemeiner entwickeln wir einen systematischen Zugang neue Lösungen aus alten zu bekommen, indem wir dem System gewisse effektive Freiheitsgrade hinzufügen. Diese sind einfach Funktionen der Zeit und wir zeigen, dass diese von einer Differentialgleichung dritter Ordnung beschrieben werden. Des Weiteren beweisen wir, dass es unter bestimmten Voraussetzungen an die Anfangswerte der effektiven Freiheitsgrade tatsächlich einen Zustand mit der beschriebenen Rückreaktion gibt. Der dritte Teil behandelt den Dunkle-Energie-Effekt eines Quantenfeldes weiterführend. Wir zeigen, dass ein bestimmter Teil der SCE, welcher über einen großen Teil des Parameterraumes sehr dominant ist, generischerweise eine durch Dunkle Energie dominierte Spät-Zeit-Entwicklung nach sich zieht. Aber auch in Parameterbereichen, in denen vorgenannter Teil weniger dominant ist, können wir zeigen, dass sich durch Dunkle Energie dominierte Spät-Zeit-Entwicklungen unter bestimmten Voraussetzungen in der Dynamik der SCE attraktiv gegenüber Störungen verhalten. Im vierten Teil untersuchen wir die Rückreaktion eines klassischen Skalarfeldes. Hierbei ist ein zentrales Ziel die Entwicklung eines systematischen Zugangs zu diesgearteten Kegelschnittgleichungen. Dahingehend bemerken wir, dass auch in der Rückreaktion eines Quantenfeldes im Zusammenhang mit nicht-verschwindenden Einpunktfunktionen solche Gleichungen zu behandeln sind. Wir finden schließlich einige interessante Eigenschaften der Lösungen zu diesem Modell. Speziell studieren wir sogenannte Small-Bang- Lösungen, die gegenseitige Beeinflussung eines skalaren Feldes/einer Einpunktfunktion und (klassischer) Dunkler Energie sowie inflationäre Früh-Zeit-Phasen, welche durch das klassische Feld zustande kommen. Der letzte Hauptteil ist der Menge der exponentiell expandierenden Lösungen der SCE gewidmet. Auf den zugrundeliegenden Raumzeiten gibt es ausgezeichnete, natürliche Vakuumzustände, sogenannte Bunch-Davies-Vakua. Man geht davon aus, dass exponentielle Phasen sowohl in der Früh-Zeit als auch in der Spät-Zeit des Universums dieses gut approximieren. Allerdings wird auch angenommen, dass die exponentiellen Raten von sehr verschiedener Größenordnung sind. Wir zeigen hier, dass die Menge exponentieller Lösungen ausreichend flexibel ist, um diese sehr verschiedenen Raten zu reproduzieren. Wir schließen den Text mit einer Diskussion der Ergebnisse sowie mit einigen Forschungsperspektiven für die Zukunft ab."]},{"key":"dc:title","label":"Title","values":["New insights into cosmological solutions of the semiclassical Einstein equation"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gottschalk, Hanno"],"dc:creator":["Rothe, Nicolai"],"dc:date.accessioned":["2025-07-11T14:49:15Z"],"dc:date.available":["2025-07-11T14:49:15Z"],"dc:date.issued":["2025"],"dc:description.abstract":["In this thesis, we study the semiclassical Einstein equation (SCE) which models the backreaction of a scalar quantum field to the curvature of the underlying space-time. We are especially interested in cosmological solutions providing insight into the effects a quantum field can have on our universe. The main body of this text is divided into five sections. Prior to this main body, we give a comprehensive introduction to quantum field theory on curved space-times and to cosmology. Moreover, we introduce the cosmological SCE and interpret it as an infinite- dimensional dynamical system governing both the metric’s and the field’s degrees of freedom. The first main-part section is devoted to the construction of so-called Minkowski-like vacua. These are certain vacuum states on cosmological space-times and allow to for- mulate a well-posed cosmological model from the SCE. We conclude the section by a numerical approach to the model, evaluating the backreaction in view of several proper- ties observed in our actual universe. A remarkable finding here is that throughout the parameter space, a quantum field’s backreaction is closely reminiscent of Dark Energy- dominated late times. In the second part, we enlarge the class of solutions to the cosmological SCE from the first part. More generally, we develop a systematic approach to obtain new solutions from given ones by introducing certain effective degrees of freedom in terms of functions of time. We show that the latter are governed by an effective third-order equation. Moreover, we prove that under certain conditions on the initial values, our approach yields proper states for the field. The third section further examines the Dark Energy effect of a quantum field. We show that a specific part of the equation, which is dominant throughout a large part of the parameter space, imposes Dark Energy-dominated late times as a generic feature. Also for the regime where the latter is less dominant, we demonstrate that Dark Energy- dominated late times are, under certain assumptions, attractors of the dynamical system of the SCE. The fourth section studies the backreaction of a classical scalar field. The main focus is to develop a systematic approach to the conic-section equations emerging from the backreaction. Note that similar equations emerge from the backreaction of a quantum field with non-vanishing one-point function. On this way, we find a variety of physically interesting features of this backreaction. For instance, we discuss so-called Small Bang solutions, the compatibility of classical fields/one-point functions with (classical) Dark Energy as well as field-driven inflationary early-time phases. The final main-part section characterizes the set of solutions to the SCE in which the universe is exponentially expanding. For these symmetric space-times there is a natu- ral choice of quantum state, the so-called Bunch-Davies state. Exponential phases are expected in our universe’s history both at early and at late time, but the ratio of the corresponding exponential rates is believed to be quite large. We prove that the set of exponential solutions to the SCE is large enough such that the aforementioned ratio can be realized. We conclude with a short discussion and further perspectives.","In dieser Arbeit untersuchen wir die semiklassische Einstein Gleichung (SCE) als Modell für die Wechselwirkung zwischen einem skalaren Quantenfeld und der Krümmung einer zugrundeliegenden Raumzeit. Dabei interessieren wir uns speziell für kosmologische Lösungen, um den Einfluss eines Quantenfeldes auf unser Universum zu verstehen. Der Hauptteil dieses Textes gliedert sich in fünf Teile. Vor diesem Hauptteil geben wir eine ausführliche Einführung in die Quantenfeldtheorie auf gekrümmten Raumzeiten sowie in die Kosmologie. Danach führen wir die kosmologische SCE ein und interpretieren diese als unendlich-dimensionales dynamisches System für die Freiheitsgrade sowohl der Metrik als auch des Feldes. Im ersten Hauptteil definieren wir die sogenannten Minkowski-artigen Vakua. Diese Zustände erlauben es, die SCE als wohlgestelltes Anfangswertproblem zu betrachten und den Effekt eines Quantenfeldes auf die Raumzeit im Hinblick auf einige physikalische Eigenschaften numerisch zu untersuchen. Bemerkenswert ist hierbei, dass sich das Quantenfeld in ähnlicher Weise wie Dunkle Energie auf die Spät-Zeit-Entwicklung eines Universums auszuwirken scheint. Ausgehend von den Minkowski-artigen Zuständen, vergrößern wir im zweiten Teil die Menge der gefundenen Lösungen der SCE. Allgemeiner entwickeln wir einen systematischen Zugang neue Lösungen aus alten zu bekommen, indem wir dem System gewisse effektive Freiheitsgrade hinzufügen. Diese sind einfach Funktionen der Zeit und wir zeigen, dass diese von einer Differentialgleichung dritter Ordnung beschrieben werden. Des Weiteren beweisen wir, dass es unter bestimmten Voraussetzungen an die Anfangswerte der effektiven Freiheitsgrade tatsächlich einen Zustand mit der beschriebenen Rückreaktion gibt. Der dritte Teil behandelt den Dunkle-Energie-Effekt eines Quantenfeldes weiterführend. Wir zeigen, dass ein bestimmter Teil der SCE, welcher über einen großen Teil des Parameterraumes sehr dominant ist, generischerweise eine durch Dunkle Energie dominierte Spät-Zeit-Entwicklung nach sich zieht. Aber auch in Parameterbereichen, in denen vorgenannter Teil weniger dominant ist, können wir zeigen, dass sich durch Dunkle Energie dominierte Spät-Zeit-Entwicklungen unter bestimmten Voraussetzungen in der Dynamik der SCE attraktiv gegenüber Störungen verhalten. Im vierten Teil untersuchen wir die Rückreaktion eines klassischen Skalarfeldes. Hierbei ist ein zentrales Ziel die Entwicklung eines systematischen Zugangs zu diesgearteten Kegelschnittgleichungen. Dahingehend bemerken wir, dass auch in der Rückreaktion eines Quantenfeldes im Zusammenhang mit nicht-verschwindenden Einpunktfunktionen solche Gleichungen zu behandeln sind. Wir finden schließlich einige interessante Eigenschaften der Lösungen zu diesem Modell. Speziell studieren wir sogenannte Small-Bang- Lösungen, die gegenseitige Beeinflussung eines skalaren Feldes/einer Einpunktfunktion und (klassischer) Dunkler Energie sowie inflationäre Früh-Zeit-Phasen, welche durch das klassische Feld zustande kommen. Der letzte Hauptteil ist der Menge der exponentiell expandierenden Lösungen der SCE gewidmet. Auf den zugrundeliegenden Raumzeiten gibt es ausgezeichnete, natürliche Vakuumzustände, sogenannte Bunch-Davies-Vakua. Man geht davon aus, dass exponentielle Phasen sowohl in der Früh-Zeit als auch in der Spät-Zeit des Universums dieses gut approximieren. Allerdings wird auch angenommen, dass die exponentiellen Raten von sehr verschiedener Größenordnung sind. Wir zeigen hier, dass die Menge exponentieller Lösungen ausreichend flexibel ist, um diese sehr verschiedenen Raten zu reproduzieren. Wir schließen den Text mit einer Diskussion der Ergebnisse sowie mit einigen Forschungsperspektiven für die Zukunft ab."],"dc:identifier.uri":["https://depositonce.tu-berlin.de/handle/11303/25150","https://doi.org/10.14279/depositonce-23971"],"dc:language.iso":["en"],"dc:rights.uri":["https://creativecommons.org/licenses/by/4.0/"],"dc:title":["New insights into cosmological solutions of the semiclassical Einstein equation"],"dc:type":["Doctoral Thesis"]},"updated_at":"2026-07-27T21:28:47Z"}