New insights into cosmological solutions of the semiclassical Einstein equation

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.

Author dc:creator

• Rothe, Nicolai

Advisor dc:contributor.advisor

• Gottschalk, Hanno

Licence dc:rights.uri

• https://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Identifier URI

https://doi.org/10.14279/depositonce-23971

OAI identifier oai:identifier

oai:depositonce.tu-berlin.de:11303/25150