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Non-Perturbative Gravity at Different Length Scales

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Non-Perturbative Gravity at Different Length Scales Non-Perturbative Gravity at different Length Scales Sarah Folkerts M¨unchen2013 Non-Perturbative Gravity at different Length Scales Sarah Folkerts Dissertation an der Fakult¨atf¨urPhysik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Sarah Folkerts aus Saarbr¨ucken M¨unchen, den 20.09.2013 Erstgutachter: Prof. Dr. Georgi Dvali Zweitgutachter: Prof. Dr. Stefan Hofmann Tag der m¨undlichen Pr¨ufung:18.12.2013 Abstract In this thesis, we investigate different aspects of gravity as an effective field theory. Building on the arguments of self-completeness of Einstein gravity, we argue that any sensible theory, which does not propagate negative-norm states and reduces to General Relativity in the low energy limit is self-complete. Due to black hole formation in high energy scattering experiments, distances smaller than the Planck scale are shielded from any accessibility. Degrees of freedom with masses larger than the Planck mass are mapped to large classical black holes which are described by the already existing infrared theory. Since high energy (UV) modifications of gravity which are ghost-free can only produce stronger gravitational interactions than Einstein gravity, the black hole shielding is even more efficient in such theories. In this light, we argue that conventional attempts of a Wilsonian UV completion are severely constrained. Furthermore, we investigate the quantum picture for black holes which emerges in the low energy description put forward by Dvali and Gomez in which black holes are described as Bose-Einstein condensates of many weakly coupled gravitons. Specifically, we investigate a non-relativistic toy model which mimics certain aspects of the graviton condensate picture. This toy model describes the collapse of a condensate of attractive bosons which emits particles due to incoherent scattering. We show that it is possible that the evolution of the condensate follows the critical point which is accompanied by the appearance of a light mode. Another aspect of gravitational interactions concerns the question whether quantum gravity breaks global symmetries. Arguments relying on the no hair theorem and wormhole solutions suggest that global symmetries can be violated. In this thesis, we parametrize such effects in terms of an effective field theory description of three-form fields. We investigate the possible implications for the axion solution of the strong CP problem. Since the axion is the (pseudo-) Goldstone boson of a broken U(1) global symmetry, quantum gravitational global symmetry violations could reinstate the CP problem even in the presence of the axion. We show that in the presence of massless neutrinos possible conflicts with the axion solution can be resolved. Demanding a viable axion solution of the strong CP problem, we derive new bounds on neutrino masses. In addition, we investigate the QCD vacuum energy screening mechanism for light quarks. It is well-known that the θ-dependence of the QCD vacuum vanishes linearly with the lightest quark mass. By an analogy with Schwinger pair creation in a strong electric field, v Abstract vi we consider vacuum screening by η0 bubble nucleation. We find that using the standard instanton approximation for the η0 potential, the linear dependence is not recovered. We take this as an indication for the non-analyticity of the QCD vacuum energy proposed by Witten. In the last part of this thesis, we are concerned with gravitational effects on cosmological scales. The recent Planck data indicate that one of the best motivated dark matter candidates, the axion, is in conflict with bounds on isocurvature perturbations. We show that the isocurvature fluctuations can be efficiently suppressed when introducing a non-minimal kinetic coupling for the axion field during inflation. Thus, the axion can be a viable dark matter candidate for a large range of parameters. We show that the same coupling allows for the Standard Model Higgs to drive inflation and the dark matter density to be produced by the axion. Gravitational effects on large scales would also be sensitive to a possible mass for the graviton. However, such a modification has been known to be plagued by inconsistencies. In light of the recent proposal of a ghost-free theory of massive gravity by de Rham, Gabadadze and Tolley, we investigate the cubic order interactions of this theory in terms of helicities of a massive spin-2 particle. We find that it is not possible to truncate the action at cubic order without introducing higher derivative terms strongly coupled at scale Λ5. Additionally, we consider possible cubic interaction terms for a massive spin-2 particle on a Minkowski background. We derive the unique interaction terms which are free of higher derivatives. Zusammenfassung In dieser Dissertation untersuchen wir verschiedene Aspekte der als effektive Feldthe- orie aufgefassten Quantengravitation. Basierend auf Argumenten der Selbstkomplet- tierung von Einstein-Gravitation zeigen wir, dass jede Theorie, die keine propagierenden Zust¨andemit negativer Norm aufweist und die sich zudem auf Einstein-Gravitation im Niederenergie-Limes reduziert, selbstkomplett ist. Durch die Formierung von schwarzen L¨ochern in Streuexperimenten bei hohen Energien, sind Distanzen, die kleiner als die Planck Skala sind, von jedwedem Zugriff abgeschirmt. Freiheitsgrade mit einer Masse, die gr¨oßerals die Planck-Masse ist, werden hierbei auf klassische schwarze L¨ocher abge- bildet, die wiederum durch die schon existierende Infrarot-Theorie beschrieben sind. In Modifikationen von Geist-freier Gravitation bei hohen Energien ist die Abschirmung durch schwarze L¨ocher sogar noch effizienter, da solche, mit Einstein-Gravitation ver- glichen, st¨arkere gravitative Wechselwirkungen erzeugen. In Angesicht dessen sind kon- ventionelle Versuche der UV Komplettierung im Wilsonschen Sinne ¨außersteingeschr¨ankt. Weiterhin betrachten wir das von Dvali und Gomez vorgeschlagene Quantenbild schwarzer L¨ocher gem¨aßdem schwarze L¨ocher als ein Bose-Einstein Kondensat von vielen schwach gekoppelten Gravitonen aufgefasst werden k¨onnen. Im Speziellen untersuchen wir ein nicht-relativistisches Analogon, welches gewisse Aspekte dieses Graviton- Kondensat- Bildes widerspiegelt. In diesem Beispielsystem kollabiert ein Kondensat attraktiver Bosonen unter durch inkoh¨arente Streuprozesse verursachter Aussendung von Teilchen. Wir zeigen, dass sich das Kondensat w¨ahrendseiner Zeitentwicklung am kritischen Punkt aufhalten kann mit dem hiermit verbundenen Auftreten einer leichten Mode. Ein weiterer Aspekt der gravitativen Wechselwirkung betrifft die Frage, in wie weit Quantengravitation globale Symmetrien bricht. Betrachtungen, die auf dem No-Hair Theorem wie auch Wurmloch-L¨osungenberuhen, legen nahe, dass globale Symmetrien verletzt werden k¨onnen.In der vorliegenden Arbeit parametrisieren wir solche Effekte in einer effektiven Feldtheorie von Dreiform-Feldern und untersuchen die m¨oglichen Im- plikationen f¨urdie Axionl¨osungdes starken CP-Problems. Da das Axion ein (Pseudo) Goldstone-Boson einer gebrochenen, globalen U(1) Symmetrie ist, k¨onnten solche, auf der Quantengravitation beruhenden, Symmetriebrechungen das CP Problem wieder einf¨uhren,trotz der Anwesenheit eines Axions. Wir zeigen, dass in der Gegenwart eines massenlosen Neutrinos die m¨oglichen Konflikte mit der Axionl¨osungaufgel¨ostwerden vii Zusammenfassung viii k¨onnen. Aus der Voraussetzung, dass eine valide Axionl¨osungdes CP-Problems ex- istiert, leiten wir neue Grenzen f¨urdie Neutrinomasse her. Weiterhin untersuchen wir den Abschirmungsmechanismus, der durch die Vakuumenergie f¨urleichte Quarks in der QCD verursacht wird. Es ist bekannt, dass die θ-Abh¨angigkeit des QCD-Vakuums mit der leichtesten Quarkmasse linear verschwindet. Analog zur Schwinger-Paarerzeugung in einem starken elektrischen Feld betrachten wir die Vakuumsabschirmung durch die Blasenbildung von η0-Vakua. Unter Verwendung des Potentials f¨ur η0, das durch Standard- Instanton-Rechnungen gegeben ist, k¨onnenwir die lineare Abh¨angigkeit nicht repro- duzieren. Wir betrachten dies als Indikation f¨urdie von Witten vorgeschlagene Nicht- Analytizit¨atder QCD-Vakuumenergie. Im letzten Teil der Arbeit betrachten wir Gravitationseffekte auf kosmologischen Skalen. Neuste Daten des Planck Satelliten weisen darauf hin, dass einer der vielversprechensten Kandidaten f¨urdie Dunkle Materie, das Axion, in Konflikt ist mit durch adiabatischen Fluktuationen vorgegebenen Grenzen. Wir zeigen, dass diese Fluktuationen effizient unterdr¨uckt werden k¨onnen, wenn f¨urdas Axionenfeld w¨ahrendder Inflation ein nicht- minimaler kinetischer Kopplungsterm eingef¨uhrtwird. Auf Grundlage dessen kann das Axion als m¨oglicher Kandidat f¨urdunkle Materie erhalten bleiben. Weiterhin zeigen wir, dass ein solcher kinetischer Term dem Higgs-Teilchen des Standardmodells erlaubt die Inflation anzutreiben und dass die Dichte der dunklen Materie tats¨achlich vom Axion erzeugt werden kann. Gravitationseffekte auf großen Skalen sind zudem potentiell von einer m¨oglich endlichen Masse des Gravitons abh¨angig.Jedoch ist bekannt, dass solche Modifikationen der Grav- itation zu Inkonsistenzen f¨uhrenk¨onnen.Unter Betrachtung des k¨urzlich von de Rham, Gabadadze and Tolley vorgeschlagenen Szenarios einer Geist-freien Theorie der massiven Gravitation untersuchen wir die Wechselwirkungen kubischer Ordnung in dieser Theo- rie, ausgedr¨uckt in den Helizit¨ateneines massiven Spin-2 Teilchens. Wir finden, dass es nicht m¨oglich ist, die entsprechende Wirkung in kubischer Ordnung zu trunkieren, ohne
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