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Theoretical Studies of Cosmic Acceleration University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2016 Theoretical Studies of Cosmic Acceleration James Stokes University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Physics Commons Recommended Citation Stokes, James, "Theoretical Studies of Cosmic Acceleration" (2016). Publicly Accessible Penn Dissertations. 2040. https://repository.upenn.edu/edissertations/2040 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2040 For more information, please contact [email protected]. Theoretical Studies of Cosmic Acceleration Abstract In this thesis we describe theoretical approaches to the problem of cosmic acceleration in the early and late universe. The first approach we consider relies upon the modification of Einstein gravity by the inclusion of mass terms as well as couplings to higher-derivative scalar fields possessing generalized internal shift symmetries - the Galileons. The second half of the thesis is concerned with the quantum- mechanical consistency of a theory of the early universe known as the pseudo-conformal mechanism which, in contrast to inflation, eliesr not on the effects of gravity but on conformal field theory (CFT) dynamics. It is possible to couple Dirac-Born-Infeld (DBI) scalars possessing generalized Galilean internal shift symmetries (Galileons) to nonlinear massive gravity in four dimensions, in such a manner that the interactions maintain the Galilean symmetry. Such a construction is of interest because it is not possible to couple such fields ot massless General Relativity in the same way. Using tetrad techniques we show that this massive gravity-Galileon theory possesses a primary constraint necessary to ensure propagation with the correct number of degrees of freedom. We study the background cosmology of this theory around cosmologically relevant spacetimes and find that, as in pure massive gravity, spatially flat solutions do not exist. Spatially open solutions do exist - consisting of a branch of self-accelerating solutions that are identical to those of pure massive gravity, and a new second branch of solutions which do not appear without the inclusion of Galileons. We study the propagating degrees of freedom of the massive gravity-Galileon theory around the self-accelerating solutions and identify the conditions necessary for the theory to remain free of ghost-like instabilities. We show that on the self-accelerating branch the kinetic terms for the vector and scalar modes of the massive graviton vanish, as in the case of pure massive gravity. We conclude our exploration of massive gravity by considering the possibility of variable-mass massive gravity, where the fixed graviton mass is replaced by the expectation value of a rolling scalar field. eW ask whether self-inflation can be driven by the self-accelerated branch of this theory, and we find that, while such solutions can exist for a short period, they cannot be sustained for a cosmologically useful time. Furthermore, we demonstrate that there generally exist future curvature singularities of the ``big brake" form in cosmological solutions to these theories. In the second half of the thesis we construct the gravitational dual of the pseudo-conformal universe, a proposed alternative to inflation in which a CFT in nearly flat space develops a time dependent vacuum expectation value. Constructing this dual amounts to finding five-dimensional domain-wall spacetimes with anti-de Sitter asymptotics, for which the wall has the symmetries of four-dimensional de Sitter space. This holographically realizes the characteristic symmetry breaking pattern O(2,4) to O(1,4) of the pseudo- conformal universe. We present an explicit example with a massless scalar field, using holographic renormalization to obtain general expressions for the renormalized scalar and stress-tensor one-point functions. We discuss the relationship between these solutions and those of four-dimensional holographic CFTs with boundaries, which break O(2,4) to O(2,3). Finally, we undertake a systematic study of one and two point functions of CFTs on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to renormalized position space correlators. Several applications are presented, including the holographic boundary CFTs as well as spacelike boundary CFTs, which provide realizations of the pseudo-conformal universe. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Physics & Astronomy First Advisor Mark Trodden Subject Categories Physics This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/2040 THEORETICAL STUDIES OF COSMIC ACCELERATION James Stokes A DISSERTATION in Physics and Astronomy Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2016 Supervisor of Dissertation Mark Trodden Professor (Department of Physics and Astronomy) Graduate Group Chairperson Marija Drndic, Professor (Department of Physics and Astronomy) Dissertation Committee: Randall Kamien, Professor (Department of Physics and Astronomy) Justin Khoury, Professor (Department of Physics and Astronomy) Elliot Lipeles, Professor (Department of Physics and Astronomy) Burt Ovrut, Professor (Department of Physics and Astronomy) THEORETICAL STUDIES OF COSMIC ACCELERATION c COPYRIGHT 2016 James Stokes This work is licensed under the Creative Commons Attribution NonCommercial-ShareAlike 3.0 License To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ Acknowledgements First and foremost, I'd like to thank Mark Trodden his excellent supervision and for con- stantly encouraging me to pursue my interests. During my PhD I have had the good fortune to collaborate with and learn from many out- standing physicists: Melinda Andrews, Garret Goon, Steven Gubser, Kurt Hinterbichler, Austin Joyce, Justin Khoury, Burt Ovrut, Alexander Polyakov, Zain Saleem, Sam Schoen- holz, Bogdan Stoica, and Mark Trodden. I am indebted to Randall Kamien and Tom Lubensky for discussions on field theory and condensed matter physics. I would like to thank all of the friends I have made during my PhD, especially my office mates Hernan Piragua and my long-term collaborator Zain Saleem. I have always enjoyed our discussions and debates from which I have learnt a great deal of physics. I thank my parents and sister for their unceasing love and support, for which I am deeply grateful. iii ABSTRACT THEORETICAL STUDIES OF COSMIC ACCELERATION James Stokes Mark Trodden In this thesis we describe theoretical approaches to the problem of cosmic acceleration in the early and late universe. The first approach we consider relies upon the modification of Eintein gravity by the inclusion of mass terms as well as couplings to higher-derivative scalar fields possessing generalized internal shift symmetries | the Galileons. The second half of the thesis is concerned with the quantum-mechanical consistency of a theory of the early universe known as the pseudo-conformal mechanism which, in contrast to inflation, relies not on the effects of gravity but on conformal field theory (CFT) dynamics. It is possible to couple Dirac-Born-Infeld (DBI) scalars possessing generalized Galilean internal shift symmetries (Galileons) to nonlinear massive gravity in four dimensions, in such a manner that the interactions maintain the Galilean symmetry. Such a construction is of interest because it is not possible to couple such fields to massless General Relativity in the same way. Using tetrad techniques we show that this massive gravity-Galileon theory possesses a primary constraint necessary to ensure propagation with the correct number of degrees of freedom. We study the background cosmology of this theory around cosmologically relevant space- times and find that, as in pure massive gravity, spatially flat solutions do not exist. Spatially open solutions do exist | consisting of a branch of self-accelerating solutions that are iden- tical to those of pure massive gravity, and a new second branch of solutions which do not appear without the inclusion of Galileons. We study the propagating degrees of freedom of the massive gravity-Galileon theory around the self-accelerating solutions and identify the conditions necessary for the theory to remain free of ghost-like instabilities. We show iv that on the self-accelerating branch the kinetic terms for the vector and scalar modes of the massive graviton vanish, as in the case of pure massive gravity. We conclude our exploration of massive gravity by considering the possibility of variable- mass massive gravity, where the fixed graviton mass is replaced by the expectation value of a rolling scalar field. We ask whether self-inflation can be driven by the self-accelerated branch of this theory, and we find that, while such solutions can exist for a short period, they cannot be sustained for a cosmologically useful time. Furthermore, we demonstrate that there generally exist future curvature singularities of the \big brake" form in cosmological solutions to these theories. In the second half of the thesis we construct the gravitational dual of the pseudo-conformal universe, a proposed alternative to inflation in which a CFT in nearly flat space develops a time dependent vacuum expectation value. Constructing
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