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Quantum and classical effects in brane-world large distance modified gravity. the DGP model with two branes
Quantum and classical effects in brane-world large distance modified gravity. the DGP model with two branes
This thesis addresses fundamental questions concerning gravitational phenomena at large distances by investigating in turn a model of modified gravity and a dark matter (DM) model. In the first part we study a generalization of the DGP model by embedding a second 3+1-dimensional (4D) brane, also endowed with a localized curvature term, in the 4+1-dimensional (5D) bulk. In this modified system we uncover phenomenologically interesting, new phenomena. We start with a classical analysis, working in both the full 5D description and the Kaluza-Klein language, and investigate the laws of gravity by calculating the gravitational potential energy between two static point sources localized on different branes. We discover a new length scale, which is equal to the geometric mean of the DGP cross-over scale (that marks the interpolation region between 4D and 5D gravity in the single-brane model) and the separation of the two branes in the extra dimension. For distances that are larger than this new length scale we recover the original DGP result, but for smaller distances the gravitational potential is weaker. Furthermore, a region emerges where a 4D observer measures a distance-independent force. We discuss a possible application of the present scenario for deriving rotation curves of low surface brightness galaxies. Moreover, since this setup allows for the existence of a sector of particle species that are interacting arbitrarily weakly with ``our'' sector, we explore the implications of this circumstance for black holes and the bound on the number of species. Next, we turn to the investigation of quantum phenomena in this system. In particular, we explore the Casimir effect perceived by the two branes in the presence of infrared (IR) transparency, meaning that the ultraviolet modes of the 5D graviton are suppressed on the branes, while the IR modes can penetrate them freely. First, we find that the DGP branes act as ``effective'' (momentum-dependent) boundary conditions for the gravitational field, so that a (gravitational) Casimir force between them indeed emerges. Second, we discover that the presence of an IR transparency region for the discrete modes modifies the standard Casimir force---as derived for ideal Dirichlet boundary conditions---in two competing ways: i) The exclusion of soft modes from the discrete spectrum leads to an increase of the Casimir force. ii) The non-ideal nature of the boundary conditions gives rise to a ``leakage'' of hard modes. As an effect of i) and ii), the Casimir force becomes weaker. Since the derivation of this result involves only the localized kinetic terms of a quantum field on parallel surfaces (with codimension one), the derived Casimir force is expected to be present in a variety of setups in arbitrary dimensions. In the second part of this thesis we investigate a DM model given by a complex scalar field with repulsive, quartic self-interactions and its effect on the structure of galactic halos. Since we consider DM particles with an ultra-light mass, they can undergo a phase transition to the superfluid phase in the inner high-density regions of a halo, thereby forming a homogeneous core. Taking into account that the gravitational Jeans instability sets an upper limit on the size of such a structure, we discuss the allowed parameter space for a scenario with kpc-size cores. We demonstrate that the parameters get severely constrained by a bound on the self-interaction cross section, obtained from observations of galaxy cluster collisions. Although this constraint is well-known, we show that in the case of ultra-light DM, which occupies a highly degenerate phase space, the bound tightens significantly due to the enhanced interaction rate. As a result, the considered scenario requires an even lighter DM species, and a thermalized core that has fragmented into a collection of smaller superfluid droplets.
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Warkentin, Max
2022
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Warkentin, Max (2022): Quantum and classical effects in brane-world large distance modified gravity: the DGP model with two branes. Dissertation, LMU München: Faculty of Physics
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Abstract

This thesis addresses fundamental questions concerning gravitational phenomena at large distances by investigating in turn a model of modified gravity and a dark matter (DM) model. In the first part we study a generalization of the DGP model by embedding a second 3+1-dimensional (4D) brane, also endowed with a localized curvature term, in the 4+1-dimensional (5D) bulk. In this modified system we uncover phenomenologically interesting, new phenomena. We start with a classical analysis, working in both the full 5D description and the Kaluza-Klein language, and investigate the laws of gravity by calculating the gravitational potential energy between two static point sources localized on different branes. We discover a new length scale, which is equal to the geometric mean of the DGP cross-over scale (that marks the interpolation region between 4D and 5D gravity in the single-brane model) and the separation of the two branes in the extra dimension. For distances that are larger than this new length scale we recover the original DGP result, but for smaller distances the gravitational potential is weaker. Furthermore, a region emerges where a 4D observer measures a distance-independent force. We discuss a possible application of the present scenario for deriving rotation curves of low surface brightness galaxies. Moreover, since this setup allows for the existence of a sector of particle species that are interacting arbitrarily weakly with ``our'' sector, we explore the implications of this circumstance for black holes and the bound on the number of species. Next, we turn to the investigation of quantum phenomena in this system. In particular, we explore the Casimir effect perceived by the two branes in the presence of infrared (IR) transparency, meaning that the ultraviolet modes of the 5D graviton are suppressed on the branes, while the IR modes can penetrate them freely. First, we find that the DGP branes act as ``effective'' (momentum-dependent) boundary conditions for the gravitational field, so that a (gravitational) Casimir force between them indeed emerges. Second, we discover that the presence of an IR transparency region for the discrete modes modifies the standard Casimir force---as derived for ideal Dirichlet boundary conditions---in two competing ways: i) The exclusion of soft modes from the discrete spectrum leads to an increase of the Casimir force. ii) The non-ideal nature of the boundary conditions gives rise to a ``leakage'' of hard modes. As an effect of i) and ii), the Casimir force becomes weaker. Since the derivation of this result involves only the localized kinetic terms of a quantum field on parallel surfaces (with codimension one), the derived Casimir force is expected to be present in a variety of setups in arbitrary dimensions. In the second part of this thesis we investigate a DM model given by a complex scalar field with repulsive, quartic self-interactions and its effect on the structure of galactic halos. Since we consider DM particles with an ultra-light mass, they can undergo a phase transition to the superfluid phase in the inner high-density regions of a halo, thereby forming a homogeneous core. Taking into account that the gravitational Jeans instability sets an upper limit on the size of such a structure, we discuss the allowed parameter space for a scenario with kpc-size cores. We demonstrate that the parameters get severely constrained by a bound on the self-interaction cross section, obtained from observations of galaxy cluster collisions. Although this constraint is well-known, we show that in the case of ultra-light DM, which occupies a highly degenerate phase space, the bound tightens significantly due to the enhanced interaction rate. As a result, the considered scenario requires an even lighter DM species, and a thermalized core that has fragmented into a collection of smaller superfluid droplets.