Logo Logo
Help
Contact
Switch language to German
Gravity in our cosmos. Einstein and beyond
Gravity in our cosmos. Einstein and beyond
Part I: While the standard cosmological model ΛCDM is the simplest model we have con- sistent with all current observations, including the accelerated expansion of the Universe, it suffers from a number of theoretical and naturalness problems. This prompts us to look for modified gravity (MG) models that reduce to General Relativity (GR) in the Solar System (SS) to within the very narrow leeway permitted by current bounds, while devi- ating significantly from GR on cosmological scales so as to self-accelerate naturally. This is often achieved by adopting screening mechanisms. We shall first review these concepts, focusing on Scalar-Tensor (ST) theories. We will show that a model of recently revived interest, disformal ST theory, supposedly with its own novel screening mechanism is ac- tually so tightly constrained by SS constraints at post-Newtonian level, in particular via its preferred frame effects singling out the CMB. This renders the model uninteresting on cosmological scales and highlights the importance of taking the right non-relativistic limit when matching with observations. The quasi-static approximation (QSA) is often imposed when examining the implica- tions of screening mechanisms in various MG models. This prohibits the propagation of scalar waves from astrophysical and cosmological sources. We investigate the claim that relaxing the QSA would lead to significant disruptions to the screening in the SS, thus tightening the parameter space for viable MG models. We solve the system (linearised in the wave perturbation) analytically, which gives us a clearer understanding of the mech- anisms at work. The geometry of the incoming wave (spherical or planar) is found to significantly affect the severity of the disruption, such that for the more physically rele- vant planar waves, disruption while theoretically possible, is far milder than previously thought. The amplification is purely of geometrical origin and from energy-conservation, thus holds independent of our linearisation. We also elucidate the physical meaning of the PPN framework and consequently the Eddington light bending parameter. Since this is science, only observable disruptions are relevant and we discuss the conditions for this to be so. Part II: Large Scale Structure (LSS) in the nonlinear regime can tell us a lot about the early Universe. In order to track the evolution of primordial fluctuations into the LSS observed today, we desire a framework that is fully nonlinear and fully relativistic (fNLfR) in which quantities are directly relatable to physical observables. Most physically- relevant setups involve a long wavelength perturbation modulating the dynamics of small scale physics, prompting the generalisation of the Fermi Normal Coordinates into the Conformal Fermi Coordinates (CFC). A long-wavelength spherically-symmetric adiabatic perturbation on an FLRW spacetime is locally equivalent to a different FLRW solution, a result that holds fNLfR: the separate universe picture. We investigate the case where the long wavelength perturbation is anisotropic, i.e. large-scale tidal fields, by deriving the set of evolutionary equations for the long mode fNLfR. We do however have to impose a natural approximation, dropping certain higher-derivative terms to close the system. The result is a very simple framework (in terms of mathematical complexity and physical relatability) for computing the fully relativistic growth of structure to second order in perturbations. In the process, we elucidate the physical meaning of these large scale tidal fields, to be distinguished from a Bianchi I spacetime.
gravity, cosmology
Ip, Hiu Yan
2018
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Ip, Hiu Yan (2018): Gravity in our cosmos: Einstein and beyond. Dissertation, LMU München: Faculty of Physics
[img]
Preview
PDF
Ip_Hiu_Yan.pdf

3MB

Abstract

Part I: While the standard cosmological model ΛCDM is the simplest model we have con- sistent with all current observations, including the accelerated expansion of the Universe, it suffers from a number of theoretical and naturalness problems. This prompts us to look for modified gravity (MG) models that reduce to General Relativity (GR) in the Solar System (SS) to within the very narrow leeway permitted by current bounds, while devi- ating significantly from GR on cosmological scales so as to self-accelerate naturally. This is often achieved by adopting screening mechanisms. We shall first review these concepts, focusing on Scalar-Tensor (ST) theories. We will show that a model of recently revived interest, disformal ST theory, supposedly with its own novel screening mechanism is ac- tually so tightly constrained by SS constraints at post-Newtonian level, in particular via its preferred frame effects singling out the CMB. This renders the model uninteresting on cosmological scales and highlights the importance of taking the right non-relativistic limit when matching with observations. The quasi-static approximation (QSA) is often imposed when examining the implica- tions of screening mechanisms in various MG models. This prohibits the propagation of scalar waves from astrophysical and cosmological sources. We investigate the claim that relaxing the QSA would lead to significant disruptions to the screening in the SS, thus tightening the parameter space for viable MG models. We solve the system (linearised in the wave perturbation) analytically, which gives us a clearer understanding of the mech- anisms at work. The geometry of the incoming wave (spherical or planar) is found to significantly affect the severity of the disruption, such that for the more physically rele- vant planar waves, disruption while theoretically possible, is far milder than previously thought. The amplification is purely of geometrical origin and from energy-conservation, thus holds independent of our linearisation. We also elucidate the physical meaning of the PPN framework and consequently the Eddington light bending parameter. Since this is science, only observable disruptions are relevant and we discuss the conditions for this to be so. Part II: Large Scale Structure (LSS) in the nonlinear regime can tell us a lot about the early Universe. In order to track the evolution of primordial fluctuations into the LSS observed today, we desire a framework that is fully nonlinear and fully relativistic (fNLfR) in which quantities are directly relatable to physical observables. Most physically- relevant setups involve a long wavelength perturbation modulating the dynamics of small scale physics, prompting the generalisation of the Fermi Normal Coordinates into the Conformal Fermi Coordinates (CFC). A long-wavelength spherically-symmetric adiabatic perturbation on an FLRW spacetime is locally equivalent to a different FLRW solution, a result that holds fNLfR: the separate universe picture. We investigate the case where the long wavelength perturbation is anisotropic, i.e. large-scale tidal fields, by deriving the set of evolutionary equations for the long mode fNLfR. We do however have to impose a natural approximation, dropping certain higher-derivative terms to close the system. The result is a very simple framework (in terms of mathematical complexity and physical relatability) for computing the fully relativistic growth of structure to second order in perturbations. In the process, we elucidate the physical meaning of these large scale tidal fields, to be distinguished from a Bianchi I spacetime.