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Register a new userApplications of Cosmological Perturbation Theory
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Added by
Adam J. Christopherson
Publication date
2011
fields
Physics
and research's language is
English
Authors
Adam J. Christopherson
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Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested standard model of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expansion of the universe, the same is not true at higher orders. This will have important implications on future measurements of the polarisation of the Cosmic Microwave Background, and could give rise to the generation of a primordial seed magnetic field. Having derived this qualitative result, we then estimate the scale dependence and magnitude of the vorticity power spectrum, finding, for simple power law inputs a small, blue spectrum. The final part of this thesis concerns higher order perturbation theory, deriving, for the first time, the metric tensor, gauge transformation rules and governing equations for fully general third order perturbations. We close with a discussion of natural extensions to this work and other possible ideas for off-shooting projects in this continually growing field.
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We compare and contrast two different metric based formulations of non- linear cosmological perturbation theory: the MW2009 approach in [K. A. Malik and D. Wands, Phys. Rept. 475 (2009), 1.] following Bardeen and the recent approach of the paper KN2010 [K. Nakamura, Advances in Astronomy 2010 (2010), 576273]. We present each formulation separately. In the MW2009 approach, one considers the gauge transformations of perturbative quantities, choosing a gauge by requiring that certain quantities vanish, rendering all other variables gauge invariant. In the KN2010 formalism, one decomposes the metric tensor into a gauge variant and gauge invariant part from the outset. We compare the two approaches in both the longitudinal and uniform curvature gauges. In the longitudinal gauge, we find that Nakamuras gauge invariant variables correspond exactly to those in the longitudinal gauge (i.e., for scalar perturbations, to the Bardeen potentials), and in the uniform curvature gauge we obtain the usual relationship between gauge invariant variables in the flat and longitudinal gauge. Thus, we show that these two approaches are equivalent.
We consider the growth of primordial dark matter halos seeded by three crossed initial sine waves of various amplitudes. Using a Lagrangian treatment of cosmological gravitational dynamics, we examine the convergence properties of a high-order perturbative expansion in the vicinity of shell-crossing, by comparing the analytical results with state-of-the-art high resolution Vlasov-Poisson simulations. Based on a quantitative exploration of parameter space, we study explicitly for the first time the convergence speed of the perturbative series, and find, in agreement with intuition, that it slows down when going from quasi one-dimensional initial conditions (one sine wave dominating) to quasi triaxial symmetry (three sine waves with same amplitude). In most cases, the system structure at collapse time is, as expected, very similar to what is obtained with simple one-dimensional dynamics, except in the quasi-triaxial regime, where the phase-space sheet presents a velocity spike. In all cases, the perturbative series exhibits a generic convergence behavior as fast as an exponential of a power-law of the order of the expansion, allowing one to numerically extrapolate it to infinite order. The results of such an extrapolation agree remarkably well with the simulations, even at shell-crossing.
Two of the most rapidly growing observables in cosmology and astrophysics are gravitational waves (GW) and the neutral hydrogen (HI) distribution. In this work, we investigate the cross-correlation between resolved gravitational wave detections and HI signal from intensity mapping (IM) experiments. By using a tomographic approach with angular power spectra, including all projection effects, we explore possible applications of the combination of the Einstein Telescope and the SKAO intensity mapping surveys. We focus on three main topics: textit{(i)} statistical inference of the observed redshift distribution of GWs; textit{(ii)} constraints on dynamical dark energy models as an example of cosmological studies; textit{(iii)} determination of the nature of the progenitors of merging binary black holes, distinguishing between primordial and astrophysical origin. Our results show that: textit{(i)} the GW redshift distribution can be calibrated with good accuracy at low redshifts, without any assumptions on cosmology or astrophysics, potentially providing a way to probe astrophysical and cosmological models; textit{(ii)} the constrains on the dynamical dark energy parameters are competitive with IM-only experiments, in a complementary way and potentially with less systematics; textit{(iii)} it will be possible to detect a relatively small abundance of primordial black holes within the gravitational waves from resolved mergers. Our results extend towards $mathrm{GW times IM}$ the promising field of multi-tracing cosmology and astrophysics, which has the major advantage of allowing scientific investigations in ways that would not be possible by looking at single observables separately.
Cosmological tensions can arise within $Lambda$CDM scenario amongst different observational windows, which may indicate new physics beyond the standard paradigm if confirmed by measurements. In this article, we report how to alleviate both the $H_0$ and $sigma_8$ tensions simultaneously within torsional gravity from the perspective of effective field theory (EFT). Following these observations, we construct concrete models of Lagrangians of torsional gravity. Specifically, we consider the parametrization $f(T)=-T-2Lambda/M_P^2+alpha T^beta$, where two out of the three parameters are independent. This model can efficiently fit observations solving the two tensions. To our knowledge, this is the first time where a modified gravity theory can alleviate both $H_0$ and $sigma_8$ tensions simultaneously, hence, offering an additional argument in favor of gravitational modification.
The tensor-vector-scalar (TeVeS) model is considered a viable theory of gravity. It produces the Milgroms modified Newtonian dynamics in the nonrelativistic weak field limit and is free from ghosts. This model has been tested against various cosmological observations. Here we investigate whether new observations such as the galaxy velocity power spectrum measured by 6dF and the kinetic Sunyaev Zeldovich effect power spectrum measured by ACT/SPT can put further constraints on the TeVeS model. Furthermore, we perform the test of TeVeS cosmology with a sterile neutrino by confronting to Planck data, and find that it is ruled out by cosmic microwave background measurements from the Planck mission.
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