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Relativistic and Nonlinear Lffects in Large Scale Structures

Allahyari Sadeghabadi, Alireza | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51615 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Mansouri, Reza; Taghizadeh Firouzjaee, Javad
  7. Abstract:
  8. Although general relativity is the underlying assumption in modern cosmology, there are still many simplifying assumptions neglecting higher order general relativistic effects. Given the precision cosmology and future surveys and the amount of data on large scales, higher order relativistic effects are to be taken into account. We will consider two categories of relativistic effects on large scale structures. First, the inhomogeneities between the source and the observer may lead to observable effects neglected so far. As future surveys will probe the universe on large scales, these effects have been the focus of recent studies. The observables being defined first, are cosmic rulers and galaxy number counts. The key point is that observables should be gauge invariant. To check their gauge invariance, we study the effects of the gradient perturbations on the observables. The gradient perturbations can be produced by gauge transformations. We show that the gradient perturbations do not contribute to the observables. The non-linear coupling of the gradient perturbations to other perturbations could have non-vanishing effects. Galaxies trace dark matter perturbations. This is expressed by a bias factor. The non-linear coupling of perturbations change this factor. We explicitly show that coupling to the gradient perturbations do not modulate the bias factor. Vector and tensor perturbations are inevitably produced at higher orders. They induce inhomogeneities on the observables. Their imprints on observables are the subject of the ongoing studies. We the second order vector and tensor perturbations and compute their effects on the galaxy bispectrum. First, we derive the second order kernel that relates the first order perturbations to the second order perturbations. Then, we compute the bispectrum produced by tensor and vector perturbations. The equilateral bispectrum vanishes for the vectors. The squeezed bispectrum is more enhanced for both cases. Computing the relative difference between the Newtonian and relativistic bispectrum, we show that second order vectors and tensors can lead to percent level corrections. The second category of relativistic effects arise due to the difference between Einstein equations and the Newton’s equations. One difference is that horizons occur in relativity. We study the formation of the black hole horizon in a spherical top hat model in a flat background. This model describes a collapsing over-dense region in a radiation dominated universe. Our goal is to improve the accuracy of the existing bounds on the threshold value of its density for the formation of primordial black holes. The threshold value is to be calculated at horizon entry. Our model has two parameters its initial Hubble’s expansion and over-density. We set the initial condition at the horizon entry. The improvement is that in our model the initial conditions for the initial over-density are provided from the perturbation theory solution, this leads to a constraint between the initial density and Hubble’s expansion. In this way the threshold value that we obtain is higher compared to previous studies. In modern cosmology we use simplifying assumptions. One of the simplifying assumptions is that we can use perturbation theory if the gravity is weak enough. One may think that when the gravity is weak the Newton’s gravity applies. However, Newton’s equations and Einstein equations are different. The key difference is that horizons occur in relativity. It is important to study if the black hole horizons arise in perturbative solutions. We study non-linear solutions to specific models where we show that the horizons arise in higher order perturbative solutions
  9. Keywords:
  10. Primordial Black Holes ; Perturbation Theory ; Relativistic Effects ; Universe Large-Scale Structure ; Galactic Number

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