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ÖgeCosmological interacting models via energy-momentum squared gravity(Graduate School, 2024-06-24) Bulduk, Bildik ; Akarsu, Özgür ; Katırcı, Nihan Ayşe ; 509201113 ; Physics EngineeringIt was recently shown in the literature that gravity models that modify the material part of the standard Einstein-Hilbert action with $f(\mathcal{L}_{\rm m})$, $f(T)$, and $f(T_{\mu\nu}T^{\mu\nu})$ terms are equivalent to general relativity, encompassing non-minimal matter interactions between the material field and its accompanying partner, uniquely formed by the function $f$. In Energy-momentum squared gravity (EMSG), the ``squared" terminology arises from the self contraction of EMT $f(T_{\mu\nu}T^{\mu\nu})$ added to Einstein Hilbert action, nontrivial interaction kernels have been obtained and these models diverge from phenomenological interacting models (constructed in ad hoc way); this is due to the function $f$ and its variations with respect to both its argument and the metric, which intricately intertwine the interaction kernel $\mathcal{Q}(f,\delta f/\delta\mathbf{T^2},\delta, \mathbf{T^2}/\delta g^{\mu\nu})$. This makes the interaction kernel as Equation of State (EoS) parameter dependent as well. Bianchi identity $\nabla^{\mu}G_{\mu\nu}=0$ implies the conservation of total energy momentum tensor (EMT of the standard source plus its EMSF partner's), $\nabla^{\mu}(T_{\mu\nu}+T_{\mu\nu}^{{\rm EMSF} })=0$, leading cosmological models having an interaction between these sectors $\nabla^{\mu}T_{\mu\nu}=\mathcal{Q}_{\nu}$ and $\nabla^{\mu}T_{\mu\nu}^{\rm EMSF}=-\mathcal{Q}_{\nu}$ where $\mathcal{Q}_{\nu}\neq0$. In this thesis, different than the literature, still consistent with the Bianchi Identity, we focus on a scenario where the sector comprising conventional fluids (standard material fields) overall interacts minimally with the sector associated with their EMSF partners, i.e., satisfying $\nabla^{\mu}T_{\mu\nu}=0=\nabla^{\mu} T_{\mu\nu}^{{\rm EMSF}}$. Specifically, we consider the case characterized by $\mathcal{Q}=0$. Accordingly, we will consider a two-fluid model (perfect fluids described by constant EoS parameters) leading to the following conservation equations, $\nabla^{\mu}\left(T_{\mu\nu,1}+T_{\mu\nu,2}\right)=0$, and $\nabla^{\mu}\left(T_{\mu\nu,1}^{\rm EMSF}+T_{\mu\nu,2}^{\rm EMSF}\right)=0$ where we name the partner arisen from EMSG corrections as ``Energy Momentum Squared Field" (EMSF). We will explore this choice in detail within the framework of scale-independent EMSG which introduces a simple interaction kernel: a kernel linear in energy density. Then, we examine alternative cosmologies wherein the sector comprising conventional fluids minimally interacts with the sector associated with their EMSF partners, represented by $\nabla^{\mu}\left(T_{\mu\nu}^1+T_{\mu\nu}^{\rm 2}\right)=-\nabla^{\mu}\left(T_{\mu\nu}^{\rm EMSF1}+T_{\mu\nu}^{\rm EMSF2}\right)=\mathcal{Q}_{\nu}$ with $\mathcal{Q}_{\nu}=0$, diverging from the more commonly studied scenarios in literature where $\mathcal{Q}_{\nu}\neq0$. We also show that this model is reminiscent of the cosmological model with energy exchange studied by Barrow and Clifton in [Phys. Rev. D 73, 103520 (2006)] where the interaction term is taken ad hoc to be proportional to energy density, $\mathcal{Q}(H\rho)$. Unlike their model, the coefficients in our work are not arbitrary constants but are dependent on the species. Moreover, with an additional sector associated with the EMSF partners of the conventional fluids in the Friedmann equation, it is possible to negate one of the fluid's contributions in the Friedmann equation via its EMSF partner for a specific choice of $\alpha$ and two sources may superpose in their energy densities in the Friedmann equation, resulting in a joint (degenerate) scale factor dependence even if $w_1 \neq w_2$ reproducing interesting cosmologies such as power-law universes where the scale factor of the universe grows as a EoS parameter dependent power of time in the presence of a perfect fluid and vacuum energy density/stiff fluid, de Sitter universe in the presence of a perfect fluid and vacuum energy density. In this thesis, we show a simple mathematical description of the exchange of energy between two standard fluids from matter modified theories within GR choosing the simplest case study, yet some non-trivial functions/behaviors are favored by observations to alleviate tensions, non-linear interactions and non-linear energy density contributions from matter-type modified theories which may work for the change of direction of energy transfer in dark sector are prospects for future research.
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ÖgeNewtonian perturbation theory in cosmology: From inflation to large-scale structure(Graduate School, 2025-01-28) Kinsiz, Rumeysa ; Arapoğlu, A. Savaş ; 509211113 ; Physics EngineeringCosmology is the scientific study of the physical characteristics of the universe, its beginning, development and organization, based on observational outcomes and theoretical foundations. The Lambda-CDM model is currently one of the most popular theories in cosmology. This model of the universe outlines the behavior of the cosmos through the use of dark matter and energy. The cosmological constant (dark energy) is an energy density used to describe the acceleration of the expansion of the universe. From this model, it can be seen that cold dark matter and dark energy contribute greatly to the total mass-energy density of the universe. While dark matter affects the dynamics of galaxies and large-scale structures, dark energy drives the accelerated expansion of the universe. However, ongoing problems led to the formulation of "inflation theory." Inflation theory is a convincing paradigm that solves fundamental questions like the flatness problem and the horizon problem, which ask why the universe appears nearly flat and why distant parts show similar properties. Inflation hypothesis argues that the universe had a rapid expansion during its formative period, which mitigated initial anomalies and established the foundational conditions for the world we observe today. Numerous mathematical models have been introduced to advance inflation theory, including scalar field inflation, Starobinsky inflation, and Higgs inflation, which explain the dynamics of early expansion and the transformation of primordial perturbations into extensive cosmic structures. We also need observational evidence from the early cosmos to prove these theoretical hypotheses. The cosmic microwave background (CMB) and large-scale structure (LSS) are two of the most critical. CMB is described as the conditions immediately after the Big Bang and gives us a perspective on what the early universe was like, while Large Scale Structure (LSS) refers to the general arrangement of galaxies and matter throughout cosmic history. To form these structures one has to consider both the observation of them and the processes by which they are formed. The growth of cosmic structures is mainly due to gravitational collapse, which amplifies small density perturbations in the early universe. This process is also understood by using Newtonian perturbation theory, which is a useful approach to describing how early anisotropies evolve into the large scale structures we see today. The concepts of Jeans length, growth function, transfer function and power spectrum are useful tools to study the evolution of structures and distribution of matter and to generate theoretical data to compare with experimental data. However, the examination of nonlinear evolution show that the creation of xxi structures has a more complex background. Different theoretical instruments have been used to analyze this complicated structure. The spherical collapse model elucidates the evolution of overdense regions into stable entities like galaxies and galaxy clusters, whereas the idea of virialization delineates the equilibrium state of these structures, especially dark matter halos. Moreover, the Press-Schechter theory offers a statistical framework for elucidating the creation of cosmic formations. This theory provides an analytical approach to assess the mass distribution of collapsed entities. The mass function forecasts the probability of structure formation across various masses, whereas biasing delineates the correlation between observable galaxies and the fundamental density field. Comprehending the genesis and evolution of the universe necessitates a comprehensive methodology that integrates theoretical, observational, and statistical analyses. Newtonian perturbation theory is a crucial instrument for examining large-scale structures, with its validity corroborated by empirical evidence and simulations.