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ÖgeA remedy for major cosmological tensions: Dark energy with an oscillating inertial mass density(Graduate School, 2022) Kıbrıs, Cihad ; Akarsu, Özgür ; 772305 ; Department of Physics EngineeringThe preponderance of observational evidence indicates that a vast portion of the energy density of the Universe today comes in dark matter and enigmatic dark energy (DE). The standard cosmological model, namely, the so-called Lambda Cold Dark Matter model ($\Lambda$CDM), resting on this dark sector as well as a small fraction of baryons has been remarkably successful in elucidating the bulk of Universe we inhabit. Though, astronomical observations improving in precision over the course of years are increasingly exposing that $\Lambda$CDM is significantly discrepant with various datasets. The direct and local measurements of the present-day expansion rate yielding $H_{0}=73.04\pm1.04 \;\, {\rm km\,s^{-1}\,Mpc}^{-1}$ are at more than $5\sigma$ tension (the Hubble $H_0$ tension) with the one $H_{0}=67.36\pm0.54 \;\, {\rm km\,s^{-1}\,Mpc}^{-1}$ inferred within the $\Lambda$CDM based on matter-baryon densities and the spacing between acoustic peaks of the CMB. The $H_0$ tension effectively propagates to the supernovae absolute magnitude $M_B$ through the distance modulus $\mu(z_i,H(z))=m_{B,i}-M_{B,i}$ where $m_{B,i}$ is the measured apparent magnitude of the supernovae observed at the redshift $z_i$, and creates a $3.4\sigma$ tension with the results calibrated by the CMB sound horizon scale. Another discrepancy regarding the expansion rate $H(z)$ within the best fit $\Lambda$CDM is the $\sim1.5\sigma$ tension between low (Galaxy BAO) and high redshift (Lyman-$\alpha$ at $z\approx2.33$) BAO data. It first emerged as a preference for smaller $H(z)$ and accompanying negative DE densities for $1.7\lesssim z\lesssim2.34$, being at $2.5\sigma$ tension with $\Lambda$CDM. In addition, $\Lambda$CDM predicts a larger weighted amplitude of matter fluctuations $S_8$ in comparison with what the independent large scale structure dynamical low-redshift probes suggest, thereby running into $2$ to $3\sigma$ tension. Given the long-standing theoretical issues such as the cosmological constant and coincidence problems related to the $\Lambda$, all these enumerated challenges and more inevitably motivate many to seek for a more complete framework either as modified theories of gravity or as minimal extensions beyond $\Lambda$CDM in the context of General Relativity (GR). In this sense, an approach that constitutes an example of the latter attempts focuses on inertial mass density $\Varrho\;=\rho+p$ parametrizations. The graduated dark energy (gDE) model proposed in Akarsu \textit{et al}. [Phys. Rev. D 101, 063528 (2020)], whose inertial mass density $\Varrho$ measures the minimum dynamical deviation $\Varrho\;\propto \rho^{\lambda}$ from the assumption of null QFT vacuum energy $\Varrho_{\Lambda}\;=0$ is one that exhibits nontrivial properties. It turns out that smaller and smaller negative values of the parameter $\lambda$ corresponds to a constant negative DE density that changes its sign from negative to positive in the past. Such a dynamical behavior would imply that $H(z)$ suppressed by the presence of a negative source at high redshifts results in an enhanced $H(z)$ at lower redshifts as the comoving angular diameter distance $D_M(z)$ to the surface of last scattering $D_M(z_*)=c\int_0^{z_*} H^{-1}(z)\d z$ is very stringently and almost model-independently constrained by the CMB for any given pre-recombination physics and should be kept unaltered. This means that if the redshift at which the sign-flip in the DE density occurs is slightly below the anomalous Ly-$\alpha$ at effective redshift $z\approx2.34$, it is quite conceivable that a dynamical DE possessing negative energy density mitigates both the $H_0$ and Ly-$\alpha$ discrepancies. The observational analysis of the gDE strongly favors a scenario in which the sign change of the gDE density is so swift it is practically identical to the cosmological constant phenomenologically flipping its sign much like the step function, except that $\Lambda<0$ in the past. It arises as a limiting case $\lambda\rightarrow-\infty$ of the gDE such that $\rho_{\rm gDE}(a)\rightarrow \rho_{\rm gDE,0}{\rm sgn}[f(a)]$ where sgn is the signum function. This limit has been comprehensively studied under the name of the $\Lambda_{\rm s}$CDM model in Akarsu \textit{et al}. [Phys. Rev. D 104, 123512 (2021)] where the late-time accelerated expansion is driven by $\Lambda_s\equiv\Lambda_{\rm s0}{\rm sgn}[z-z_{\dagger}]$ with $z_\dagger$ being the switching redshift rather than the usual $\Lambda$. The confrontation with the data sets encompassing CMB, Pantheon SNIa with and without SH0ES $M_B$ priors and BAO, shows that $\Lambda_{\rm s}$CDM simultaneously ameliorates six of the present significant tensions, namely $H_0$, $M_B$, $S_8$, Ly-$\alpha$, $t_0$ and $\omega_b$ tensions.
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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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ÖgeTesting spatial curvature and anisotropic expansion of the universe on top of the lambda-ACDM model(Graduate School, 2022) Özyiğit, Maya ; Akarsu, Özgür ; 766671 ; Physics Engineering ProgrammeIn this thesis, we explore the possible advantages of extending the standard $\Lambda$CDM model by more realistic backgrounds compared to its spatially flat Robertson-Walker (RW) spacetime assumption, while preserving the underpinning physics; in particular, by simultaneously allowing non-zero spatial curvature and anisotropic expansion on top of $\Lambda$CDM, viz., the An-$o\Lambda$CDM model. This is to test whether the latest observational data still support spatial flatness and/or isotropic expansion in this case, and, if not, to explore the roles of spatial curvature and expansion anisotropy (due to its stiff fluid-like behavior) in addressing some of the current cosmological tensions associated with $\Lambda$CDM. We first present the theoretical background and explicit mathematical construction of An-$o\Lambda$CDM. We replace, in the simplest manner, the spatially flat RW spacetime assumption of the $\Lambda$CDM model with the simplest more realistic background that simultaneously allows non-zero spatial curvature and anisotropic expansion; namely, considered the simplest anisotropic generalizations of the RW spacetime, viz., the Bianchi type I, V, and IX spacetimes (having the simplest homogeneous and flat, open, and closed spatial sections, respectively) combined in one Friedmann equation. Then we constrain the parameters of this model and its particular cases, namely, An-$\Lambda$CDM (allowing anisotropic expansion), $o\Lambda$CDM (allowing non-zero spatial curvature), and $\Lambda$CDM, by using the latest data sets from different observational probes, viz., Planck CMB(+Lens), BAO, SnIa Pantheon, and CC data, and discuss the results in detail. Ultimately, we conclude that, within the setup under consideration, (i) the observational data confirm the spatial flatness and isotropic expansion assumptions of $\Lambda$CDM, though a very small amount of expansion anisotropy cannot be excluded, e.g., $\Omega_{\sigma0}\lesssim10^{-18}$ (95\% C.L.) for An-$\Lambda$CDM from CMB+Lens data, (ii) the introduction of spatial curvature or anisotropic expansion, or both, on top $\Lambda$CDM does not offer a possible relaxation to the $H_0$ tension, and (iii) the introduction of anisotropic expansion neither affects the closed space prediction from the CMB(+Lens) data nor does it improve the drastically reduced value of $H_0$ led by the closed space.
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ÖgeTransition dynamic in the LSCDM model: Implications for bound cosmic structures(Graduate School, 2024-06-27) Çam, Arman ; Akarsu, Özgür ; 509201112 ; Physics EngineeringWe explore the predictions of $\Lambda_{\rm s}$CDM, a novel framework suggesting a rapid anti-de Sitter (AdS) to de Sitter (dS) vacua transition in the late Universe, on bound cosmic structures. In its simplest version, $\Lambda_{\rm s}$ abruptly switches sign from negative to positive, attaining its present-day value at a redshift of ${z_\dagger\sim 2}$ i.e., $\Lambda_{\rm s} \equiv \Lambda{\rm sgn}(z_{\dagger}-z)$. We will show that in the case of an abrupt sign-switching cosmological constant, there occurs a type II (sudden) singularity at the transition redshift, $z_{\dagger}$, where the total pressure of the universe diverges to infinity and the total energy density remains constant and finite. To avoid type II singularity, one can ``smooth-out'' the sudden sign-switch and describe it by using sigmoid functions (e.g., $\tanh$, logistic). However, since this correction would introduce an additional parameter ($\sigma$) to the model, we decided to examine the scenario in which the sign change of the cosmological constant is abrupt. This will also allow us to study the behavior of structure formation in the most extreme case without adding an extra parameter to our analysis. We will start our analysis by studying the spherical collapse model for a universe that contains dust (consisting of cold dark matter and baryons) and cosmological constant ($\Lambda$). For this universe, we will derive the equations describing the dynamics of the overdensity as a function of the background universe. Due to the shell crossing---and consequently the breakdown of the homogeneity and isotropy after the turnaround---, one cannot use the Friedmann equations (i.e., spherical collapse model) to describe the dynamics of the overdensity. Thus, we must refer to the semi-Newtonian approach and use the virialization condition to describe its dynamics. In the next step, we will extend our analysis of the spherical collapse model to include $\Lambda_{\rm s}$CDM, by incorporating the sign-switching cosmological constant ($\Lambda_{\rm s}$) into our calculations. To understand this process more clearly, we will separate our discussion into three parts. In the first part, we will study the evolution of the overdensity, if it enters turnaround under the effect of the positive cosmological constant (i.e., $\Lambda_{\rm s} \equiv +\Lambda$). In the second part, we will discuss the dynamics of the overdensity, if it enters turnaround under the effect of the negative cosmological constant (i.e., $\Lambda_{\rm s} \equiv -\Lambda$). In the third and final part, we will discuss the halos that completely virializes before the AdS-dS transition, and study the effect of the type II singularity on the bounded cosmic structures. At a first glance, it's clear that depending on the time of the transition, the overdensity will be effected differently. In summary, we can identify three primary influences which effects the structure formation in the $\Lambda_{\rm s}$CDM model: (i) the negative cosmological constant (AdS) phase for $z > z_\dagger$, (ii) the abrupt transition marked by a type II (sudden) singularity, leading to a sudden increase in the universe's expansion rate at $z=z_\dagger$, and (iii) an increased expansion rate in the late universe under a positive cosmological constant for $z < z_\dagger$, compared to $\Lambda$CDM. We find that the virialization process of cosmic structures, and consequently their matter overdensity, varies depending on whether the AdS-dS transition precedes or follows the turnaround. Specifically, structures virialize with either increased or reduced matter overdensity compared to the Planck/$\Lambda$CDM model, contingent on the timing of the transition. Despite its profound nature, the singularity exerts only relatively weak effects on such systems, thereby reinforcing the model's viability in this context.