The separable analytical solution in standard perturbation theory for an Einstein de Sitter (EdS) universe can be generalized to the wider class of such cosmologies (``generalized EdS'', or gEdS) in which a fraction of the pressure-less fluid does not cluster. We derive the corresponding kernels in both Eulerian perturbation theory (EPT) and Lagrangian perturbation theory, generalizing the canonical EdS expressions to a one-parameter family where the parameter can be taken to be the exponent $α$ of the growing mode linear amplification $D(a) \propto a^α$. For the power spectrum (PS) at one loop in EPT, the contribution additional to standard EdS is given, for each of the `13' and `22' terms, as a function of two infra-red safe integrals. In the second part of the paper we show that the calculation of cosmology-dependent corrections in perturbation theory in standard (e.g. LCDM-like) models can be simplified, and their magnitude and parameter dependence better understood, by relating them to our analytic results for gEdS models. At second order the time dependent kernels are equivalent to the analytic kernels of the gEdS model with $α$ replaced by a single redshift dependent effective growth rate $α_2(z)$. At third order the time evolution can be conveniently parametrized in terms of two additional such effective growth rates. For the PS calculated at one loop order, the correction to the PS relative to the EdS limit can be expressed in terms of just $α_2(z)$, one additional effective growth rate function and the four infra-red safe integrals of the gEdS limit. This is much simplified compared to expressions in the literature that use six or eight red-shift dependent functions and are not explicitly infra-red safe. Using the analytic gEdS expression for the PS with $α=α_2(z)$ gives a good approximation (to $\sim 25 \%$) for the exact result.
We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are the closed orbits of a symmetry group. If these surfaces have non-positive Euler characteristic (or in the case of 2-spheres, if the initial 2-spheres are large enough) and also if the initial spatial slice is expanding everywhere, then we prove that asymptotically the spacetime becomes physically indistinguishable from de Sitter space on ar…
Standard Perturbation Theory for Interacting Dark Sector cosmologies I: Breakdown of Einstein de Sitter kernels
Universidade Federal da Bahia（巴伊亚联邦大学）；Instituto Federal de Educação, Ciência e Tecnologia da Bahia（巴伊亚联邦教育、科学与技术学院）；Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）
We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of b…
A Quantum Gravitational Mechanism for Isotropization of de Sitter Cosmologies
Brown University（布朗大学）；Imperial College London（帝国理工学院）；Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；Flatiron Institute（平顿研究所）
De Sitter solutions play an important role in cosmology because the knowledge of unstable de Sitter solutions can be useful to describe inflation, whereas stable de Sitter solutions are often used in models of late-time acceleration of the Universe. The Einstein-Gauss-Bonnet gravity cosmological models are actively used both as inflationary models and as dark energy models. To modify the Einstein equations one can add a nonlinear function of the Gauss-Bonnet term or a function of the scalar field multiplied on the Gauss-Bonnet term. The effective potential method essentially simplifies the sea…
