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In this study, we model the dark matter and baryon matter distribution in the Cosmic Web by means of highly nonlinear Schr{o}dinger type and reaction diffusion wave mechanical descriptions. The construction of these wave mechanical models of the structure formation is achieved by introducing the Fisher information measure and its comparison with a highly nonlinear term called the quantum potential in the wave equations. Strikingly, the comparison of the nonlinear term and the Fisher information measure provides a dynamical distinction between lack of self-organization and self-organization in the dynamical evolution of the cosmic components. Mathematically equivalent to the standard cosmic fluid equations, these approaches make it possible to follow the evolution of the matter distribution even into the highly nonlinear regime by circumventing singularities. In addition, these wave formalisms are extended to two-fluid descriptions of the coupled dark matter and baryon matter distributions in the linear regime, in the Einstein de Sitter Universe (EdS) to construct toy models of the cosmic components in this relatively simple Universe model. Based on these two different wave mechanical formalisms, here fully analytical results for the dark matter and baryon distributions are provided. Also, numerical realizations of the emerging weblike patterns are presented from the nonlinear dynamics of the baryon component corresponding to soliton-like solutions. These soliton-like solutions might represent a proper description of filamentary structures even in the linear regime.
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It is generally argued that the present cosmological observations support the accelerating models of the universe, as driven by the cosmological constant or `dark energy. We argue here that an alternative model of the universe is possible which explains the current observations of the universe. We demonstrate this with a reinterpretation of the magnitude-redshift relation for Type Ia supernovae, since this was the test that gave a spurt to the current trend in favour of the cosmological constant.
Reconstruction techniques are commonly used in cosmology to reduce complicated nonlinear behaviours to a more tractable linearized system. We study a new reconstruction technique that uses the Moving-Mesh algorithm to estimate the displacement field from nonlinear matter distribution. We show the performance of this new technique by quantifying its ability to reconstruct linear modes. We study the cumulative Fisher information $I(<k_n)$ about the initial matter power spectrum in the matter power spectra in 130 $N$-body simulations before and after reconstruction, and find that the nonlinear plateau of $I(<k_n)$ is increased by a factor of $sim 50$ after reconstruction, from $I simeq 2.5 times 10^{-5} /({rm Mpc}/h)^3$ to $I simeq 1.3 times 10^{-3}/({rm Mpc}/h)^3$ at large $k$. This result includes the decorrelation between initial and final fields, which has been neglected in some previous studies. We expect this technique to be beneficial to problems such as baryonic acoustic oscillations, redshift space distortions and cosmic neutrinos that rely on accurately disentangling nonlinear evolution from underlying linear effects.
The Fisher Information Matrix (FIM) has been the standard approximation to the accuracy of parameter estimation on gravitational-wave signals from merging compact binaries due to its ease-of-use and rapid computation time. While the theoretical failings of this method, such as the signal-to-noise ratio (SNR) limit on the validity of the lowest-order expansion and the difficulty of using non-Gaussian priors, are well understood, the practical effectiveness compared to a real parameter estimation technique (e.g. Markov-chain Monte Carlo) remains an open question. We present a direct comparison between the FIM error estimates and the Bayesian probability density functions produced by the parameter estimation code lalinference_mcmc. In addition to the low-SNR issues usually considered, we find that the FIM can greatly overestimate the uncertainty in parameter estimation achievable by the MCMC. This was found to be a systematic effect for systems composed of binary black holes, with the disagreement increasing with total mass. In some cases, the MCMC search returned standard deviations on the marginalized posteriors that were smaller by several orders of magnitude than the FIM estimates. We conclude that the predictions of the FIM do not represent the capabilities of real gravitational-wave parameter estimation.
It is well known that a suggestive relation exists that links Schrodingers equation (SE) to the information-optimizing principle based on Fishers information measure (FIM). The connection entails the existence of a Legendre transform structure underlying the SE. Here we show that appeal to this structure leads to a first order differential equation for the SEs eigenvalues that, in certain cases, can be used to obtain the eigenvalues without explicitly solving SE. Complying with the above mentioned equation constitutes a necessary condition to be satisfied by an energy eigenvalue. We show that the general solution is unique.
Using estimates of dark halo masses from satellite kinematics, weak gravitational lensing, and halo abundance matching, combined with the Tully-Fisher and Faber-Jackson relations, we derive the mean relation between the optical, V_opt, and virial, V_200, circular velocities of early- and late-type galaxies at redshift z~0. For late-type galaxies V_opt ~ V_200 over the velocity range V_opt=90-260 km/s, and is consistent with V_opt = V_maxh (the maximum circular velocity of NFW dark matter haloes in the concordance LCDM cosmology). However, for early-type galaxies V_opt e V_200, with the exception of early-type galaxies with V_opt simeq 350 km/s. This is inconsistent with early-type galaxies being, in general, globally isothermal. For low mass (V_opt < 250 km/s) early-types V_opt > V_maxh, indicating that baryons have modified the potential well, while high mass (V_opt > 400 km/s) early-types have V_opt < V_maxh. Folding in measurements of the black hole mass - velocity dispersion relation, our results imply that the supermassive black hole - halo mass relation has a logarithmic slope which varies from ~1.4 at halo masses of ~10^{12} Msun/h to ~0.65 at halo masses of 10^{13.5} Msun/h. The values of V_opt/V_200 we infer for the Milky Way and M31 are lower than the values currently favored by direct observations and dynamical models. This offset is due to the fact that the Milky Way and M31 have higher V_opt and lower V_200 compared to typical late-type galaxies of the same stellar masses. We show that current high resolution cosmological hydrodynamical simulations are unable to form galaxies which simultaneously reproduce both the V_opt/V_200 ratio and the V_opt-M_star (Tully-Fisher/Faber-Jackson) relation.
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