Number Density Of Structures Research Articles

Late time sky as a probe of steps and oscillations in primordial Universe

The standard model of cosmology with nearly Gaussian, isotropic, scale invariant and adiabatic initial conditions describes the cosmological observations well. However, the study of any deviation from the mentioned conditions will open up a new horizon to the physics of early universe. In this work, we study the effect of the oscillatory and step-like features in potentials of inflationary models in late time large scale structure observations. Mainly we study the matter power spectrum, number density of the structures, dark matter halo bias and specifically CMB lensing. We show that the oscillatory models can introduce some degeneracy with late time effects on BAO scale. We also conclude that high frequency oscillatory models which are favored by Planck data do not have significant effect on the non linear structure formation. Finally we show that inflationary models with step functions which deviates from the standard model in small scales l ⩽ 1 Mpc can be constrained by future experiments via CMB lensing. We propose the idea that CMB lensing is a bias independent observation which can be used as a small scale physics probe due to distribution of the lenses in low redshifts. Meantime this model can alter the prediction of the cosmological model for the number density of small structures and can be used as a probable explanation for galactic scale crisis of ΛCDM.

Matrix formalism of excursion set theory: A new approach to statistics of dark matter halo counting

Excursion set theory (EST) is an analytical framework to study the large-scale structure of the Universe. EST introduces a procedure to calculate the number density of structures by relating the cosmological linear perturbation theory to the nonlinear structures in late time. In this work, we introduce a novel approach to reformulate the EST in matrix formalism. We propose that the matrix representation of EST will facilitate the calculations in this framework. The method is to discretize the two-dimensional plane of variance and density contrast of EST, where the trajectories for each point in the Universe lived there. The probability of having a density contrast in a chosen variance is represented by a probability ket. Naturally, the concept of the transition matrix pops up to define the trajectories. We also define the probability transition rate which is used to obtain the first up-crossing of trajectories and the number count of the structures. In this work we show that the discretization let us study the non-Markov processes by forcing them to look like a Wiener process. Also we discuss that the zero drift processes with Gaussian and also non-Gaussian initial conditions can be studied by this formalism. The continuous limit of the formalism is discussed, and the known Fokker-Planck dispersion equation is recovered. Finally we show that the probability of the most massive progenitors can be extracted in this framework.

Development of flute-mark assemblages, 2. Evolution of trios of defects

Experiments using a bed of hardened Plaster of Paris dissolved beneath a turbulent water stream (practical analogue of natural mud-bed erosion) show that trios of defects evolve into compound flute marks which, at a critical age, become indistinguishable from structures evolved from single defects. The critical age is comparable with 0.6, defined in terms of the erosion velocity of the bed surrounding the mark, duration of erosion, and the overall size of the assemblage of defects. Marks formed from single defects (Allen, 1971) and from paired defects (Allen, 1973) also lose evidence of their parents broadly at this value of the age. Marks grown from trios increase in maximum depth on a similar law to the marks formed from single and paired defects. A natural assemblage of flute marks may be expected during an early stage of evolution to show a progressive reduction in the number-density of structures, as a consequence of the merging of marks produced at sufficiently closely spaced unstable defects.