| Abstract : | The observed large scale structure in the Universe is characterised by two main variables: the fractional overdensity and the peculiar velocity. When the fluctuations are small, the overdensity is proportional to the velocity divergence; the proportionality constant (which is the linear growth rate) is sensitive to the underlying cosmological model. By measuring the density and velocity fields through galaxy and weak lensing surveys it is possible, modulo the bias, to constrain the cosmological model. Indeed, many upcoming surveys such as EUCLID etc. aim to constrain cosmological parameters, by measuring the growth rate.
However, the linear relation breaks down when the density contrasts are high. In this talk, we will examine the relation between the two fields in the non-linear regime using a dynamical systems approach. By considering, spherical symmetry, we show that the non-linear density-velocity divergence relation is an invariant of the underlying dynamics and depends only on cosmological parameters which describe the evolution and not on the initial conditions. We demonstrate, how in principle, such invariant relations can be exploited to break parameter degeneracies. Finally, we comment on extensions of this relation to ellipsoidal geometries and modified gravity models.
References:
1. `Non-linear density-velocity divergence relation from phase space dynamics’.
Sharvari Nadkarni-Ghosh.
2013 MNRAS, 428
2. `Phase space dynamics of triaxial collapse: joint density–velocity evolution ’.
Sharvari Nadkarni-Ghosh and Akshat Singhal
2016 MNRAS, 457
3. `One-point probability distribution function from spherical collapse: Early Dark Energy (EDE) vs. ΛCDM' Ankush Mandal and Sharvari Nadkarni-Ghosh 2019 MNRAS, 498
4. `Non-linear density-velocity dynamics in f(R) gravity from spherical collapse’.
Sharvari Nadkarni-Ghosh and Sandip Chowdhury, 2022 MNRAS 511 |
