We describe the TreePM method for carrying out large N-Body simulations to study formation and evolution of the large scale structure in the Universe. This method is a combination of Barnes and Hut tree code and Particle-Mesh code. It combines the automatic inclusion of periodic boundary conditions of PM simulations with the high resolution of tree codes. This is done by splitting the gravitational force into a short range and a long range component. We describe the splitting of force between these two parts. We outline the key differences between TreePM and some other N-Body methods.

Distribution of cold gas in the post-reionization era provides an important link between distribution of galaxies and the process of star formation. Redshifted $21$-cm radiation from the hyperfine transition of neutral hydrogen allows us to probe the neutral component of cold gas, most of which is to be found in the interstellar medium of galaxies. Existing and upcoming radio telescopes can probe the large scale distribution of neutral hydrogen via HI intensity mapping. In this paper, we use an estimate of the HI power spectrum derived using an ansatz to compute the expected signal from the large scale HI distribution at $z \sim 3$. We find that the scale dependence of bias at small scales makes a significant difference to the expected signal even at large angular scales. We compare the predicted signal strength with the sensitivity of radio telescopes that can observe such radiation and calculate the observation time required for detecting neutral hydrogen at these redshifts. We find that OWFA (Ooty Wide Field Array) offers the best possibility to detect neutral hydrogen at $z \sim 3$ before the SKA (Square Kilometer Array) becomes operational. We find that the OWFA should be able to make a $3 \sigma$ or a more significant detection in $2000$ hours of observations at several angular scales. Calculations done using the Fisher matrix approach indicate that a $5\sigma$ detection of the binned HI power spectrum via measurement of the amplitude of the HI power spectrum is possible in $1000$ h (Sarkar et al. 2017).

Dynamical models for dark energy are an alternative to the cosmological constant. It is important to investigate properties of perturbations in these models and go beyond the smooth FRLW cosmology. This allows us to distinguish different dark energy models with the same expansion history. For this, one oftenneeds the potential for a particular expansion history. We study how such potentials can be reconstructed by obtaining closed formulae for potential or reducing the problem to quadrature. We consider three classes of models here: tachyons, quintessence and interacting dark energy.We present results for the constant $\omega$ and the CPL parametrization. The method given here can be generalized to any arbitrary form of $\omega(z)$.