AR_final file_2018-19

10 − 2 10 − 1 10 0 10 1 a/a 0 10 0 10 1 10 2 H ( a ) /H 0 Braneworld (numerical) Λ CDM Figure 1: This figure shows that the expansion rate on the braneworld containing a Quintessence field with a coth-like potential coincides with the expansion rate of the ΛCDM model. those formulae could be valid for a wide range of magnitude thresholds. Figure 2, shows the 2PCF and luminosity function coming from our model us- ing the fitting formulae of the HOD parameters. Constraining the dark energy statefinder hierarchy in a kinematic approach A popular model towards understanding dark en- ergy is the cosmographic approach. Niladri Paul , Ankan Mukherjee and H.K. Jassal adopted a kine- matic approach for constraining the extended null diagnostic of concordance cosmology, known as the statefinder hierarchy. They made a Taylor series ex- pansion of the Hubble parameter for the reconstruc- tion of the parameters. The coefficients of the Tay- lor series expansion were related to the kinematical parameters like the deceleration parameter, cosmo- logical jerk parameter, etc. They constrained the present values of the kinematical parameters from the estimated values of those series coefficients. A Markov chain Monte Carlo analysis was carried out using the observational measurements of Hub- ble parameter at different redshifts, the distance modulus data of type Ia supernovae and baryon acoustic oscillation data to estimate the coefficient of series expansion of the Hubble parameters. The parameters in the statefinder diagnostic are related to the kinematical parameters. The present values of statefinder parameters were constrained. They found that the first set in the statefinder hierarchy allows LCDM to be well within the 1 − σ confidence region, whereas the second set was in disagreement with the corresponding LCDM values at more than 1 − σ level. Another dark energy diagnostic, namely the Om-parameters, has been found to be consis- tent with concordance cosmology. Figure 3 shows the plot of Om ( z ) from their model-independent approach as a function of redshift. It is seen that that ΛCDM model value is still within 1 − σ region of the model-independent value. Perturbation growth on the phantom brane According to the braneworld paradigm, the Universe is a four-dimensional hypersurface (the ( 58 )