We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The estimatio
n of angular diameter distance comes from the samples of galaxy clusters (real and mock) and FRIIb radio galaxies. We parameterize the distance duality relation as a function of redshift in four different ways and we find that the mock data set, which assumes a spherical isothermal $beta$ model for the galaxy clusters does not accommodate the distance duality relation while the real data set which assumes elliptical $beta$ model does.
The geometrically frustrated magnet Ni3V2O8 undergoes a series of competing magnetic ordering at low temperatures. Most importantly, one of the incommensurate phases has been reported to develop a ferroelectric correlation caused by spin frustration.
Here we report an extensive thermodynamic, dielectric and magnetic study on clean polycrystalline samples of this novel multiferroic compound. Our low temperature specific heat data at high fields up to 14 Tesla clearly identify the development of a new magnetic field induced phase transition below 2 K that shows signatures of simultaneous electric ordering. We also report temperature and field dependent dielectric constant that enables us to quantitatively estimate the strength of magneto-electric coupling in this improper ferroelectric material.
