The mass splitting and the decay width of pentaquark ( + ) at the higher angular momentum states have been investigated in the framework of flux tube model considering the diquark-diquark-antiquark configuration for + along with statistical model. A quasi particle model for diquark has been considered. The Regge trajectory of + has also been investigated with interesting some observations. Keywords Exotic particle · Quasiparticle · Decay width · Regge trajectory · Mass spectrum Diakonov et al. theoretically proposed the low mass (1530 MeV) and total decay width ( < 15 MeV) of + baryon in the framework of chiral soliton model [1] denoting the exotic baryon as a pentaquark state. The LEPS collaboration [2] reported the first experimental evidence of a sharp baryon resonance peak at 1540 ± 10 MeV with a width smaller than 25 MeV whereas, SAPHIR [3] detector detected the resonance peak at 1540 ± 4 ± 2 MeV with < 25 MeV at 90 percent c.l. ZEUS collaboration [4] reported the experimental existence of pentaquark ( + ) suggesting the mass to be 1521.5 ± 1.5 MeV and decay width 6.1 ± 1.6 MeV whereas CLAS collaboration [5,6] suggested the value to be 1555 ± 10 MeV and decay width ≤ 26 MeV. Since LEPS collaboration reported the existence of + resonance several groups confirm the state whereas a number of experiments gives null result. The next generation of experiments have been taken by JLAB, CLAS for further search.The theoretical states of + has been studied by Doi [7] in the direct QCD calculation. The low lying states of this exotic baryon have been investigated in the context of pseudoscalar vector skryme model by . Diakonov [9] has made a mean field approach to study the pentaquark excitation using SU(3) flavor symmetries. Iwasaki

The scaling properties of the early universe during its evolution have been studied in terms of the mass fractal dimension, "d ". The speed of sound in the mixed phase of radiation and matter dominated era has been investigated and the possibility of a firstorder phase transition between the two eras has been explored.