We show how the motion through the extra dimensions of a gas of branes and antibranes can, under certain circumstances, produce an era of inflation as seen by observers trapped on a 3-brane, with the inflaton being the inter-brane separation. Although most of our discussion refers to arbitrary p-branes, when we need to be specific we assume that they are D-branes of Type II or Type I string theory. For realistic brane couplings, such as those arising in string theory, the inter-brane potentials are too steep to inflate the universe for acceptably long times. However, for special regions of the parameter space of brane-antibrane positions the brane motion is slow enough for there to be sufficient inflation. Inflation would be more generic in models where the inter-brane interactions are much weaker. The spectrum of primordial density fluctuations predicted has index n slightly less than 1, and an acceptable amplitude, provided that the extra dimensions have linear size 1/r ∼ 10 12 GeV. Reheating occurs as in hybrid inflation, with the tachyonic instability of the brane-antibrane system taking over for small separations. The tachyon field can induce a cascade mechanism within which higher-dimension branes annihilate into lower-dimension ones. We argue that such a cascade naturally stops with the production of 3-branes in 10-dimensional string theory.

We argue that the early universe may be described by an initial state of space-filling branes and anti-branes. At high temperature this system is stable. At low temperature tachyons appear and lead to a phase transition, dynamics, and the creation of D-branes. These branes are cosmologically produced in a generic fashion by the Kibble mechanism. From an entropic point of view, the formation of lower dimensional branes is preferred and D3 brane-worlds are exponentially more likely to form than higher dimensional branes. Virtually any brane configuration can be created from such phase transitions by adjusting the tachyon profile. A lower bound on the number defects produced is: one D-brane per Hubble volume.

Using only general properties of the tachyon potential we show that inflation may be generic when many branes and anti-branes become coincident. Inflation may occur because of: (1) the assistance of the many diagonal tachyon fields; (2) when the tachyons condense in a staggered fashion; or (3) when some of them condense very late. We point out that such inflation is in some sense a stringy implementation of chaotic inflation and may have important applications for "regularizing" a lopsided or singular cosmological compact surface.

The time-varying density of D-branes and anti-D-branes in an expanding universe is calculated. The D-brane anti-brane annihilation rate is shown to be too small to compete with the expansion rate of a FRW type universe and the branes over-close the universe. This brane problem is analogous to the old monopole problem. Interestingly however, it is shown that small dimension D-branes annihilate more slowly than high dimension branes. Hence, an initially brany universe may be filled with only low dimension branes at late times. When combined with an appropriate late inflationary theory this leads to an attractive dynamical way to create a realistic braneworld scenario.

Hawking's argument about non-unitary evolution of black holes is often questioned on the ground that it doesn't acknowledge the quantum correlations in radiation process. However, recently it has been shown that adding 'small' correction to leading order Hawking analysis, accounting for the correlations, doesn't help to restore unitarity. This paper generalizes the bound on entanglement entropy by relaxing the 'smallness' condition and configures the parameters for possible recovery of information from an evaporating black hole. The new bound effectively puts an upper limit on increase in entanglement entropy. It also facilitates to relate the change in entanglement entropy to the amount of correction to Hawking state.

We examine a non-Abelian SUSY SU (2) × U (1) gauge theory and a SUSY U (1) theory originally used to investigate the microphysics of cosmic strings in supersymmetric theories. We show that both theories automatically include hybrid inflation. In the latter theory we use a D term to break the symmetry. SUSY is broken during inflation and restored afterwards. Cosmic strings are formed at the end of inflation. The temperature anisotropy is calculated and found to vary as (MGUT /MP ) 2 .

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Land Registry documents are legally binding documents provided by the government to owners of land as proof of their ownership. In developing countries such as Bangladesh, it is essential to combat the challenges which a traditional Land Registry system faces. To keep a digital ledger of information about land assets in a transparent an secured manner, Blockchain technology can be used to overcome the hurdle. However, any Blockchain system could fail in the hands of an attacker if the right kind of consensus protocol is not used to secure the chain. The thesis proposes a novel approach on enhancing the Delegated Proof of Stake consensus to provide a private ledger based system secure for transacting land assets which can be easily integrated into the existing traditional Land Registry system for smooth operation. Witnesses are elected genetically while blocks have been customized to cover all the intricate details of the Land Registry Documentation while the system Architecture have been improved to include all sides of the stakeholders. Designated nodes have different roles which enhances the overall model to a structured Hierarchy and also withstand attacks. With the implementation of a Blockchain based system to maintain Land Registry document will allow for data transparency, and immutability therefore making counterfeits and forging almost impossible. This also cuts down the hassle of collecting different documents from different agencies making it easier to obtain land registry documents.