In these lectures I review recent attempts to apply string theory to cosmology, including string cosmology and various models of brane cosmology. In addition, the review includes an introduction to inflation as well as a discussion of transplanckian signatures. I also provide a critical discussion of the possible role of holography. The material is based on lectures given in January 2004 at the...

Brane cosmology takes the unconventional form H ∼ √ρ. To recover the standard cosmology, we have to assume that the matter density is much less than the brane tension. We show that the assumption can be justified even near the end of inflation if we fine-tune the coupling constant of the inflaton potential. As a consequence, the standard cosmology is recovered after inflation. PACS: 98.80-k; 04...

In a recent paper, a cosmological model based on El Naschie E infinity cantorian spacetime was presented [1]. In that work it was claimed that the present accelerated expansion of the Universe can be obtained as the effect of a scaling law on newtonian cosmology with a certain time dependent gravitational constant (G). In the present work we show that it may be problematic to explain the presen...

The Standard Big Bang (SBB) cosmology has become an extremely successful model that has been well tested by experiment. However, the model is incomplete. The underlying theory of classical general relativity and the description of matter as an ideal gas breaks down at the high temperatures of the early Universe, and the solutions of the theory in fact have an initial singularity. Moreover, SBB ...

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintes...

In this short review we study the state of the art of the great challenge of contemporary physics which is reconcile Quantum Theory and its best contribution the Standard Model of Particle Physics and General Relativity. The reconciliation passes undoubtedly through the idea of a fractal universe. Mathematics Subject Classification: Primary 83F05. Secondary 83C45

In Gauss-Bonnet braneworld cosmology, the Friedmann equation of our four-dimensional universe on 3-brane is modified in a high energy regime (Gauss-Bonnet regime), while the standard expansion law is reproduced in low energies (standard regime). We investigate the Gauss-Bonnet braneworld cosmological effect on the thermal relic density of cold dark matter when the freeze-out of the dark matter ...

In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly in the framework of loop quantum cosmology. We investigate the phenomenological implications of this model in the semi-classical regime an...

A brief review of p-adic and adelic cosmology is presented. In particular, p-adic and adelic aspects of gravity, classical cosmology, quantum mechanics, quantum cosmology and the wave function of the universe are considered. p-Adic worlds made of p-adic matters, which are different from real world of ordinary matter, are introduced. Real world and p-adic worlds make the universe as a whole. p-A...