• bouncing models
• cosmology
• pre-big bang
• string cosmology
• string theory

One of the most fascinating and puzzling research area in the nowadays physics is the quantum gravity problem, i.e. the unification of quantum field theories (QFT) with general relativity (GR) or, from a more pragmatic point of view, the high energy description of the theory of gravity. It’s well known that GR contains singularities, as a classical theory, and it is also a non renormalizable theory of gravity as a quantum theory. String theory is one of the quantum gravity candidates which tries to solve these problems avoiding the divergencies of QFT introducing interactions among extended objects, i.e. introducing some non-localities in order to improve convergence of amplitude integrals. From the very beginning of all quantum gravity theories, and so for string theory, it was important to construct the very early universe cosmological scenarios embedded in the theory considered in order to test the various models and have important phenomenological counterparts.
In this thesis we consider a generic model of primordial universe before the Big-Bang, in particular a contracting Universe in the Einstein Frame (and expanding in the String Frame) with a gas of very small black holes with radius of order of string length, the so-called string holes. Such a gas could arise in the high density regime thanks to the instabilities of matter during a generic cosmological contraction. After a remark on the instability of solutions (in the phase space) which describe such a phase of string hole gas we try to improve the model proposed by J.Quintin, R.H.Brandenberger, M.Gasperini and G.Veneziano (in Phys.Rev.D98 (2018) 10, 103519) adding a viscosity term, due to the black holes’ dense fluid itself, to the action of the model and studying the stability of the new set of equations.
In particular we add the viscosity term to the action at zero order in alpha’ and we find that there is a solution to the equations of motion but the potential is still fine tuned as in previous work. Then we analyze the case of the first order alpha’ corrections to the action obtained, in particular we analyze the action with the O(d,d) symmetry, and we find that there is a solution and it is stable for some set of values of \omega, where \omega is the constant of proportionality in the usual equation of state for barotropic fluids p=\omega \rho.



Finally, we use a result proposed by O.Hohm and B.Zweiberg with equations of motion that describe the cosmological scenario with the full alpha’ expansion. In this case we obtain that in the absence of viscosity there is no solution, instead adding the viscosity term the situation is greatly improved and there is a solution and such a solution is stable. These informations give constraints to \omega and to some first coefficients of the solution expanded in power of alpha’, because the solution exists and is stable for certain range of \omega values and for certain coefficients.
We conclude this thesis with the discussion of the consequences of the obtained solutions, namely a possible bouncing scenarios with a graceful exit to the standard cosmological evolution.