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The (n + 1)-dimensional Milne universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with p= κρ, κ = (4 - n)/3n. We then consider the n = 2 case and make SL(2, ℤ) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2, ℤ). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.

The random walk type eternal inflation in brane inflationary scenarios is reviewed. Unlike inflation in field theory with standard kinetic term, the DBI nature of the action describing the brane motion introduces extra constraints on eternal inflation. Constraints also appear due to the finite size of extra dimensions. In the context of false vacuum eternal inflation, we note that the Coleman–De Luccia instanton for a D-brane receives corrections due to the DBI nature of the action. This can enhance vacuum decay for a fine-tuned region of parameter space. Finally, some recent work on the stochastic Langevin description of the D-brane motion is reviewed. This leads to a modification to the Hawking–Moss probability distribution.

The axion–dilaton string effective action is expressed in Einstein frame metric in a manifestly S-duality invariant form. It is shown that the moduli can be redefined to describe surface of a (2+1)-dimensional pseudosphere. The classical cosmological solutions of axion–dilaton are revisited. The Wheeler–DeWitt equation for the system is exactly solved and complete set of eigenfunctions are presented. The wave function factorizes and the one depending on the moduli is obtained by appealing to the underlying S-duality symmetry. Axion and dilaton parametrize , the S-duality group, and the Hamiltonian is expressed as a sum of the Ricci scalar and the Casimir of SU(1, 1). Therefore, the complete set of wave functions, depending on the moduli, is obtained from group theory technique. The evidence for the existence of a W-infinity algebra in axion–dilaton cosmology is presented and the origin of the algebra is primarily due to high degree of degeneracies in the wave functions. It is qualitatively argued that axion–dilaton quantum cosmology exhibits chaotic behavior in the semiclassical limit.

Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed-point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed-points on moduli space with nonvanishing flux. We also discuss the more general target space dualities associated with these fixed-points.

The aim of this work is to provide a basis to interpret the dilaton as the dark matter of the universe, in the context of a particular cosmological model derived from type IIB supergravity theory with fluxes. In this theory, the dilaton is usually interpreted as a quintessence field. But, with this alternative interpretation we find that (in this supergravity model) the model gives a similar evolution and structure formation of the universe compared with the ΛCDM model in the linear regime of fluctuations of the structure formation. Some free parameters of the theory are fixed using the present cosmological observations. In the nonlinear regime there are some differences between the type IIB supergravity theory with the traditional CDM paradigm. The supergravity theory predicts the formation of galaxies earlier than the CDM and there is no density cusp in the center of galaxies. These differences can distinguish both models and might give a distinctive feature to the phenomenology of the cosmology coming from superstring theory with fluxes.

Compactification of type IIB theory on torus, in the presence of fluxes, is considered. The reduced effective action is expressed in manifestly S-duality invariant form. Cosmological solutions of the model are discussed in several cases in the Pre-Big Bang scenario.

We present exact solutions of string cosmological models characterized by five-dimensional metrics (with four-dimensional real Lie groups as isometry groups), space independent dilaton and vanishing torsion. As an example we consider VII₀⊕R model and show that it is equivalent to the (4+1)-dimensional cosmological model coupled to perfect fluid with negative deceleration parameters (accelerating universe).

In what has become a standard eternal inflation picture of the string landscape there are many problematic consequences and a difficulty defining probabilities for the occurrence of each type of universe. One feature in particular that might be philosophically disconcerting is the infinite cloning of each individual and each civilization in infinite numbers of separated regions of the multiverse. Even if this is not ruled out due to causal separation one should ask whether the infinite cloning is a universal prediction of string landscape models or whether there are scenarios in which it is avoided. If a viable alternative cosmology can be constructed one might search for predictions that might allow one to discriminate experimentally between the models. We present one such scenario although, in doing so, we are forced to give up several popular presuppositions including the absence of a preferred frame and the homogeneity of matter in the universe. The model also has several ancillary advantages. We also consider the future lifetime of the current universe before becoming a light trapping region.

We discuss various space–time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass.¹ In this alternative cosmology, the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions.

We proceed to investigate exact solutions of homogeneous anisotropic string cosmological models characterized by five-dimensional space–time metrics (with real four-dimensional isometry Lie groups), nonvanishing dilaton and anti-symmetric B field.

In this paper, we study the consequences of the existence of timelike and spacelike Ricci collineation vectors (RCVs) for string cloud in the context of general relativity. Necessary and sufficient conditions are derived for a space-time with string cloud to admit a timelike RCV parallel to u^a and a spacelike RCV parallel to x^a. Also, some results are obtained.

We obtain some cosmological model that are exact solutions of Einstein field equations. The metric utilized is the nonstatic Gödel-type cosmological model and the curvature source is a string cloud with scalar field and heat flow. The solutions have nonzero expansion, shear, and rotating. The properties of the solutions are studied and the temperature distribution is also given explicitly.

Conformal collineations (a generalization of conformal motion) and Ricci inheritance collineations, defined by £_ξ R_ab=2α R_ab, for string cloud and string fluids in general relativity are studied. By investigating the kinematical and dynamical properties of such fluids and using the field equations, some recent studies on the restrictions imposed by conformal collineations are extended, and new results are found.

In this paper, we study the consequences of the existence of conformal collineations (CC) for string cloud in the context of general relativity. Especially, we interest in special conformal collineation (SCC), generated by a special affine conformal collineation (SACC) in the string cloud. Some results on the restrictions imposed by a conformal collineation symmetry in the string cloud are obtained.

We discuss whether the future extrapolation of the present cosmological state may lead to a singularity even in case of "conventional" (negative) pressure of the dark energy field, namely w=p/ρ≥-1. The discussion is based on an often neglected aspect of scalar–tensor models of gravity: the fact that different test particles may follow the geodesics of different metric frames, and the need for a frame-independent regularization of curvature singularities.

Quantum cosmology may permit to determine the initial conditions of the Universe. In particular, it may select a specific model between many possible classical models. In this work, we study a quantum cosmological model based on the string effective action coupled to matter. The Schutz's formalism is employed in the description of the fluid. A radiation fluid is considered. In this way, a time coordinate may be identified and the Wheeler–DeWitt equation reduces in the minisuperspace to a Schrödinger-like equation. It is shown that, under some quite natural assumptions, the expectation values indicate a null axionic field and a constant dilatonic field. At the same time the scale factor exhibits a bounce revealing a singularity-free cosmological model. In some cases, the mininum value of the scale factor can be related to the value of gravitational coupling.

We review recent developments in the field of string cosmology with particular emphasis on open problems having to do mainly with geometric asymptotics and singularities. We discuss outstanding issues in a variety of currently popular themes, such as tree-level string cosmology asymptotics, higher-order string correction effects, M-theory cosmology, braneworlds and finally ambient cosmology.

We study a string inspired cosmological with variable potential through the Lagrangian invariance method in order to determine the form of the potential. We have studied four cases by combining the different fields, that is, the dilaton $\varphi ,$ the potential $V(\varphi ),$ the $H$-field and the matter field (a perfect fluid). In all the studied cases, we found that the potential can only take two possible forms: $V=V_0$ and $V=V_0{e}^{m\varphi },$ where $V_0$ and $m$ are numerical constants. We conclude that when we take into account the Kalb–Ramond field, i.e. the $H$-field, then it is only possible to get a constant potential, $V=V_0.$ Nevertheless, if this field is not considered, then we get two possible solutions for the potential: $V=V_0$ and $V=V_0{e}^{m\varphi }.$ In all the cases, if the potential is constant, $V=V_0,$ then we get a de Sitter like solution for the scale factor of the metric, $a(t)$, which verifies the $T$-duality property, while if the potential varies, then we get a power-law solution for the scale factor, $a=t^{a_1},$$a_1\in ℝ.$

In this paper, we find exact string cosmological solutions for FRW cosmology, by using the Hojman symmetry approach. The string cosmology under consideration includes a scalar field $\psi (t)$ with the potential $W(\psi )$, and a totally antisymmetric field strength $H_{\mu \nu \rho }$ which is specifically defined in terms of the scale factor $a(t)$. We show that for this string cosmology, Hojman conserved quantities exist using which new exact solutions for the scale factor and the scalar field are obtained for specific potentials $W(\psi )$ with some free parameters. The presence of these parameters, together with those of arising from Hojman symmetry, is an important advantage using which one can construct the solutions $a(t)$ and $\psi (t)$ with variety of cosmological behaviors.

In this paper, we have investigated Bianchi type-III bulk-viscous string cosmological models in the frame-work of scalar–tensor theory of gravitation. To solve the field equations for the bulk-viscous fluid and perfect fluid under the following physically relevant conditions: (i) Expansion scalar ($𝜃$) in the model is directly proportional to the shear scalar ($\sigma$). (ii) $p=\omega \rho$, where $\omega (0\le \omega \le 1)$ is a constant (iii) $\xi ={\xi }_0{\rho }^{\gamma }$, where ${\xi }_0$ and $\gamma (>0)$ are real constants. The observed phase transition of the presented universe from the early decelerating phase to the present epoch is in good accordance with the astronomical measurements. A detailed discussion on energy conditions and stability of the all models is analyzed through graphical representation.