This is a summary of lectures in superstring cosmology given by the author at the CORFU 2009 School and Workshops "Theory - Cosmology - Phenomenology", Corfu Institute, Greece, Sept 6-13, 2009. These lectures are based on some recent developments and ideas, in the framework of superstring theory, concerning the evolution and structure of the universe in (i) the very early "non-geometric"' cosmological era, (ii) the intermediate "radiation-like" era and (iii) the late time cosmological era characterized by the electroweak phase transition.
These lecture notes begin with a review of the first nonleading contributions to the derivative expansion of the M theory effective action compactified on a two-torus. The form of these higher-derivative interactions is shown to follow from ten-dimensional type IIB supersymmetry as well as from one-loop quantum corrections to classical eleven-dimensional supergravity. The detailed information concerning D-instanton effects encoded in these terms is related to the problem of evaluating the Witten index for $N$ D-particles in the type IIA theory. Using the AdS/CFT conjecture, it also leads to ve…
We study the cosmology of perturbative heterotic superstring theory during the radiation-like era for semi-realistic backgrounds with initial $\N=1$ supersymmetry. This analysis is valid for times after the Hagedorn era (or alternatively inflation era) but before the electroweak symmetry breaking transition. We find an attraction to a radiation-like era with the ratio of the supersymmetry breaking scale to temperature stabilized. This provides a dynamical mechanism for setting the supersymmetry breaking scale and its corresponding hierarchy with the Planck scale. For the internal space, we fin…
This text is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for `uplifting terms', i.e. methods to produce de Sitter vacua. We concentrate on N=1 and N=2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed in short at the end.
Superstring theory predicts the existence of a scalar field, the dilaton. I review some basic features of the dilaton interactions and explain their possible consequences in cosmology and particle physics.
The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an introduction to this theory, beginning with an overview of the Newtonian theory of fluctuations, moving on to the analysis of fluctuations in the realm of classical general relativity, and culminating with a discussion of the quantum theory of cosmological perturbations. I will illustrate the formalism with applications to inflationary cosmology. I will review the bas…
We review cosmological solutions of type II superstrings and M-theory, emphasizing the role of non-vanishing Ramond form backgrounds. Compactifications on flat and, more generally, maximally symmetric spatial subspaces are presented. We give a physical discussion of both inflating and subluminally expanding cosmological solutions of such theories and explore their singularity structure. An explicit example, in the context of the type IIA superstring, is constructed. We then analyze compactifications of M-theory on Ricci flat manifolds. The external part of U--duality and its relation to cosmol…
The continuous and discrete symmetries of a dimensionally reduced type IIB superstring action are employed to generate four-dimensional cosmological solutions with non-trivial Neveu-Schwarz/Neveu-Schwarz and Ramond-Ramond form-fields from the dilaton-moduli-vacuum solutions.
We consider whether current notions about superstring theory below the Planck scale are compatible with cosmology. We find that the anticipated form for the dilaton interaction creates a serious roadblock for inflation and makes it unlikely that the universe ever reaches a state with zero cosmological constant and time-independent gravitational constant.
A stability analysis is made in the context of the previously discovered non-singular cosmological solution from 1-loop corrected superstring effective action. We found that this solution has an instability in graviton mode, which is shown to have a close relation to the avoidance of initial singularity via energy condition. We also estimate the condition for the breakdown of the background solution due to the overdominance of the graviton.
We briefly review the status of the ``graceful exit'' problem in superstring cosmology and present a possible resolution. It is shown that there exists a solution to this problem in two-dimensional dilaton gravity provided quantum corrections are incorporated. This is similar to the recently proposed solution of Rey. However, unlike in his case, in our one-loop corrected model the graceful exit problem is solved for any finite number of massless scalar matter fields present in the theory.
We review a recently proposed approach to construct superstring cosmological evolutions, which are free of Hagedorn instabilities and initial singularities. We illustrate these ideas in hybrid models in two dimensions.
We construct a new cosmological model considering the superstring-inspired E_6 unification in the 4-dimensional space at the early stage of the Universe. We develop a concept of parallel existence in Nature of the ordinary and shadow worlds with different cosmological evolutions.
The pressureless tachyonic matter recently found in superstring field theory has an over-abundance problem in cosmology. We argue that this problem is naturally solved in the brane inflationary scenario if almost all of the tachyon energy is drained (via its coupling to the inflaton and matter fields) to heating the universe, while the rest of the tachyon energy goes to a network of cosmic strings (lower-dimensional BPS D-branes) produced during the tachyon rolling at the end of inflation.
It is shown that the general solution near a spacelike singularity of the Einstein-dilaton-p-form field equations relevant to superstring theories and M-theory exhibits an oscillatory behaviour of the Belinskii-Khalatnikov-Lifshitz type. String dualities play a significant role in the analysis.
In this work, we review the results of Refs [1]-[5] dedicated to the description of the early Universe cosmology induced by quantum and thermal effects in superstring theories. The present evolution of the Universe is described very accurately by the standard Lambda-CDM scenario, while very little is known about the early cosmological eras. String theory provides a consistent microscopic theory to account for such missing epochs. In our framework, the Universe is a torus filled with a gas of superstrings. We first show how to describe the thermodynamical properties of this system, namely energ…
We show global existence theorems for Gowdy symmetric spacetimes with type IIB stringy matter. The areal and constant mean curvature time coordinates are used. Before coming to that, it is shown that a wave map describes the evolution of this system.
We study massive spin-1/2 fermion production in nonsingular superstring cosmology, taking into account one-loop quantum corrections to a superstring effective action with dilaton and modulus fields. While no creation occurs in the massless limit, massive fermions can be produced by the existence of a time-dependent frequency. Due to the increase of the Hubble expansion rate during the modulus-driven phase, the occupation of number of fermions continues to grow until the point of the graceful exit, after which fermion creation ceases with the decrease of the Hubble rate.
We address the important issue of stabilizing the dilaton in the context of superstring cosmology. Scalar potentials which arise out of gaugino condensates in string models are generally exponential in nature. In a cosmological setting this allows for the existence of quasi scaling solutions, in which the energy density of the scalar field can, for a period, become a fixed fraction of the background density, due to the friction of the background expansion. Eventually the field can be trapped in the minimum of its potential as it leaves the scaling regime. We investigate this possibility in var…
We review the status of the fourth-order (quartic in the spacetime curvature) terms induced by superstrings/M-theory (compactified on a warped torus) in the leading order with respect to the Regge slope parameter, and study their (non-perturbative) impact on the evolution of the Hubble scale in the context of the four-dimensional FRW cosmology. After taking into account the quantum ambiguities in the definition of the off-shell superstring effective action, we propose the generalized Friedmann equations, find the existence of their (de Sitter) exact inflationary solutions without a spacetime s…
We review the cosmology induced by finite temperature and quantum effects on non-supersymmetric string models. We show the evolution is attracted to radiation-like solutions after the Hagedorn era and before the electroweak phase transition. This mechanism generates a hierarchy between the Planck mass and the supersymmetry breaking scale. A dynamical change of space-time dimension can take place.
We study moduli stabilization by thermal effects in the cosmological context. The implementation of finite temperature, which spontaneously breaks supersymmetry, induces an effective potential at one loop level. At the points where extra massless states appear in the string spectrum, the potential develops local minima whose depth depends on the temperature. Moduli attracted to these points acquire dynamical masses which decrease with cosmological evolution. This makes the coherent scalar oscillations dilute before nucleosynthesis, and the cosmological moduli problem is avoided. In particular,…
It is shown that the never ending oscillatory behaviour of the generic solution, near a cosmological singularity, of the massless bosonic sector of superstring theory can be described as a billiard motion within a simplex in 9-dimensional hyperbolic space. The Coxeter group of reflections of this billiard is discrete and is the Weyl group of the hyperbolic Kac-Moody algebra E$_{10}$ (for type II) or BE$_{10}$ (for type I or heterotic), which are both arithmetic. These results lead to a proof of the chaotic (``Anosov'') nature of the classical cosmological oscillations, and suggest a ``chaotic …
We study the cosmological implications of the one-loop terms in the string expansion. In particular, we find non-singular solutions which interpolate between a contracting universe and an expanding universe, and show that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies. In addition, we perform numerical calculations to show that the non-singular cosmologies do not require a careful choice of initial conditions, and estimate the likely magnitude of higher order terms in the string expansion.
This is the written version of a talk given at the Santa Barbara Workshop on Supersymmetry in December of 1995. It summarizes a collection of results on superstring cosmology obtained by the author and various collaborators, and contains some speculations about the resolution of the cosmological constant and vacuum selection problems in string theory.
In a universe whose elementary constituents are point particles there does not seem to be any obvious mechanism for avoiding the initial singularities in physical quantities in the standard model of cosmology. In contrast in string theory these singularities can be absent even at the level where spacetime is treated classically. This is a consequence of the basic degrees of freedom of strings in compact spaces, which necessitate a reinterpretation of what one means by a very small universe. We discuss the basic degrees of freedom of a string at the classical and quantum level, the minimum size…
Aspects of superstring cosmology are reviewed with an emphasis on the cosmological implications of duality symmetries in the theory. The string effective actions are summarized and toroidal compactification to four dimensions reviewed. Global symmetries that arise in the compactification are discussed and the duality relationships between the string effective actions are then highlighted. Higher-dimensional Kasner cosmologies are presented and interpreted in both string and Einstein frames, and then given in dimensionally reduced forms. String cosmologies containing both non-trivial Neveu-Schw…
We are presenting the basic ingredients of a stringy mechanism able to resolve both the Hagedorn instabilities of finite temperature superstrings as well as the initial singularity of the induced cosmology in arbitrary dimensions. These are shown to be generic in a large class of (4,0) type II superstring vacua, where non-trivial "gravito-magnetic" fluxes lift the Hagedorn instabilities of the thermal ensemble and the temperature duality symmetry is restored. This symmetry implies a universal maximal critical temperature. In all such models there are three characteristic regimes, each with a d…
We discuss various superstring effective actions and, in particular, their common sector which leads to the so-called pre-big-bang cosmology (cosmology in a weak coupling limit of heterotic superstring). Then, we review the main ideas of the Horava-Witten theory which is a strong coupling limit of heterotic superstring theory. Using the conformal relationship between these two theories we present Kasner asymptotic solutions of Bianchi type IX geometries within these theories and make predictions about possible emergence of chaos. Finally, we present a possible method of generating Horava-Witte…
Cosmological tensions in the era of precision cosmology: Insights from Tensions in Cosmology 2025
University of Sheffield（谢菲尔德大学）；University of Malta（马耳他大学）；National Observatory of Athens（雅典国家天文台）；University of Science and Technology of China（中国科学技术大学）；Universidad Católica del Norte（天主教主教大学）
Assuming that superstring theory is the fundamental theory which unifies all forces of Nature at the quantum level, I argue that there are key limitations on the applicability of effective field theory techniques in describing early universe cosmology.
Some spatially homogeneous Bianchi type I cosmological models filled with homogeneous ``electric'' $p$-form fields are shown to mimic the never-ending oscillatory behaviour of generic string cosmologies established recently. The validity of the ``Kasner-free-flights plus collisions-on-potential-walls'' picture is also illustrated in the case of known, non-chaotic, superstring solutions.
Making use of the T-duality symmetry of superstring theory, and of the double geometry from Double Field Theory, we argue that cosmological singularities of a homogeneous and isotropic universe disappear. In fact, an apparent big bang singularity in Einstein gravity corresponds to a universe expanding to infinite size in the dual dimensions.
In the context of brane gas cosmology in superstring theory, we show why it is impossible to simultaneously stabilize the dilaton and the radion with a general gas of strings (including massless modes) and D-branes. Although this requires invoking a different mechanism to stabilize these moduli fields, we find that the brane gas can still play a crucial role in the early universe in assisting moduli stabilization. We show that a modest energy density of specific types of brane gas can solve the overshoot problem that typically afflicts potentials arising from gaugino condensation.
Starting from an initial classical four dimensional flat background of the heterotic or type II superstrings, we are able to determine at the string one-loop level the quantum corrections to the effective potential due to the spontaneous breaking of supersymmetry by "geometrical fluxes". Furthermore, considering a gas of strings at finite temperature, the full "effective thermal potential" is determined, giving rise to an effective non-trivial pressure. The backreaction of the quantum and thermal corrections to the space-time metric as well as to the moduli fields induces a cosmological evolut…
Most current cosmological models of the very early universe are based on local point particle effective field theories coupled to gravity. I will discuss some conceptual limitations of this approach and argue that an improved description of the early universe needs to go beyond this framework. I will outline a couple of ideas based on superstring theory.
We consider different aspects of the problem of cosmological singularity such as the BKL oscillatory approach to singularity, the new features of the cosmological dynamics in the neighbourhood of the singularity in multidimensional and superstring cosmological models and their connections with such a modern branch of mathematics as infinite-dimensional Lie algebras. Besides, we consider some new types of cosmological singularities which were widely discussed during last decade after the discovery of the phenomenon of cosmic acceleration.
We consider braneworld scenarios including the leading correction to the Einstein-Hilbert action suggested by superstring theory, the Gauss-Bonnet term. We obtain and study the complete set of equations governing the cosmological dynamics. We find they have the same form as those in Randall-Sundrum scenarios but with time-varying four-dimensional gravitational and cosmological constants. Studying the bulk geometry we show that this variation is produced by bulk curvature terms parameterized by the mass of a black hole. Finally, we show there is a coupling between these curvature terms and matt…
We develop a concept of parallel existence of the ordinary (O) and hidden (H) worlds. We compare two cases: 1) when the hidden sector of the Universe is a mirror counterpart of the ordinary world, and 2) when it is a superstring-inspired shadow world described, in contrast to the mirror world, by a symmetry group (or by a chain of groups), which does not coincide with the ordinary world symmetry group. We construct a cosmological model assuming the existence of the superstring-inspired E_6 unification, broken at the early stage of the Universe to SO(10)\times U(1)_Z - in the O-world, and to SU…
We have developed a concept of parallel existence of the ordinary (O) and mirror (M), or shadow (Sh) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking $E_6\to SU(3)^3$ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. $E_6$ unification, inspired by superstring theory, restores the broken mirror parity at the scale $\sim 10^{18}$ GeV. With the aim to explain the tiny cosmological constant, in the second part we cons…
Field theories which violate the null energy condition (NEC) are of interest for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter $w<-1$. We discuss the consistency of two recently proposed models that violate the NEC. The ghost condensate model requires higher-order derivative terms in the action. It leads to a heavy ghost field and unbounded energy. We estimate the rates of particles decay and discuss possible mass limitations to protect stability of matter in the ghost condensate model. The nonlocal stringy …
We start with a particular cosmological model derived from type IIB supergravity theory with fluxes, where usually the dilaton is interpreted as a Quintessence field. Instead of that, in this letter we interpret the dilaton as the dark matter of the universe. With this alternative interpretation we find that in this supergravity model gives a similar evolution and structure formation of the universe compared with the $Λ$CDM 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 non-…
We revisit the cosmological history in the presence of light moduli by including possible thermal effects in the scalar potential. The well known cosmological moduli problem regards initial energy stored in the moduli due to a misalignment from its final position during inflation. We show that finite temperature corrections to the scalar potential, in general, induce similar effects and these are likely to overcome the ones from the misalignment. This changes important parameters like the preferred window for the numbers of e-fold during inflation and the final reheating temperature in a model…
