We explore the cosmological content of Salam-Sezgin six dimensional supergravity, and find a solution to the field equations in qualitative agreement with observation of distant supernovae, primordial nucleosynthesis abundances, and recent measurements of the cosmic microwave background. The carrier of the acceleration in the present de Sitter epoch is a quintessence field slowly rolling down its exponential potential. Intrinsic to this model is a second modulus which is automatically stabilized and acts as a source of cold dark matter with a mass proportional to an exponential function of the quintessence field (hence realizing VAMP models within a String context). However, any attempt to saturate the present cold dark matter component in this manner leads to unacceptable deviations from cosmological data -- a numerical study reveals that this source can account for up to about 7% of the total cold dark matter budget. We also show that (1) the model will support a de Sitter energy in agreement with observation at the expense of a miniscule breaking of supersymmetry in the compact space; (2) variations in the fine structure constant are controlled by the stabilized modulus and are negligible; (3) ``fifth''forces are carried by the stabilized modulus and are short range; (4) the long time behavior of the model in four dimensions is that of a Robertson-Walker universe with a constant expansion rate (w = -1/3). Finally, we present a String theory background by lifting our six dimensional cosmological solution to ten dimensions.
We provide the cosmological solutions for Randall-Sundrum models with the bulk energy-momentum $\hat T^5_5$ incorporated. It alters the Friedmann equation for the brane scale factor. We make a specific choice of $\hat T^5_5$ which is adjusted to stabilize the extra dimension. This makes it possible to compactify the extra dimension with a single positive tension brane, and this model provides a RS-type solution to the cosmological constant problem. When the same idea is applied to the RS model with two branes, the wrong sign of Friedmann equation for the negative tension brane can be resolved …
We examine the cosmology and hierarchy of scales in models with branes immersed in a five-dimensional curved spacetime subject to radion stabilization. When the radion field is time-independent and the inter-brane spacing is stabilized, the universe can naturally find itself in the radiation-dominated epoch. This feature is independent of the form of the stabilizing potential. We recover the standard Friedmann equations without assuming a specific form for the bulk energy-momentum tensor. In the models considered, if the observable brane has positive tension, a solution to the hierarchy proble…
We consider the cosmology and hierarchy of scales in models with branes immersed in a five-dimensional curved spacetime subject to radion stabilization. The universe naturally find itself in the radiation-dominated epoch when the inter-brane spacing is static and stable, independent of the form of the stabilizing potential. We recover the standard Friedmann equations without assuming a specific form for the bulk energy-momentum tensor. We address the hierarchy problem in the context of a quartic and exponential stabilizing potential, and find that in either case the presence of a negative tens…
We show that there exist massive perturbative states of the ten dimensional Green-Schwarz closed superstring that are stabilized against collapse due to presence of fermionic zero modes on its worldsheet. The excited fermionic degrees of freedom backreact on the spacetime motion of the string in the same way as a neutral persistent current would, rendering these string loops stable. We point out that the existence of these states could have important consequences as stable loops of cosmological size as well as long lived states within perturbative string theory.
We give an overview of the status of string cosmology. We explain the motivation for the subject, outline the main problems, and assess some of the proposed solutions. Our focus is on those aspects of cosmology that benefit from the structure of an ultraviolet-complete theory.
These notes provide a brief introduction to modern cosmology, focusing primarily on theoretical issues. Some attention is paid to aspects of potential interest to students of string theory, on both sides of the two-way street of cosmological constraints on string theory and stringy contributions to cosmology. Slightly updated version of lectures at the 1999 Theoretical Advanced Study Institute at the University of Colorado, Boulder.
String gas cosmology is a string theory-based approach to early universe cosmology which is based on making use of robust features of string theory such as the existence of new states and new symmetries. A first goal of string gas cosmology is to understand how string theory can effect the earliest moments of cosmology before the effective field theory approach which underlies standard and inflationary cosmology becomes valid. String gas cosmology may also provide an alternative to the current standard paradigm of cosmology, the inflationary universe scenario. Here, the current status of strin…
We study the stability of extra dimensions in string gas cosmology at late times. Vacuum energy and, interestingly, baryons lead to decompactification after they become dynamically important. The string gas can stabilise the effect of baryons, but not that of vacuum energy. However, we find that the interplay of baryons and strings can lead to acceleration in the visible dimensions, without the need for vacuum energy.
String gas cosmology is an approach towards studying the effects of superstring theory on early universe cosmology which is based on new symmetries and new degrees of freedom of string theory. Within this context, it appears possible to stabilize the moduli which describe the size and shape of the extra spatial dimensions without the need of introducing many extra tools such as warping and fluxes. In this lecture, the recent progress towards moduli stabilization in string gas cosmology is reviewed, and outstanding problems for the scenario are discussed.
The weakly coupled vacuum of $E_8\otimes E_8$ heterotic string theory remains an attractive scenario for phenomenolgy and cosmology. The particle spectrum is reviewed and the issues of gauge coupling unification, dilaton stabilization and modular cosmology are discussed. A specific model for condensation and supersymmetry breaking, that respects known constraints from string theory and is phenomenologically viable, is described.
New Developments in String Gravity and String Cosmology are reported: 1-String driven cosmology and its Predictions. 2-The primordial gravitational wave background in string cosmology. 3-Non-singular string cosmologies from Exact Conformal Field Theories. 4-Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time, 5-Hawking Radiation in String Theory and the String Phase of Black Holes. 6-New Dual Relation between Quantum Field Theory regimes and String regimes in Curved Backgrounds, and the 'QFT/String Tango'. 7- New Coherent String States and Minimal Uncertainty …
In string gas cosmology, extra dimensions are stabilised by a gas of strings. In the matter-dominated era, competition between matter pushing the extra dimensions to expand and the string gas pulling them back can lead to oscillations of the extra dimensions and acceleration in the visible dimensions. We fit this model to supernova data, taking into account the Big Bang Nucleosynthesis constraint on the energy density of the string gas. The fit to the Union set of supernova data is acceptable, but the fit to the ESSENCE data is poor.
We study the role of rolling tachyons in the cosmological model with dilatonic gravity. In the string frame, flat space solutions of both initial-stage and late-time are obtained in closed form. In the Einstein frame, we show that every expanding solution is decelerating.
An overview is presented of some cosmological aspects of string theory. Recent developments are emphasised, especially the attempts to derive inflation or alternatives to inflation from the dynamics of branes in string theory. Time dependent backgrounds with potential cosmological implications, such as those provided by negative tension branes and S-branes and the rolling string tachyon are also discussed.
We consider an ensemble of closed strings in a compact space with stable one cycles and compute the speed of sound resulting from string thermodynamics. Possible applications to the issue of Jeans instability in string gas cosmology are mentioned.
We begin the study of a class of string-motivated effective supergravity theories in light of current data from the CERN Large Hadron Collider (LHC). The case of heterotic string theory, in which the dilaton is stabilized via non-perturbative corrections to the Kahler metric, will be considered first. This model is highly constrained and therefore predictive. We find that much of the reasonable parameter space afforded to the model -- representing the strong dynamics of a presumed gaugino condensation in the hidden sector -- is now observationally disfavored by the LHC results. Most of the the…
We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.
String theoretic axion is a prime candidate for the QCD axion solving the strong CP problem. For a successful realization of the QCD axion in string theory, one needs to stabilize moduli including the scalar partner (saxion) of the QCD axion, while keeping the QCD axion unfixed until the low energy QCD instanton effects are turned on. We note that a simple generalization of KKLT moduli stabilization provides such set-up realizing the axion solution to the strong CP problem. Although some details of moduli stabilization are different from the original KKLT scenario, this set-up leads to the mir…
Axions are produced during a period of dilaton-driven inflation by amplification of quantum fluctuations. We show that for some range of string cosmology parameters and some range of axion masses, primordial axions may constitute a large fraction of the present energy density in the universe in the form of cold dark matter. Due to the periodic nature of the axion potential energy density fluctuations are strongly suppressed. The spectrum of primordial axions is not thermal, allowing a small fraction of the axions to remain relativistic until quite late.
In spite of the phenomenological successes of the inflationary universe scenario, the current realizations of inflation making use of scalar fields lead to serious conceptual problems which are reviewed in this lecture. String theory may provide an avenue towards addressing these problems. One particular approach to combining string theory and cosmology is String Gas Cosmology. The basic principles of this approach are summarized.
In spite of the phenomenological successes of the inflationary universe scenario, the current realizations of inflation making use of scalar fields lead to serious conceptual problems which are reviewed in this lecture. String theory may provide an avenue towards addressing these problems. One particular approach to combining string theory and cosmology is String Gas Cosmology. The basic principles of this approach are summarized.
The interplay between string theory and cosmology is very promising. Since string theory will yield a quantum theory of space-time and unify all forces of nature, it has the potential of addressing many of the conceptual problems of the current models of early Universe cosmology. In turn, cosmology is the most obvious testing ground in the effort to construct non-perturbative string theory, and can provide the crucial connection between theory and experiment/observation.
Super--inflation driven by dilaton/moduli kinetic energy is naturally realized in compactified string theory. Discussed are selected topics of recent development in string inflationary cosmology: kinematics of super-inflation, graceful exit triggered by quantum back reaction, and clasical and quantum power spectra of density and metric perturbations.
The purpose of this review is to discuss recent developments occurring at the interface of cosmology with string and M-theory. We begin with a short review of 1980s string cosmology and the Brandenberger-Vafa mechanism for explaining spacetime dimensionality. It is shown how this scenario has been modified to include the effects of p-brane gases in the early universe. We then introduce the Pre-Big-Bang scenario (PBB), Hořava-Witten heterotic M-theory and the work of Lukas, Ovrut and Waldram, and end with a discussion of large extra dimensions, the Randall-Sundrum model and Brane World cosmolog…
It has recently been shown that a Hagedorn phase of string gas cosmology may provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion. A distinctive signature of this structure formation scenario would be a slight blue tilt of the spectrum of gravitational waves. In this paper we give more details of the computations leading to these results.
Classical string cosmology consists of two branches related to each other by scale-factor duality: a super-inflation branch and a Friedmann-Robertson-Walker (FRW) branch. Curvature and string coupling singularity separates the two branches, hence posing `graceful exit problem' to super-inflationary string cosmology. In an exactly soluble two-dimensional compactification model it is shown that quantum back reaction retards curvature and string coupling growth and connects the super-inflation branch to the FRW branch without encountering a singularity. This may offer an attractive solution to th…
The general properties of the gravity wave backgrounds of cosmological origin are reviewed and briefly discussed, with emphasis on the relic background expected from an early pre-big bang phase typical of string cosmology models.
We derive the 4D low energy effective field theory for a closed string gas on a time dependent FRW background. We examine the solutions and find that although the Brandenberger-Vafa mechanism at late times no longer leads to radion stabilization, the radion rolls slowly enough that the scenario is still of interest. In particular, we find a simple example of the string inspired dark matter recently proposed by Gubser and Peebles.
Production of spin 1/2 fermions and gravitinos by the standard mechanism of amplification of quantum fluctuations during the dilaton-driven inflation phase in models of string cosmology is highly suppressed. Constraints on string cosmology models from gravitational production of gravitinos, contrary to expectations, are similar to constraints on other models.
We provide the first complete analysis of cosmological evolution in the Randall-Sundrum model with stabilized dilaton. We give the exact expansion law for matter densities on the two branes with arbitrary equations of state. The effective four-dimensional theory leads to standard cosmology at low energy. The limit of validity of the low energy theory and possible deviations from the ordinary expansion law in the high energy regime are finally discussed.
String gas cosmology is rewritten in the Einstein frame. In an effective theory in which a gas of closed strings is coupled to a dilaton gravity background without any potential for the dilaton, the Hagedorn phase which is quasi-static in the string frame corresponds to an expanding, non-accelerating phase from the point of view of the Einstein frame. The Einstein frame curvature singularity which appears in this toy model is related to the blowing up of the dilaton in the string frame. However, for large values of the dilaton, the toy model clearly is inapplicable. Thus, there must be a new s…
I review some aspects of non-critical strings in connection with Lorentz-Invariance violating approaches to quantum gravity. I also argue how non-critical strings may provide a unifying framework where string Cosmology and quantum gravity may be tackled together.
Using general arguments we determine the allowed region for the end point frequency and the peak energy density of the stochastic background of gravity waves expected in string cosmology. We provide an accurate estimate of the minimal experimental sensitivity required to detect a signal in the Hz to GHz range.
Inflationary cosmology has provided a predictive and phenomenologically very successful scenario for early universe cosmology. Attempts to implement inflation using scalar fields, however, lead to models with serious conceptual problems. I will discuss some of the problems, explain why string theory could provide solutions to a subset of these problems, and give a brief overview of ``string gas cosmology'', one of the approaches to merge string theory and early universe cosmology.
We study string-gas cosmology in dilaton gravity, inspired by the fact that it naturally arises in a string theory context. Our main interest is the thermodynamical treatment of the string-gas and the resulting implications for the cosmology. Within an adiabatic approximation, thermodynamical equilibrium and a small, toroidal universe as initial conditions, we numerically solve the corresponding equations of motions in two different regimes describing the string-gas thermodynamics: (i) the Hagedorn regime, with a single scale factor, and (ii) an almost-radiation dominated regime, which include…
A long-standing problem of theoretical physics is the exceptionally small value of the cosmological constant $Λ\sim 10^{-120}$ measured in natural Planckian units. Here we derive this tiny number from a toroidal string cosmology based on closed strings. In this picture the dark energy arises from the correlation between momentum and winding modes that for short distances has an exponential fall-off with increasing values of the momenta.The freeze-out by the expansion of the background universe for these transplanckian modes may be interpreted as a frozen condensate of the closed-string modes i…
String cosmology is revisited from cosmological viewpoint of holographic principle put forward by `t Hooft, and by Fischler and Susskind. It is shown that the holography requires existence of a `graceful exit' mechanism, which renders the Universe nonsingular by connecting pre- and post-big bang phases smoothly. It is proven that flat Universe is consistent with the holography only if it starts with an absolutely cold and vacuous state. Particle entropy produced during the `graceful exit' apparently saturates the holography bound. Open Universe can always satisfy the holography no matter what …
After 25 years of its existence, inflationary theory gradually becomes the standard cosmological paradigm. However, we still do not know which of the many versions of inflationary cosmology will be favored by the future observational data. Moreover, it may be quite nontrivial to obtain a natural realization of inflationary theory in the context of the ever changing theory of all fundamental interactions. In this paper I will describe the history and the present status of inflationary cosmology, including recent attempts to implement inflation in the context of string theory.
We reexamine the graceful exit problem in the Pre-Big-Bang inflationary scenario. The dilaton-gravity action is generalized by adding the axion and a general axion/dilaton potential. We provide a phase space analysis of the dynamics which leads us to extend the previous no-go theorem and rule out the branch change necessary for graceful exit in this context.
The standard electroweak theory admits a string solution, the Z string, in which only the electrically neutral Higgs fields are excited. This solution is unstable at zero temperature: Z strings decay by exciting charged Higgs modes. In the early Universe, however, there was a long period during which the Higgs particles were out of equilibrium but the photon field was in thermal equilibrium. We show that in this phase Z strings are stabilized by interactions of the charged Higgs modes with the photons. In a first temperature range immediately below the electroweak symmetry breaking scale, the …
String Gas Cosmology is a model of the evolution of the very early universe based on fundamental principles and key new degrees of freedom of string theory which are different from those of point particle field theories. In String Gas Cosmology the universe starts in a quasi-static Hagedorn phase during which space is filled with a gas of highly excited string states. Thermal fluctuations of this string gas lead to an almost scale-invariant spectrum of curvature fluctuations. Thus, String Gas Cosmology is an alternative to cosmological inflation as a theory for the origin of structure in the u…
It has been pointed out that cosmic string solutions can exist in gauge field theories with broken symmetry even when $π_1(G/H)$ is trivial. The stability of such semilocal defects is not guaranteed by topology and depends on dynamical considerations. In the literature it has been tacitly assumed that if stable, such strings would form in the Early Universe in a manner analogous to the formation of a network of more robust topologically-stable strings. In this paper we find that except for unnaturally small values of the correlation length, a network of semilocal strings does not form. Instead…
We review the current observational status of string cosmology when confronted with experimental datasets. We begin by defining common observational parameters and discuss how they are determined for a given model. Then we review the observable footprints of several string theoretic models, discussing the significance of various potential signals. Throughout we comment on present and future prospects of finding evidence for string theory in cosmology, and on significant issues for the future.
In this Note we study supersymmetry breaking via gaugino condensation in string gas cosmology. We show that the same gaugino condensate which is introduced to stabilize the dilaton breaks supersymmetry. We study the constraints on the scale of supersymmetry breaking which this mechanism leads to.
In String Gas Cosmology, the simplest shape modulus fields are naturally stabilized by taking into account the presence of string winding and momentum modes. We determine the resulting effective potential for these fields and show that it obeys the de Sitter conjecture, one of the swampland criteria for effective field theories to be consistent with superstring theory.
The origin of dark matter in the universe may be weakly interacting scalar particles produced by amplification of quantum fluctuations during a period of dilaton-driven inflation. We present two interesting cases, the case of small fluctuations, and the resulting nonthermal spectrum, and the case of large fluctuations of a field with a periodic potential, the QCD axion.
I discuss some (unconventional) aspects of String Cosmology of relevance to supersymmetric dark matter searches at the Large Hadron Collider (LHC) at CERN. In particular, I analyse the role of time-dependent dilaton fields in relaxing some of the stringent constraints that characterise minimal supersymmetric models in standard cosmology. I also study briefly CPT-violating aspects of brane Universe models with space-time brane defects at early epochs and their potential relevance to the observed Baryon Asymmetry.
We review the status of String Gas Cosmology after the 2015 Planck data release. String gas cosmology predicts an almost scale-invariant spectrum of cosmological perturbations with a slight red tilt, like the simplest inflationary models. It also predicts a scale-invariant spectrum of gravitational waves with a slight blue tilt, unlike inflationary models which predict a red tilt of the gravitational wave spectrum. String gas cosmology yields two consistency relations which determine the tensor to scalar ratio and the slope of the gravitational wave spectrum given the amplitude and tilt of the…
We study small perturbations around the exactly marginal time-dependent string configuration of [1], and demonstrate the lack of the appropriate linearization. This implies that this configuration is an isolated fixed point of the $α^{'}$ flow in the pertinent space of theories.
We critically assess the twin prospects of describing the observed universe in string theory, and using cosmological experiments to probe string theory. For the purposes of this short review, we focus on the limitations imposed by our incomplete understanding of string theory. After presenting an array of significant obstacles, we indicate a few areas that may admit theoretical progress in the near future.
Starting from an exact (in the Regge slope alpha') functional method for a bosonic stringy sigma-model, we investigate four-dimensional cosmological string solutions in graviton, dilaton and antisymmetric tensor backgrounds, compatible with world-sheet conformal invariance, and valid beyond perturbative expansions in powers of alpha'. The antisymmetric tensor field, playing the role of an axion in the four-dimensional target space time, leads to spatial anisotropies of the emergent Robertson-Walker expanding Universe, and, upon coupling the system to the electromagnetic field, it results in no…
We compute the running of the spectrum of cosmological perturbations in String Gas Cosmology, making use of a smooth parametrization of the transition between the early Hagedorn phase and the later radiation phase. We find that the running has the same sign as in simple models of single scalar field inflation. Its magnitude is proportional to $(1 - n_s)$ ($n_s$ being the slope index of the spectrum), and it is thus parametrically larger than for inflationary cosmology, where it is proportional to $(1 - n_s)^2$.
We introduce a very early universe model based on the thermodynamics of a gas of closed strings in a background which is non-perturbative in $α'$. Upon considering the fully $α'$-corrected equations extended to include certain anisotropic cosmological backgrounds, we describe the evolution of the system in three different stages parametrized by the gas' equation of state. Using standard string thermodynamical arguments, we start with an isotropic 10-dimensional universe inside the string scale and evolve it towards a universe with four large spacetime dimensions and six stabilized internal dim…
A class of grand unified theories with symmetry breaking scale of order $10^{16} GeV$ have a Higgs particle with mass in the $TeV$ scale. The cosmology of such theories is very different from usual. We study the cosmic strings obtained in such theories. These strings are much fatter than usual and their mass per unit length is reduced, resulting in a significant reduction in their cosmological effects. We also study the temperature evolution of such models.
Recently, all duality invariant $α'$-corrections to the massless NS-NS sector of string theory on time-dependent backgrounds were classified and the form of their contribution to the action were calculated. In this paper we introduce matter sources in the resulting equations of motion in an O$(d,d)$ covariant way. We show that either starting with the corrected equations and sourcing them with matter or considering corrections to the matter sourced lowest order equations give the same set of equations that defines string cosmology to all orders in $α'$. We also discuss perturbative and non-per…
We continue the study of a class of string-motivated effective supergravity theories in light of current data from the CERN Large Hadron Collider (LHC). In this installment we consider Type IIB string theory compactified on a Calabi-Yau orientifold in the presence of fluxes, in the manner originally formulated by Kachru, et al. We allow for a variety of potential uplift mechanisms and embeddings of the Standard Model field content into D3 and D7 brane configurations. We find that an uplift sector independent of the Kahler moduli, as is the case with anti-D3 branes, is inconsistent with data un…
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.
The discrepancy in measurements of the Hubble constant indicates new physics in dark energy, dark matter, or both. Drawing inspiration from string theory, we explore possible solutions to overcome the $H_0$ problem. We investigate the interplay between the cosmological determination of $ΔN_{\rm eff}{}$ and $Z'{}$ searches at the LHC Run3.
