We consider early time cosmic evolution in string gas cosmology dominated by open strings attached to D-branes. After reviewing statistical properties of open strings in D-brane backgrounds, we use dilaton-gravity equations to determine the string frame fields. Although, there are distinctions in the Hagedorn regime thermodynamics and dilaton coupling as compared to closed strings, it seems difficult to avoid Jeans instability and assume thermal equilibrium simultaneously, which is already a known problem for closed strings. We also examine characteristics of a possible subsequent large radius regime in this setup.
It is well known that one-loop free energy of closed strings diverges above the Hagedorn temperature. One explanation for this divergence is that a `winding mode' in the Euclidean time direction becomes tachyonic above the Hagedorn temperature. The Hagedorn transition of closed strings has been proposed as a phase transition via condensation of this winding tachyon. However, we have not known the stable minimum of the potential of this winding tachyon so far. On the other hand, we have previously calculated the finite temperature effective potential of open strings on D-brane--anti-D-brane pai…
Following the conjectured duality between near-horizon NS5-branes and little string theory, the string-corrected thermodynamics of near-horizon NS5-branes is studied and found to agree with the statistical thermodynamics of a 5+1 dimensional supersymmetric string theory near the Hagedorn temperature. Specifically, tree-level corrections to the temperature are argued to vanish, in accordance with the duality, while the one-loop string correction to the NS5-brane thermodynamics is shown to generate the correct temperature dependence of the entropy.
We demonstrate an inflationary solution to the cosmological horizon problem during the Hagedorn regime in the early universe. Here the observable universe is confined to three spatial dimensions (a three-brane) embedded in higher dimensions. The only ingredients required are open strings on D-branes at temperatures close to the string scale. No potential is required. Winding modes of the strings provide a negative pressure that can drive inflation of our observable universe. Hence the mere existence of open strings on branes in the early hot phase of the universe drives Hagedorn inflation, whi…
In order to study the thermodynamic properties of brane-antibrane systems, we compute the finite temperature effective potential of tachyon T in this system on the basis of boundary string field theory. At low temperature, the minimum of the potential shifts towards T=0 as the temperature increases. In the D9-antiD9 case, the sign of the coefficient of |T|^2 term of the potential changes slightly below the Hagedorn temperature. This means that a phase transition occurs near the Hagedorn temperature. On the other hand, the coefficient is kept negative in the Dp-antiDp case with p <= 8, and thus…
We examine the Hagedorn behavior of little string theory using its conjectured duality with near-horizon NS5-branes. In particular, by studying the string-corrected NS5-brane supergravity solution, it is shown that tree-level corrections to the temperature vanish, while the leading one-loop string correction generates the correct temperature dependence of the entropy near the Hagedorn temperature. Finally, the Hagedorn behavior of ODp-brane theories, which are deformed versions of little string theory, is considered via their supergravity duals.
In this paper, we investigate thermal equilibrium in string gas cosmology which is dominated by closed string.We consider two interesting regimes, Hagedorn and radiation regimes.We find that for short strings in small radius of Hagedorn regime very large amount of energy requested to have thermal equilibrium but for long strings in such system a few energy is sufficient to have thermal equilibrium. On the other hand in the large radius of Hagedorn regime, which pressure is not negligible, we obtain a relation between the energy and pressure in terms of cosmic time which is satisfied by thermal…
Banks, Fischler, Klebanov and Susskind have proposed a model for black hole thermodynamics based on the principle that the entropy is of order the number of particles at the phase transition point in a Boltzmann gas of D0-branes. We show that the deviations from Boltzmann scaling found in $d<6$ noncompact spatial dimensions have a simple explanation in the analysis of self-gravitating random walks due to Horowitz and Polchinski. In the special case of $d=4$ we find evidence for the onset of a phase transition in the Boltzmann gas analogous to the well-known Hagedorn transition in a gas of free…
We calculate the equation of state of a gas of strings at high density in a large toroidal universe, and use it to determine the cosmological evolution of background metric and dilaton fields in the entire large radius Hagedorn regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure in this regime is not vanishing but of O(1), while the equation of state is proportional to volume, which makes our solutions significantly different from previously published approximate solutions. For example, we are able to calculate the duration of the high-density "Hagedorn" phase, which …
We demonstrate an inflationary solution to the cosmological horizon problem during the Hagedorn regime in the early universe. Here the observable universe is confined to three spatial dimensions (a three-brane) embedded in higher dimensions. The only ingredients required are open strings on D-branes at temperatures close to the string scale. No potential is required. Winding modes of the strings provide a negative pressure that can drive inflation of our observable universe. Hence the mere existence of open strings on branes in the early hot phase of the universe drives Hagedorn inflation, whi…
We examine the cosmological effects of the Hagedorn phase in models where the observable universe is pictured as a D-brane. It is shown that, even in the absence of a cosmological constant, winding modes cause a negative `pressure' that can drive brane inflation of various types including both power law and exponential. We also find regimes in which the cosmology is stable but oscillating (a bouncing universe) with the Hagedorn phase softening the singular behavior associated with the collapse.
We present non-extremal generalizations of N_f=2N_c supergravity duals obtained by adding flavor branes to the Chamseddine-Volkov-Maldacena-Nunez background and taking their backreaction into account. For a particular range of parameters we obtain a one parameter family of analytic black hole solutions with regular horizons. These solutions have a temperature that is always above the Hagedorn temperature of little string theory. We find that including flavor branes and their backreaction increases the minimum temperature of these systems from T = 1/(4π), for the background without flavor, to T…
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.
We analyze the thermodynamics of NS 5-branes as the temperature approaches the NS 5-branes' Hagedorn temperature, and conclude that the dynamics of ``Little String Theory'' is a new universality class of interacting strings. First we point out how to vary the temperature of the near extremal solution by taking into account $g_s$ corrections. The Hagedorn temperature is shown to be a limiting temperature for the theory. We then compare the thermodynamics to that of a toy model made of free strings and find basic discrepancies. This suggests a need for a new class of string interactions. We sugg…
We study the behaviour of Polyakov confining string in the Georgi-Glashow model in three dimensions near confining-deconfining phase transition described in hep-th/0010201. In the string language, the transition mechanism is the decay of the confining string into D0 branes (charged W bosons of the Georgi-Glashow model). In the world-sheet picture the world-lines of heavy D0 branes at finite temperature are represented as world-sheet vortices of a certain type, and the transition corresponds to the condensation of these vortices. We also show that the ``would be'' Hagedorn transition in the con…
The Hagedorn transition in non-commutative open string theory (NCOS) is relatively simple because gravity decouples. For NCOS theories in no more than five spacetime dimensions, the Hagedorn transition is second order, and the high temperature phase involves long, nearly straight fundamental strings separating from the D-brane on which the NCOS theory is defined. Above five spacetime dimensions interaction effects become important below the Hagedorn temperature. Although this complicates studies of the transition, we believe that the high temperature phase again involves long strings liberated…
The partition function of BFSS matrix model is studied for two different classical backgrounds upto 1-loop level. One of the backgrounds correspond to a membrane wrapped around a compact direction and another to a localized cluster of $D0$-branes. It is shown there exist phase transitions between these two configurations - but only in presence of an IR cut-off. The low temperature phase corresponds to a string (wrapped membrane) phase and so we call this the Hagedorn phase transition. While the presence of an IR cut-off seemingly is only required for perturbative analysis to be valid, the phys…
We study the thermodynamics and the small fluctuations of a linear dilaton black hole, in an S-dual version of the near-horizon limit of type IIB NS5 branes. The thermodynamical analysis shows that the black hole is in a Hagedorn phase, with marginal stability. The dynamical analysis confirms that the speed of sound of the dual theory vanishes and that there are no evident instabilities at the level of supergravity. We clarify the physical meaning of some singularities of the retarded correlator that were thought to lead to instabilities.
It has recently been shown that a Hagedorn phase of string gas cosmology can 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. In this paper we compute the spectrum of tensor metric fluctuations (gravitational waves) in this scenario, and show that it is also nearly scale-invariant. However, whereas the spectrum of scalar modes has a small red-tilt, the spectrum of tensor modes has a small blue tilt, unlike what occurs in slow-roll inflation. This provides a possible obse…
We use the Matrix formalism to investigate what happens to strings above the Hagedorn temperaure. We show that it is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of $N$ D-0-branes arranged to form a string having $N$ units of light cone momentum. We find that at high temperatures the favoured phase is one where the string world sheet has disappeared and the low energy degrees of freedom consists of $N^2$ massless particles (``gluons''). The nature of the transition is very similar to the deconfinement transition in large-…
The thermodynamics of a gas of strings and D-branes near the Hagedorn transition is described by a coupled set of Boltzmann equations for weakly interacting open and closed long strings. The resulting distributions are dominated by the open string sector, indicating that D-branes grow to fill space at high temperature.
We compute semi-classically the Hawking emission for different types of black hole in type II string theory. In particular we analyze the thermal transition between NS5 branes and Little String Theory, finding compelling evidence for information recovering. We find that once the near horizon limit is taken the emission of a full family of models is exactly thermal even if back-reaction is taken into account. Consequently these theories are non-unitary and can not convey any information about the black hole internal states. It is argue that this behaviour matches the string theory expectations.…
String theory in Euclidean flat space with a spacelike linear dilaton contains a D1-brane which looks like a semi-infinite hairpin. In addition to its curved shape, this ``hairpin brane'' has a condensate of the open string tachyon stretched between its two sides. The tachyon smears the brane and shifts the location of its tip. The Minkowski continuation of the hairpin brane describes a D0-brane freely falling in a linear dilaton background. Effects that in Euclidean space are attributed to the tachyon condensate, give rise in the Minkowski case to a stringy smearing of the trajectory of the D…
We discuss the thermal properties of string gases propagating in various D-brane backgrounds in the weak-coupling limit, and at temperatures close to the Hagedorn temperature. We determine, in the canonical ensemble, whether the Hagedorn temperature is limiting or non-limiting. This depends on the dimensionality of the D-brane, and the size of the compact dimensions. We find that in many cases the non-limiting behaviour manifest in the canonical ensemble is modified to a limiting behaviour in the microcanonical ensemble and show that, when there are different systems in thermal contact, the en…
We numerically determine the time dependence of the scale factor from the lattice QCD equation of state, which can be used to define a QCD driven cosmology. We compare a lattice approach to QCD cosmology at late times with other models of the low temperature equation of state including the hadronic resonance gas model, Hagedorn model and AdS/CFT.
We investigate the thermodynamic properties of D-brane-anti-D-brane pairs and non-BPS D-branes on the basis of boundary string field theory. We calculate the finite temperature effective potential of N D-brane-anti-D-brane pairs in a non-compact background and in a toroidal background. In the non-compact background case, a phase transition occurs slightly below the Hagedorn temperature, and the D9-anti-D9 pairs become stable. Moreover, the total energy at the critical temperature is a decreasing function of N as long as the 't Hooft coupling is very small. This leads to the conclusion that a l…
Combining a variety of results in string theory and general relativity, a picture of the black hole interior is developed wherein spacetime caps off at an inner horizon, and the inter-horizon region is occupied by a Hagedorn gas of a very low tension state of fractionated branes. This picture leads to natural resolutions of a variety of puzzles concerning quantum black holes. Gravity Research Foundation 2015 Fourth Prize Award for Essays on Gravitation.
An sp-brane can be viewed as the creation and decay of an unstable D(p+1)-brane. It is argued that the decaying half of an sp-brane can be described by a variant of boundary Liouville theory. The pair creation of open strings by a decaying s-brane is studied in the minisuperspace approximation to the Liouville theory. In this approximation a Hagedorn-like divergence is found in the pair creation rate, suggesting the s-brane energy is rapidly transferred into closed string radiation.
We discuss marginal deformations of string vacua with Massive boson-fermion Degeneracy Symmetry (MSDS), in connection to the cosmological evolution of the Universe from an early non-geometrical era. In particular, we discuss recent results on the stringy mechanism that resolves both Hagedorn divergences and the Initial Singularity problem. Based on a talk given at the Workshop on Cosmology & Strings, Corfu Institute, Greece, Sept 10, 2010.
In the modified measure formulation the string tension appear as an additional dynamical degree of freedom and these tensions are not universal, but rather each string generates its own tension, which can have a different value for each string. We consider new background field that can couple to these strings, the tension scalar is capable of changing locally along the world sheet the value of the tension of the extended object. When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For t…
In order to study the thermodynamic properties of brane-antibrane systems in the toroidal background, we compute the finite temperature effective potential of tachyon T in this system on the basis of boundary string field theory. We first consider the case that all the radii of the target space torus are about the string scale. If the Dp-antiDp pair is extended in all the non-compact directions, the sign of the coefficient of |T|^2 term of the potential changes slightly below the Hagedorn temperature. This means that a phase transition occurs near the Hagedorn temperature. On the other hand, i…
We review our recent work on the low-energy actions and the realizations of strong-weak coupling dualities in non-perturbative phases of compact antisymmetric tensor field theories due to p-brane condensation. As examples we derive and discuss the confining string and confining membrane actions obtained from compact vector and tensor theories in 4D. We also mention the relevance of our results for the description of the Hagedorn phase transition of finite temperature strings.
We include the brane curvature scalar to study its cosmological implication in the brane world cosmology. This term is usually introduced to obtain the well-defined stress-energy tensor on the boundary of anti de Sitter-Schwarzschild space. Here we treat this as the perturbed term for cosmological purpose. We find corrections to the well-known equation of the brane cosmology. It contains new interesting terms which may play the important role in the brane cosmology.
The dynamics of a probe particle or wrapped brane moving in the two-dimensional Rindler space can be described by a time-dependent tachyon field theory. Using knowledge of tachyon condensation, we learn that the infalling brane gets thermalised and produces open string pairs at the Hagedorn temperature when entering into the near-horizon Rindler wedge. It is shown that the Hagedorn temperature of the infalling brane is equal to the Hawking temperature of the host black hole detected in the same time coordinate. The infalling brane will decay completely into closed strings, mainly massive modes…
We revisit the idea that the quantum dynamics of open strings ending on $N$ D3-branes in the large $N$ limit can be described at large `t Hooft coupling by classical closed string theory in the background created by the D3-branes in asymptotically flat spacetime. We study the resulting thermodynamics and compute the Hagedorn temperature and other properties of the D3-brane worldvolume theory in this regime. We also consider the theory in which the D3-branes are replaced by negative branes and show that its thermodynamics is well behaved. We comment on the idea that this theory can be thought o…
Recently, S. Antonini and B. Swingle builded a holographic model for braneworld cosmology by introducing an ``end-of-the-world" (ETW) brane moving in a charged black hole spactime. In this paper, we will show that a holographic description of braneworld cosmology is possible for a general black hole spacetime with a pure tension brane if one implements a mixed boundary condition on the ETW brane. As a simple example, we study AdS-Schwarzschild black holes and show that a sensible Euclidean braneworld solution is compatible with localization of gravity on the ETW brane.
In this paper we consider the ZZ brane decay in a D-dimensional background with a linear dilaton and a Liouville potential switched on. We mainly calculate the closed string emission rate during the decay process. For the case of a spacelike dilaton we find a similar Hagedorn behavior, in the closed string UV region, with the brane decay in the usual 26d and 2d bosonic string theory. This means that all of the energy of the original brane converts into outgoing closed strings. In the IR region the result is finite. We also give some comments about the case that the dilaton is null.
We consider the mirage cosmology by an unstable probe brane whose action is represented by BDI action with tachyon. We study how the presence of tachyon affects the evolution of the brane inflation. At the early stage of the brane inflation, the tachyon kinetic term can play an important role in curing the superluminal expansion in mirage cosmology.
We study the effect of the Dp-brane gas in string cosmology. When one kind of Dp-brane gas dominates, we find that the cosmology is equivalent to that of the Brans-Dicke theory with the perfect fluid type matter. We obtain $γ$, the equation of state parameter, in terms of p and the space-time dimension.
Within an adiabatic approximation, thermodynamical equilibrium and a small, nine dimensional, toroidal universe as initial conditions, we analyze the evolution of the dimensions in two different regimes: (i) the Hagedorn regime, with a single scale factor with a nearly constant time evolution (ii) an almost-radiation dominated regime, including the leading corrections due to the lightest Kaluza Klein and winding modes, in which for some initial conditions the large dimensions continue to expand and the small ones remain small.
We discuss the application of general features of intersecting brane model constructions in cosmology. In particular, we describe a scenario for D-term inflation which arises straightforwardly in IBM constructions wherein open non-vectorlike strings play the role of the inflaton. We also show that baryogenesis driven by hidden sector mixed anomalies can naturally arise in intersecting brane models.
Recently Verlinde proposed that gravity is an entropic force caused by information changes when a material body moves away from the holographic screen. In this note we apply this argument to brane cosmology, and show that the cosmological equation can be derived from this holographic scenario.
We discuss the brane cosmology in the 5D anti de Sitter Schwarzschild (AdSS$_5$) spacetime. A brane with the tension $σ$ is defined as the edge of an AdSS$_5$ space. We point out that the location of the horizon is an apparently, singular point at where we may not define an embedding of the AdSS$_5$ spacetime into the moving domain wall (MDW). We resolve this problem by introducing a radially infalling brane (RIB) in AdSS$_5$ space, where an apparent singularity turns out to be a coordinate one. Hence the CFT/FRW-cosmology is well-defined at the horizon. As an example, an universal Cardy formu…
We study the late-time behavior of a universe in the framework of brane gas cosmology. We investigate the evolution of a universe with a gas of supergravity particles and a gas of branes. Considering the case when different dimensions are anisotropically wrapped by various branes, we have derived Friedman-like equations governing the dynamics of wrapped and unwrapped subvolumes. We point out that the compact internal dimensions are wrapped by three or higher dimensional branes.
We construct a DGP inspired braneworld scenario where a scalar field non-minimally coupled to the induced Ricci curvature is present on the brane. We show that this model allows for an embedding of the standard Friedmann cosmology in the sense that the cosmological evolution of the background metric on the brane can be described by the standard Friedmann equation. The relation between our framework and the dark-energy formalism is explored.
We address the possibility of finding domain wall solutions from cosmological solutions in brane cosmology. We find first-order equations for corresponding cosmology/domain wall solutions induced on 3-branes. The quadratic term of energy density in the induced Friedmann equation plays a non-standard role and we discuss the way the standard cosmological and domain wall models are recovered as the brane tension becomes large and show how they can be described by four-dimensional supergravity action in such a limit. Finally, we show that gravity on the 3-brane is locally localized as one moves aw…
We derive exact solutions of the Einstein equations in the context of the Randall-Sundrum model with matter on the brane and in the bulk. We present two models in which the brane moves within a time-dependent bulk. We study the cosmological evolution on the brane. Our solutions display novel behaviour, such as an expansion driven only by the bulk matter and the appearance of a ``mirage'' dust component on the brane.
In these lecture notes I give a pedagogical introduction to the thermodynamics of ideal string gases. The computation of thermodynamic quantities in the canonical ensemble formalism will be shown in detail with explicit examples. Attention will be given mainly to the thermodynamical consequences of string degrees of freedom, where I will especially address i) the Hagedorn temperature, a critical temperature above which the canonical ensemble description breaks down, which can be the onset point of some instability of the string gas; ii) the phase structure arising from compactification, embodi…
We study cosmology on a BPS D3-brane evolving in the 10D SUGRA background describing a non-BPS brane. Initially the BPS brane is taken to be a probe whose dynamics we determine in the non-compact non-BPS background. The cosmology observed on the brane is of the FRW type with a scale factor $S(τ)$. In this mirage cosmology approach, there is no self-gravity on the brane which cannot inflate. Self-gravity is then included by compactifying the background space-time. The low energy effective theory below the compactification scale is shown to be bi-metric, with matter coupling to a different metri…
Large extra dimensions provide interesting extensions of our parameter space for gravitational theories. There exist now brane models which can perfectly reproduce standard four-dimensional Friedmann cosmology. These models are not motivated by observations, but they can be helpful in developing new approaches to the dimensionality problem in string theory. I describe the embedding of standard Friedmann cosmology in the DGP model, and in particular the realization of our current (dust+Lambda)-dominated universe in this model.
We consider brane cosmology studying the shortest null path on the brane for photons, and in the bulk for gravitons. We derive the differential equation for the shortest path in the bulk for a 1+4 cosmological metric. The time cost and the redshifts for photons and gravitons after traveling their respective path are compared. We consider some numerical solutions of the shortest path equation, and show that there is no shortest path in the bulk for the Randall-Sundrum vacuum brane solution, the linear cosmological solution of Binétruy, et al for $ω= -1, -{2/3}$, and for some expanding brane uni…
We calculate the thermal partition functions of open strings on the S-brane backgrounds (the bouncing or rolling tachyon backgrounds) both in the bosonic and superstring cases. According to hep-th/0302146, we consider the discretized temperatures compatible with the pure imaginary periodicity of tachyon profiles. The ``effective Hagedorn divergence'' is shown to appear no matter how low temperature is chosen (including zero-temperature). This feature is likely to be consistent with the large rate of open string pair production discussed in hep-th/0209090 and also emission of closed string mass…
We use a new, exact approach in calculating the energy density measured by an observer living on a brane embedded in a charged black hole spacetime. We find that the bulk Weyl tensor gives rise to non-linear terms in the energy density and pressure in the FRW equations for the brane. Remarkably, these take exactly the same form as the ``unconventional'' terms found in the cosmology of branes embedded in pure AdS, with extra matter living on the brane. Black hole driven cosmologies have the benefit that there is no ambiguity in splitting the braneword energy momentum into tension and additional…
Braneworld cosmology for a domain wall embedded in the charged (Anti)-de Sitter-Schwarzschildblack hole of the five--dimensional Einstein-Gauss-Bonnet-Maxwell theory is considered. The effective Friedmann equation for the brane is derived by introducing the necessary surface counterterms required for a well-defined variational principlein the Gauss--Bonnet theory and for the finiteness of the bulk space. The asymptotic dynamics of the brane cosmology is determined and it is found that solutions with vanishingly small spatial volume are unphysical. The finiteness of the bulk action is related t…
The cosmology of the Randall-Sundrum scenario for a positive tension brane in a 5-D Universe with localized gravity has been studied extensively recently. Here we extend it to more general situations. We consider the time-dependent situation where the two sides of the brane are different AdS/Schwarzschild spaces. We show that the expansion rate in these models during inflation could be larger than in brane worlds with compactified extra dimensions of fixed size. The enhanced expansion rate could lead to the production of density perturbations of substantially larger amplitude.
We study the effect of the solitonic degree of freedom in string cosmology following the line of Rama. The gas of solitonic p-brane is treated as a perfect fluid in a Brans-Dicke type theory. In this paper, we find analytic solutions for a few solvable cases of equation of states with general Brans-Dicke parameter $ω$ and study the cosmology of the solutions. In some cases the solutions are free from initial singularity.
We study the thermodynamics of open superstrings in the presence of $p$-dimensional D-branes. We get some finite temperature dualities relating the one-loop canonical free energy of open strings to the self-energy of D-branes at dual temperature. For the open bosonic string the inverse dual temperature is, as expected, the dual length under T-duality, $4π^{2}α^{'}/β$. On the contrary, for the $SO(N)$, type-I superstring the dual temperature is given by $β$-duality, $2π^{2}α^{'}/β$. We also study the emergence of the Hagedorn singularity in the dual description as triggered by the coupling of t…
