22 pages including 13 figures; minor changes in abstract and references; typos corrected, figure added, BPS equations added; version accepted for publication in Phys. Rev. D
(p,q)-strings are bound states of p F-strings and q D-strings and are predicted to form at the end of brane inflation. As such these cosmic superstrings should be detectable in the universe. In this paper we argue that they can be detected by the way that massive and massless test particles move in the space-time of these cosmic superstrings, in particular we study solutions to the geodesic equation in the space-time of field theoretical (p,q)-strings. The geodesics can be classified according to the test particle's energy, angular momentum and momentum in the direction of the string axis. We discuss how the change of the magnetic fluxes, the ratio between the symmetry breaking scale and the Planck mass, the Higgs to gauge boson mass ratios and the binding between the F- and D-strings, respectively, influence the motion of the test particles. While massless test particles can only move on escape orbits, a new feature as compared to the infinitely thin string limit is the existence of bound orbits for massive test particles. In particular, we observe that - in contrast to the space-time of a single Abelian-Higgs string - bound orbits for massive test particles in (p,q)-string space-times are possible if the Higgs boson mass is larger than the gauge boson mass. We also compute the effect of the binding between the p- and the q-string on observables such as the light deflection and the perihelion shift. While light deflection can also be caused by other matter distributions, the possibility of a negative perihelion shift seems to be a feature of finite width cosmic strings that could lead to the unmistakable identification of such objects. In Melvin space-times, which are asymptotically non-conical, massive test particles have to move on bound orbits, while massless test particles can only escape to infinity if their angular momentum vanishes.
We study field theoretical models for cosmic (p,q)-superstrings in a curved space-time. We discuss both string solutions, i.e. solutions with a conical deficit, but also so-called Melvin solutions, which have a completely different asymptotic behaviour. We show that globally regular gravitating (p,q)-strings exist only in a finite domain of the parameter space and study the dependence of the domain of existence on the parameters in the model. We find that due to the interaction between strings, the parameter range where string solution exist is wider than for non-interacting strings.
We develop methods by which cosmic superstring interactions can be studied in detail. These include the reconnection probability and emission of radiation such as gravitons or small string loops. Loop corrections to these are discussed, as well as relationships to $(p,q)$-strings. These tools should allow a phenomenological study of string models in anticipation of upcoming experiments sensitive to cosmic string radiation.
In these lectures, I review the current status of cosmic strings and cosmic superstrings. I first discuss topological defects in the context of Grand Unified Theories, focusing in particular in cosmic strings arising as gauge theory solitons. I discuss the reconciliation between cosmic strings and cosmological inflation, I review cosmic string dynamics, cosmic string thermodynamics and cosmic string gravity, which leads to a number of interesting observational signatures. I then proceed with the notion of cosmic superstrings arising at the end of brane inflation, within the context of brane-wo…
Using thermal quantization of geodesics confined under horizons and reasonable conjecture on massless modes, we evaluate quantum spectrum of Kerr black hole masses compatible with superstring symmetries.
Whilst standard field theoretic Cosmic Strings cannot end, Cosmic Superstrings can form three string junctions, at which each string ends. This opens up a new class of possible boundary conditions for such strings and we show that, at least when the junctions are close together, a string ending of two such junctions will generically have cusps. Cusps are of particular interest as they are strong emitters of radiation (both gravitational and particle) and hence are possible observables. The detection of cusps from Cosmic Superstrings between junctions would be a rare observational window into t…
I will briefly review the formation and evolution of cosmic superstrings, in the context of brane-world cosmological models within M-theory. These objects can play the role of cosmic strings, offering a variety of astrophysical consequences, which I will briefly discuss.
In the context of brane world scenario, cosmic superstrings can be formed in D-brane annihilation at the end of the brane inflationary era. The cosmic superstring network has a scaling solution and the characteristic scale of the network is proportional to the square root of the reconnection probability.
Brane inflation predicts the production of cosmic superstrings with tension 10^{-12}<Gμ<10^{-7}. Superstring theory predicts also the existence of a dilaton with a mass that is at most of the order of the gravitino mass. We show that the emission of dilatons imposes severe constraints on the allowed evolution of a cosmic superstring network. In particular, the detection of gravitational wave burst from cosmic superstrings by LIGO is only possible if the typical length of string loops is much smaller than usually assumed.
It is possible that superstrings, as well as other one-dimensional branes, could have been produced in the early universe and then expanded to cosmic size today. I discuss the conditions under which this will occur, and the signatures of these strings. Such cosmic superstrings could be the brightest objects visible in gravitational wave astronomy, and might be distinguishable from gauge theory cosmic strings by their network properties.
Cosmic superstrings are expected to be formed at the end of brane inflation, within the context of brane-world cosmological models inspired from string theory. By studying properties of cosmic suprestring networks, and comparing their phenomenological consequences against observational data, we aim at pinning down the successful and natural inflationary model and get an insight into the stringy description of our universe.
The existence of cusps on non-periodic strings ending on D-branes is demonstrated and the conditions, for which such cusps are generic, are derived. The dynamics of F-, D-string and FD-string junctions are investigated. It is shown that pairs of FD-string junctions, such as would form after intercommutations of F- and D-strings, generically contain cusps. This new feature of cosmic superstrings opens up the possibility of extra channels of energy loss from a string network. The phenomenology of cusps on such cosmic superstring networks is compared to that of cusps formed on networks of their f…
We explore the generic motion of cosmic (super)strings when the internal compact dimensions are warped, using the Klebanov-Strassler solution as a prototypical throat geometry. We find that there is no dynamical mechanism which localises the string at the tip of the throat, but rather that the motion seems to explore both internal and external degrees of freedom democratically. This indicates that cosmic (super)strings formed by inflationary brane-antibrane annihilation will have sufficient internal motion for the gravitational wave signals from the string network to be suppressed relative to …
The unique, conical spacetime created by cosmic strings brings about distinctive gravitational lensing phenomena. The variety of these distinctive phenomena is increased when the strings have non-trivial mutual interactions. In particular, when strings bind and create junctions, rather than intercommute, the resulting configurations can lead to novel gravitational lensing patterns. In this brief note, we use exact solutions to characterize these phenomena, the detection of which would be strong evidence for the existence of complex cosmic string networks of the kind predicted by string theory-…
In a simple reanalysis of the KKLMMT scenario, we argue that the slow roll condition in the D3-anti-D3-brane inflationary scenario in superstring theory requires no more than a moderate tuning. The cosmic string tension is very sensitive to the conformal coupling: with less fine-tuning, the cosmic string tension (as well as the ratio of tensor to scalar perturbation mode) increases rapidly and can easily saturate the present observational bound. In a multi-throat brane inflationary scenario, this feature substantially improves the chance of detecting and measuring the properties of the cosmic …
Motivated by recent developments in superstring theory in the cosmological context, we examine a field theory which contains string networks with 3-way junctions. We perform numerical simulations of this model, identify the length scales of the network that forms, and provide evidence that the length scales tend towards a scaling regime, growing in proportion to time. We infer that the presence of junctions does not in itself cause a superstring network to dominate the energy density of the early Universe.
The dominant method of energy loss by a loop of cosmic D-strings in models of warped brane inflation is studied. It is shown that the energy loss via Ramond-Ramond field radiation can dominate by many orders of magnitude over the energy radiation via gravitational wave emission. The ratio of these two energy loss mechanisms depends on the energy scale of inflation, the mass scale of string theory and whether it is a single-throat or a multi-throat inflationary scenario. This can have important consequences for the detection of cosmic superstrings in the near future. It is argued that the bound…
This paper has been withdrawn. The interpretation of tension spectrum of cosmic superstrings in terms of KK momentum is invalid as presented in section 2. A new paper based on calculations of the KK spectrum presented here will be submitted.
Cosmic superstrings are introduced to non-experts. First D-branes and $(p,q)$ strings are discussed. Then we explain how tachyon condensation in the early universe may have produced F, D and $(p,q)$ strings. Warped geometries which can render horizon sized superstrings relatively light are discussed. Various warped geometries including the deformed conifold in the Klebanov-Strassler geometry are reviewed and their warp factors are calculated. The decay rates for strings in the KS geometry are calculated and reasons for the necessity of orientifolds are reviewed. We then outline calculations of…
We study superstring theories on the Penrose limit of the enhancon geometry realized by the D(p+4)-branes wrapped on a K3 surface. We first examine the null geodesics with fixed radius in general brane backgrounds, which give solvable superstring theories with constant masses. In most cases, the superstring theories contain negative mass-squared. We clarify a condition that the world-sheet free fields have positive mass-squared. We then apply this condition to the enhancon geometry and find that the null geodesics with fixed radius exist only for p=0 case. They define the superstring theories …
Cosmic superstring loops generically contain strings of different tensions that meet at Y-junctions. These loops evolve non-periodically in time, and have cusps and kinks that interact with the junctions. We study the effect of junctions on the gravitational wave signal emanating from cosmic string cusps and kinks. We find that earlier results on the strength of individual bursts from cusps and kinks on strings without junctions remain largely unchanged, but junctions give rise to additional contributions to the gravitational wave signal coming from strings expanding at the speed of light at a…
We generalize the calculation of cosmic superstring reconnection probability to non-trivial backgrounds. This is done by modeling cosmic strings as wound tachyon modes in the 0B theory, and the spacetime effective action is then used to couple this to background fields. Simple examples are given including trivial and warped compactifications. Generalization to $(p,q)$ strings is discussed.
We analyze theoretical constraints on the consistency of brane inflation leading to cosmic superstring formation and on the subsequent radiation of these cosmic superstrings. We first investigate the implications of recently elucidated supergravity constraints on models of brane inflation. We show that both D3/D7 and D3/anti-D3 brane inflation are subject to non-trivial constraints. Both models can be shown to satisfy those constraints, but for the case of D3/D7 there may be important consequences for the inflationary mechanism. We then analyze the strong theoretical constraints on the types o…
Cosmic strings are predicted by many field-theory models, and may have been formed at a symmetry-breaking transition early in the history of the universe, such as that associated with grand unification. They could have important cosmological effects. Scenarios suggested by fundamental string theory or M-theory, in particular the popular idea of brane inflation, also strongly suggest the appearance of similar structures. Here we review the reasons for postulating the existence of cosmic strings or superstrings, the various possible ways in which they might be detected observationally, and the s…
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 propose a model with a U(1)_A x U(1)_B gauge symmetry which contains topological strings carrying magnetic flux under each of the U(1)s. By calculating the tension of the first few low energy strings we show that bound states, containing flux under each of the U(1)s, are stable against decay to their constituents of lower winding number. As the model contains only Abelian gauge symmetries this model provides a pragmatic solution to the numerical modelling of cosmic-superstrings. Whilst these defects do not satisfy a BPS bound we argue that they bear sufficient similarities to warrant such a…
Cosmic superstrings are produced at the end of brane inflation. Their properties are similar to cosmic strings arising in grand unified theories. Like cosmic strings they can give rise to a primordial magnetic field, as a result of vortical motions stirred in the ionised plasma by the gravitational pull of moving string segments. The resulting magnetic field is both strong enough and coherent enough to seed the galactic dynamo and explain the observed magnetic fields of the galaxies.
We compute the gravitational waveform produced by cosmic superstring reconnections. This is done by first constructing the superstring reconnection trajectory, which closely resembles that of classical, instantaneous reconnection but with the singularities smoothed out due to the string path integral. We then evaluate the graviton vertex operator in this background to obtain the burst amplitude. The result is compared to the detection threshold for current and future gravitational wave detectors, finding that neither bursts nor the stochastic background would be detectable by Advanced LIGO. Th…
We review the properties and evolution of strings networks containing both a spectrum of string tensions as well as Y-junctions, namely a point at which three different strings meet. Such a situation is expected in cosmic superstring networks, where the tension of the different strings is determined by the fundamental string tension $μ_F$ as well as the string coupling $g_s$. We discuss evolution of such a network, and the proliferation of kinks as they travel through junctions. These effects can leave observational signals on B-modes and gravitational waves, which can then in turn constrain t…
Axionic cosmic string solutions are investigated in a superstring motivated model with a pseudo-anomalous U(1) gauge symmetry. The inclusion of a gauge field and spatially varying dilaton allow local defect solutions with finite energy per unit length to be found. Fermion zero modes (whose presence is implied by supersymmetry) are also analysed. The corresponding fermion currents suggest strong cosmological bounds on the model. It is shown that the unusual form of the axion strings weakens these bounds. Other cosmological constraints on the underlying theory are also discussed.
Brane inflation in superstring theory ends when branes collide, initiating the hot big bang. Cosmic superstrings are produced during the brane collision. The cosmic superstrings produced in a D3-brane-antibrane inflationary scenario have a spectrum: $(p,q)$ bound states of $p$ fundamental (F) strings and $q$ D-strings, where $p$ and $q$ are coprime. By extending the velocity-dependent one-scale network evolution equations for abelian Higgs cosmic strings to allow a spectrum of string tensions, we construct a coupled (infinite) set of equations for strings that interact through binding and self…
We present the first complete Markov chain Monte Carlo analysis of cosmological models with evolving cosmic (super)string networks, using the unconnected segment model in the unequal-time correlator formalism. For ordinary cosmic string networks, we derive joint constraints on Lambda cold dark matter (CDM) and string network parameters, namely the string tension Gmu, the loop-chopping efficiency c_r and the string wiggliness α. For cosmic superstrings, we obtain joint constraints on the fundamental string tension Gmu_F, the string coupling g_s, the self-interaction coefficient c_s, and the vol…
We propose that the periodic fast radio bursts of FRB 180916.J0158+65 are sourced by axion emission (mass $m_{a} \sim 10^{-14}$ eV) from cosmic superstrings. Some of the emitted axions are converted to photons by magnetic fields as they travel along the line of sight to Earth. An impulsive burst of axion emission generates a photon signal typically lasting for milliseconds and varying with frequency in the observed manner. We find a range of parameters in our cosmic string network model consistent with the properties of FRB 180916.J0158+65. We suggest followup gravitational wave observations t…
We show that the late time rolling of the Cubic Superstring Field Theory (CSSFT) non-local tachyon in the FRW Universe leads to a cosmic acceleration with a periodic crossing of the w=-1 barrier. An asymptotic solution for the tachyon and Hubble parameter by linearizing the non-local equations of motion is constructed explicitly. For a small Hubble parameter the period of oscillations is a number entirely defined by the parameters of the CSSFT action.
In this talk we discuss aspects of TeV-scale gravitational collapse to black holes and string balls and their subsequent evaporation. Special emphasis is placed on the interplay of the string/black hole correspondence principle. These ideas are then explored in the context of cosmic ray physics. First, the potential for observing showers mediated by black holes or superstring excitations is examined. Next, existing data from neutrino telescopes are used to constrain the parameter space for the unseen dimensions of the universe. Finally, we close with a discussion of future prospects.
Cosmic superstrings of string theory differ from conventional cosmic strings of field theory. We review how the physical and cosmological properties of the macroscopic string loops influence experimental searches for these relics from the epoch of inflation. The universe's average density of cosmic superstrings can easily exceed that of conventional cosmic strings having the same tension by two or more orders of magnitude. The cosmological behavior of the remnant superstring loops is qualitatively distinct because the string tension is exponentially smaller than the string scale in flux compac…
We study the cosmic microwave background temperature and polarisation spectra sourced by multi-tension cosmic superstring networks. First we obtain solutions for the characteristic length scales and velocities associated with the evolution of a network of F-D strings, allowing for the formation of junctions between strings of different tensions. We find two distinct regimes describing the resulting scaling distributions for the relative densities of the different types of strings, depending on the magnitude of the fundamental string coupling g_s. In one of them, corresponding to the value of t…
We study the formation of three-string junctions between (p,q)-cosmic superstrings, and collisions between such strings and show that kinematic constraints analogous to those found previously for collisions of Nambu-Goto strings apply here too, with suitable modifications to take account of the additional requirements of flux conservation. We examine in detail several examples involving collisions between strings with low values of p and q, and also examine the rates of growth or shrinkage of strings at a junction. Finally, we briefly discuss the formation of junctions for strings in a warped …
We study the formation and evolution of an interconnected string network in large-scale field-theory numerical simulations, both in flat spacetime and in expanding universe. The network consists of gauge U(1) strings of two different kinds and their bound states, arising due to an attractive interaction potential. We find that the network shows no tendency to ``freeze'' and appears to approach a scaling regime, with all characteristic lengths growing linearly with time. Bound strings constitute only a small fraction of the total string length in the network.
We show that the naive application of the Kibble mechanism seriously underestimates the initial density of cosmic superstrings that can be formed during the annihilation of D-branes in the early universe, as in models of brane-antibrane inflation. We study the formation of defects in effective field theories of the string theory tachyon both analytically, by solving the equation of motion of the tachyon field near the core of the defect, and numerically, by evolving the tachyon field on a lattice. We find that defects generically form with correlation lengths of order M_s^{-1} rather than H^{-…
We model the behaviour of a network of interacting (p,q) strings from IIB string theory by considering a field theory containing multiple species of string, allowing us to study the effect of non-intercommuting events due to two different species crossing each other. This then has the potential for a string dominated Universe with the network becoming so tangled that it freezes. We give numerical evidence, explained by a one-scale model, that such freezing does not take place, with the network reaching a scaling limit where its density relative to the background increases with N, the number of…
In these lectures I discuss the possibility that superstrings of cosmic length might exist and be observable. I first review the original idea of cosmic strings arising as gauge theory solitons, and discuss in particular their network properties and the observational bounds that rule out cosmic strings as the principal origin of structure in our universe. I then consider cosmic superstrings, including the `fundamental' F-strings and also D-strings and strings arising from wrapped branes. I discuss the conditions under which these will exist and be observable, and ways in which different kinds …
We study the geodesic equations in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of these equations for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of ma…
We study the geodesic equation in the space-time of an Abelian-Higgs string and discuss the motion of massless and massive test particles. The geodesics can be classified according to the particles energy, angular momentum and linear momentum along the string axis. We observe that bound orbits of massive particles are only possible if the Higgs boson mass is smaller than the gauge boson mass, while massless particles always move on escape orbits. Moreover, neither massive nor massless particles can ever reach the string axis for non-vanishing angular momentum. We also discuss the dependence of…
We analyze the null geodesic equations in five dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equation emanating from central singularity for smooth initial distribution of dust. Moreover, we also show that the null geodesics can extend to null infinity in a certain case, which imply the violation of cosmic censorship conjecture.
The complete quantum theory of closed superstrings is constructed using string diagrams endowed with metric having constant curvature $-1$. The elementary string diagrams are equipped with the analytic local coordinates induced from the hyperbolic metric and a distribution of a set of picture changing operators constructed using the identities satisfied by the simple closed geodesics on a hyperbolic Riemann surface. However, a slight modification near the boundary of the string vertices is needed to make them satisfy the geometric condition imposed by the quantum Batalin-Vilkovisky master equa…
Towards the end of the brane inflationary epoch in the brane world, cosmic strings (but not texture, domain walls or monopoles) are copiously produced during brane collision. These cosmic strings are D$p$-branes with $(p-1)$ dimensions compactified. We elaborate on this prediction of the superstring theory description of the brane world. Using the data on the temperature anisotropy in the cosmic microwave background, we estimate the cosmic string tension $μ$ to be around $G μ\simeq 10^{-7}$. This in turn implies that the anisotropy in the cosmic microwave background comes mostly from inflation…
There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around $t\rightarrow 0$, where $t$ is the physical time. One is related to the past geodesic completeness of the inflationary trajectory due to the presence of a cosmological singularity, and the other one is related to the homogeneity condition required to inflate a local space-time patch of the universe. We will show that both the problems have a common origin, arising from how the causal structure of null and timelike geodesics are structur…
We study the geodesic motion of test particles in the space-time of two Abelian-Higgs strings interacting via their magnetic fields. These bound states of cosmic strings constitute a field theoretical realization of p-q-strings which are predicted by inflationary models rooted in String Theory, e.g. brane inflation. In contrast to previously studied models describing p-q-strings our model possesses a Bogomolnyi-Prasad-Sommerfield (BPS) limit. If cosmic strings exist it would be exciting to detect them by direct observation. We propose that this can be done by the observation of test particle m…
