Cosmic Superstrings Research Articles

Gravitational waves from cosmic superstrings and gauge strings

We perform a phenomenological comparison of the gravitational wave (GW) spectrum expected from cosmic gauge string networks and superstring networks comprised of multiple string types. We show how violations of scaling behavior and the evolution of the number of relativistic degrees of freedom in the early Universe affect the GW spectrum. We derive simple analytical expressions for the GW spectrum from superstrings and gauge strings that are valid for all frequencies relevant to pulsar timing arrays (PTAs) and laser interferometers. We analyze the latest data from PTAs and show that superstring networks are consistent with 32 nHz data from NANOGrav, but are excluded by 3.2 nHz data at 3σ unless the string coupling gs< 0.2 or the strings evolve in only about 10% of the volume of the higher-dimensional space. We also point out that while gauge string networks are excluded by NANOGrav-15 data at 3σ, they are completely compatible with EPTA and PPTA data. Finally, we study correlations between GW signals at PTAs and laser interferometers.

Cosmological Background Interpretation of Pulsar Timing Array Data.

We discuss the interpretation of the detected signal by pulsar timing array (PTA) observations as a gravitational wave background of cosmological origin. We combine NANOGrav 15-years and EPTA-DR2new datasets and confront them against backgrounds from supermassive black hole binaries (SMBHBs), and cosmological signals from inflation, cosmic (super)strings, first-order phase transitions, Gaussian and non-Gaussian large scalar fluctuations, and audible axions. We find that scalar-induced, and to a lesser extent audible axion and cosmic superstring signals, provide a better fit than SMBHBs. These results depend, however, on modeling assumptions, so further data and analysis are needed to reach robust conclusions. Independently of the signal origin, the data strongly constrain the parameter space of cosmological signals, for example, setting an upper bound on primordial non-Gaussianity at PTA scales as |f_{nl}|≲2.34 at 95%C.L.

The D3-D¯3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D}3 $$\\end{document}-brane inflation model revisited

Combining previous results, the D3-D¯3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D}3 $$\\end{document}-brane pair potential U(T, ϕ) is presented here, where the inflaton ϕ measures the separation between the D3-brane and the anti-D3-brane, and the complex scalar mode T becomes tachyonic when the annihilation of the branes happens as they collide. Besides the distinct form of the inflationary potential, this hybrid inflationary model differs from a typical hybrid model in 2 important aspects: (1) U(T, ϕ) becomes complex when T becomes tachyonic, where Im U(T, ϕ) plays an important role in the dynamics towards the end of the inflationary epoch; (2) tunnelling during the inflationary epoch can happen; this is particularly relevant if there are multiple D3-D¯3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D}3 $$\\end{document}-brane pairs in different warped throats. Besides the production of cosmic superstrings, the model offers the possibility of first order phase transition that may generate large enough density perturbation for the primordial black hole production. Stochastic gravitational wave background from these sources remain to be fully investigated.

Cosmic superstrings revisited in light of NANOGrav 15-year data

Cosmic superstrings revisited in light of NANOGrav 15-year data

Multitension strings in high-resolution U(1)×U(1) simulations

Topological defects are a fossil relic of early Universe phase transitions, with cosmic strings being the best motivated example. While in most cases one studies Nambu-Goto or Abelian-Higgs strings, one also expects that cosmologically realistic strings should have additional degrees of freedom in their worldsheets, one specific example being superstrings from Type IIB superstring theory. Here we continue the scientific exploitation of our recently developed multi-GPU field theory cosmic strings code to study the evolution of U(1)$\times$U(1) multitension networks, which are a numerically convenient proxy: these contain two lowest-tension strings networks able to interact and form bound states, providing a convenient first approximation to the behaviour expected from cosmic superstrings. (...) We rely on the largest field theory simulations of this model so far, specifically $4096^3$, $\Delta x = 0.5$ boxes. We present robust evidence of scaling for the lightest strings, measured through a complete and self-consistent set of correlation length and velocity diagnostics. We also find a linearly growing average length of the bound state segments, consistent with a scaling behaviour. (In previously reported lower-resolution simulations, such behaviour had only been identified with carefully engineered initial conditions, rich in those segments.) Finally, while we see no evidence of a large population of bound states forming at early stages of the network evolution, we do present tentative evidence for an asymptotic constant value of the fraction of bound states, with this value being different in the radiation and the matter eras. Our work demonstrates that our GPU-accelerated field theory code can by successfully extended beyond the simple Abelian-Higgs approximation, and enables future detailed studies of realistic string networks and of their observational signatures.

Comparison of cosmic string and superstring models to NANOGrav 12.5-year results

We compare the spectrum of the stochastic gravitational wave background produced in several models of cosmic strings with the common-spectrum process recently reported by NANOGrav. We discuss theoretical uncertainties in computing such a background, and show that despite such uncertainties, cosmic strings remain a good explanation for the potential signal, but the consequences for cosmic string parameters depend on the model. Superstrings could also explain the signal, but only in a restricted parameter space where their network behavior is effectively identical to that of ordinary cosmic strings.

Abelian–Higgs cosmic string evolution with multiple GPUs

Topological defects form at cosmological phase transitions by the Kibble mechanism. Cosmic strings and superstrings can lead to particularly interesting astrophysical and cosmological consequences, but this study is currently limited by the availability of accurate numerical simulations, which in turn is bottlenecked by hardware resources and computation time. Aiming to eliminate this bottleneck, in recent work we introduced and validated a GPU-accelerated evolution code for local Abelian–Higgs strings networks. While this leads to significant gains in speed, it is still limited by the physical memory available on a graphical accelerator. Here we report on a further step towards our main goal, by implementing and validating a multiple GPU extension of the earlier code, and further demonstrate its good scalability, both in terms of strong and weak scaling. A 81923 production run, using 4096 GPUs, runs in 33.2 min of wall-clock time on the Piz Daint supercomputer.

Prospects of cosmic superstring detection through microlensing of extragalactic point-like sources

ABSTRACT The existence of cosmic superstrings may be probed by astronomical time domain surveys. When crossing the line of sight to point-like sources, strings produce a distinctive microlensing signature. We consider two avenues to hunt for a relic population of superstring loops: frequent monitoring of (1) stars in Andromeda, lensed by loops in the haloes of the Milky-Way and Andromeda and (2) supernovae at cosmological distances, lensed by loops in the intergalactic medium. We assess the potential of such experiments to detect and/or constrain strings with a range of tensions, 10−15 ≲ Gμ/c2 ≲ 10−6. The practical sensitivity is tied to cadence of observations which we explore in detail. We forecast that high-cadence monitoring of ∼105 stars on the far side of Andromeda over a year-long period will detect microlensing events if Gμ/c2 ∼ 10−13, while ∼106 stars will detect events if 10−13.5 &amp;lt; Gμ/c2 &amp;lt; 10−11.5; the upper and lower bounds of the accessible tension range continue to expand as the number of stars rises. We also analyse the ability to reject models in the absence of fluctuations. While challenging, these studies are within reach of forthcoming time-domain surveys. Supernova observations can hypothetically constrain models with 10−12 &amp;lt; Gμ/c2 &amp;lt; 10−6 without any optimization of the survey cadence. However, the event rate forecast suggests it will be difficult to reject models of interest. As a demonstration, we use observations from the Pantheon Type Ia supernova cosmology data set to place modest constraints on the number density of cosmic superstrings in a poorly tested region of the parameter space.

Dynamics of junctions and the multitension velocity-dependent one-scale model

The dynamics of string junctions and their influence on the evolution of cosmic superstring networks are studied in full detail. We review kinematic constraints for colliding strings in a Friedmann-Lema\^itre-Robertson-Walker background and obtain the average distribution of possible string configurations after string collisions. The study of small-scale structure enables us to investigate the average growth/reduction rate of string junctions for a given cosmic string network. Incorporating the averaged junction dynamics into the velocity-dependent one-scale model for multi-tension string networks, we improve the semi-analytic description and quantitative understanding of cosmic superstring network evolution.

Detection of low tension cosmic superstrings

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 compactifications in string theory. Low tension superstring loops live longer, experience less recoil (rocket effect from the emission of gravitational radiation) and tend to cluster like dark matter in galaxies. Clustering enhances the string loop density with respect to the cosmological average in collapsed structures in the universe. The enhancement at the Sun's position is ∼ 105. We develop a model encapsulating the leading order string theory effects, the current understanding of the string network loop production and the influence of cosmological structure formation suitable for forecasting the detection of superstring loops via optical microlensing, gravitational wave bursts and fast radio bursts. We evaluate the detection rate of bursts from cusps and kinks by LIGO- and LISA-like experiments. Clustering dominates rates for G μ < 10−11.9 (LIGO cusp), G μ<10−11.2 (LISA cusp), G μ < 10−10.6 (LISA kink); we forecast experimentally accessible gravitational wave bursts for G μ>10−14.2 (LIGO cusp), G μ>10−15 (LISA cusp) and G μ>10− 14.1 (LISA kink).

Highly excited strings I: Generating function

This is the first of a series of detailed papers on string amplitudes with highly excited strings (HES). In the present paper we construct a generating function for string amplitudes with generic HES vertex operators using a fixed-loop momentum formalism. We generalise the proof of the chiral splitting theorem of D'Hoker and Phong to string amplitudes with arbitrary HES vertex operators (with generic KK and winding charges, polarisation tensors and oscillators) in general toroidal compactifications E=RD−1,1×TDcr−D (with generic constant Kähler and complex structure target space moduli, background Kaluza–Klein (KK) gauge fields and torsion). We adopt a novel approach that does not rely on a “reverse engineering” method to make explicit the loop momenta, thus avoiding a certain ambiguity pointed out in a recent paper by Sen, while also keeping the genus of the worldsheet generic. This approach will also be useful in discussions of quantum gravity and in particular in relation to black holes in string theory, non-locality and breakdown of local effective field theory, as well as in discussions of cosmic superstrings and their phenomenological relevance. We also discuss the manifestation of wave/particle (or rather wave/string) duality in string theory.

Probing cosmic superstrings with gravitational waves

We compute the stochastic gravitational wave background generated by cosmic superstrings using a semi-analytical velocity-dependent model to describe their dynamics. We show that heavier string types may leave distinctive signatures on the stochastic gravitational wave background spectrum within the reach of present and upcoming gravitational wave detectors. We examine the physically motivated scenario in which the physical size of loops is determined by the gravitational backreaction scale and use NANOGRAV data to derive a conservative constraint of $G\mu_F<3.2 \times 10^{-9}$ on the tension of fundamental strings. We demonstrate that approximating the gravitational wave spectrum generated by cosmic superstring networks using the spectrum generated by ordinary cosmic strings with reduced intercommuting probability (which is often done in the literature) leads, in general, to weaker observational constraints on $G\mu_F$. We show that the inclusion of heavier string types is required for a more accurate characterization of the region of the $(g_s,G\mu_F)$ parameter space that may be probed using direct gravitational wave detectors. In particular, we consider the observational constraints that result from NANOGRAV data and show that heavier strings generate a secondary exclusion region of parameter space.

CMB constraints on cosmic strings and superstrings

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 \alpha. 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 volume of compact extra dimensions w. This constitutes the most comprehensive CMB analysis of LambdaCDM cosmology + strings to date. For ordinary cosmic string networks our updated constraint on the string tension is, in relativistic units, Gmu<1.1x10^-7, while for cosmic superstrings our constraint on the fundamental string tension is Gmu_F<2.8x10^-8, both obtained using Planck2015 temperature and polarisation data.

Cosmic superstring networks with Y-junctions: Evolution, B-modes and gravitational waves

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 μF as well as the string coupling gs. 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 the underlying parameters of the theory.

Time evolution of a warped cosmic string

The time evolution of a self-gravitating U(1) cosmic string on a warped five-dimensional (5D) axially symmetric spacetime is numerically investigated. Although cosmic strings are theoretically predicted in four-dimensional (4D) general relativistic models, there is still no observational evidence of their existence. From recent observations of the cosmic microwave background (CMB), it is concluded that these cosmic strings cannot provide a satisfactory explanation for the bulk of density perturbations. They even could not survive inflation. It is conjectured that only in a 5D warped braneworld model there will be observable imprint of these so-called cosmic superstrings on the induced effective 4D brane metric for values of the symmetry breaking scale larger than the grand unified theory (GUT) values. The warp factor makes these strings consistent with the predicted mass per unit length on the brane. However, in a time-dependent setting, it seems that there is a wavelike energy–momentum transfer to infinity on the brane, a high-energy braneworld behavior. This in contrast to earlier results in approximation models. Evidence of this information from the bulk geometry could be found in the gravitational cosmic background radiation via gravitational wave energy–momentum affecting the brane evolution. Fluctuations of the brane when there is a U(1) gauge field present, are comparable with the proposed brane tension fluctuations, or branons, whose relic abundance can be a dark matter candidate. We briefly made a connection with the critical behavior at the threshold of black hole formation found by Choptuik several decades ago in self-gravitating time-dependent scalar field models. The critical distinction between dispersion of the scalar waves and singular behavior fade away when a time-dependent warp factor is present.

Cosmic super-strings and Kaluza-Klein modes

Cosmic super-strings interact generically with a tower of relatively light and/or strongly coupled Kaluza-Klein (KK) modes associated with the geometry of the internal space. In this paper, we study the production of spin-2 KK particles by cusps on loops of cosmic F- and D-strings. We consider cosmic super-strings localized either at the bottom of a warped throat or in a flat internal space with large volume. The total energy emitted by cusps in KK modes is comparable in both cases, although the number of produced KK modes may differ significantly. We then show that KK emission is constrained by the photo-dissociation of light elements and by observations of the diffuse gamma ray background. We show that this rules out regions of the parameter space of cosmic super-strings that are complementary to the regions that can be probed by current and upcoming gravitational wave experiments. KK modes are also expected to play an important role in the friction-dominated epoch of cosmic super-string evolution.

Constraints on Cosmic Superstrings from Kaluza-Klein Emission

Cosmic superstrings interact generically with a tower of light and/or strongly coupled Kaluza-Klein (KK) modes associated with the geometry of the internal space. We study the production of KK particles by cosmic superstring loops, and show that it is constrained by big bang nucleosynthesis. We study the resulting constraints in the parameter space of the underlying string theory model and highlight their complementarity with the regions that can be probed by current and upcoming gravitational wave experiments.

Scaling laws for weakly interacting cosmic (super)string andp-brane networks

In this paper we find new scaling laws for the evolution of $p$-brane networks in $N+1$-dimensional Friedmann-Robertson-Walker universes in the weakly-interacting limit, giving particular emphasis to the case of cosmic superstrings ($p=1$) living in a universe with three spatial dimensions (N=3). In particular, we show that, during the radiation era, the root-mean-square velocity is ${\bar v} =1/{\sqrt 2}$ and the characteristic length of non-interacting cosmic string networks scales as $L \propto a^{3/2}$ ($a$ is the scale factor), thus leading to string domination even when gravitational backreaction is taken into account. We demonstrate, however, that a small non-vanishing constant loop chopping efficiency parameter $\tilde c$ leads to a linear scaling solution with constant $L H \ll 1$ ($H$ is the Hubble parameter) and ${\bar v} \sim 1/{\sqrt 2}$ in the radiation era, which may allow for a cosmologically relevant cosmic string role even in the case of light strings. We also determine the impact that the radiation-matter transition has on the dynamics of weakly interacting cosmic superstring networks.

Constraints on the Fundamental String Coupling fromB-Mode Experiments

We study signatures of cosmic superstring networks containing strings of multiple tensions and Y junctions, on the cosmic microwave background (CMB) temperature and polarization spectra. Focusing on the crucial role of the string coupling constant g(s), we show that the number density and energy density of the scaling network are dominated by different types of string in the g(s) ~ 1 and g(s) ≪ 1 limits. This can lead to an observable shift in the position of the B-mode peak--a distinct signal leading to a direct constraint on g(s). We forecast the joint bounds on g(s) and the fundamental string tension μ(F) from upcoming and future CMB polarization experiments, as well as the signal to noise in detecting the difference between B-mode signals in the limiting cases of large and small g(s). We show that such a detectable shift is within reach of planned experiments.

Theoretical constraints on brane inflation and cosmic superstring radiation

We analyze theoretical constraints on the radiation modes of cosmic superstrings. Given that cosmic superstrings are formed at the end of brane inflation, we first investigate the implications of recently elucidated supergravity constraints on brane inflation models. We show that both D3/D7 and $ {{{{\text{D}}3}} \left/ {{\overline {{\text{D}}3} }} \right.} $ brane inflation are subject to non-trivial constraints. Both inflationary models can be shown to satisfy those constraints, but for the case of D3/D7 there seem to be important consequences for the dynamics of the inflationary mechanism. Bearing this in mind, we analyze the theoretical constraints on the nature of the allowed radiation by cosmic superstrings in the context of a warped background where brane-antibrane inflation takes place. Clearly such constraints do not apply to field theoretic cosmic strings, or to cosmic strings that arise in a background without warping. We argue that in a warped background where one might expect axionic radiation to be enhanced relative to gravitational radiation, neither F-strings nor D-strings can emit axionic radiation, and FD-strings cannot give rise to Neveu-Schwarz-Neveu-Schwarz particle emission, while their Ramond-Ramond particle emission is not well-defined.