Cosmic strings and gravitational waves

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1 DECIGO meeting, 18 Oct Kyoto Univ. Takashi Hiramatsu Yukawa Institute for Theoretical Physics (YITP) Kyoto University

2 Stochastic Gravitational Wave Background Stochastic Gravitational Wave Background Cosmic Strings Field-theoretic Simulations Summary 2/28

4 * Kuroyanagi, Hiramatsu, Yokoyama, arxiv: ** Hiramatsu, Kawasaki, Saikawa, JCAP 1402 (2014) 031 For details, see a talk file by Kuroyanagi-san in DECIGO-10 (19 Nov 2011) 4/28

5 Cosmic Strings Stochastic Gravitational Wave Background Cosmic Strings Field-theoretic Simulations Summary 5/28

6 1D (linear) topological defect (soliton) associated with spontaneous symmetry breaking in high energies Kibble, J.Phys.A9 (1976) 1387 Old days : seeds of large scale structure Inflation Recent : a probe of extremely high-energy universe. The size of visible Unievrse 6/28

7 a simple extension of a particle motion 7/28

8 8/28

9 Phase transition of a scalar field High temperature : Quadratic Low temperature : Wine-bottle 9/28

10 Abelian-Higgs (AH) model Temperature-dependent potential

11 Evolution equtaions Gauge condition : (or ) Potential energy : Ratio of coupling constants Basically, physical properties of strings are detemined by Type-I Critical Type-II 11/28

12 Bettencourt et al., PRL 78 (1997) 2066 Type I (string core) attractive no force critical Some topics on cosmic strings 12/28

13 Physical property of a string String width : Energy density : String tension : 13/28

14 Constraints on the string tension GUT string was already excluded by CMB and pulsar timing observatories. for NG by PLANCK 2013 Planck collaboration, A&A 571 (2014) A25 for AH by PLANCK 2013 by NANOGrav 9th-year Arzoumanian et al., arxiv:

15 If strings stay still after their formation, Eventually, become dominant! If the characteristic scale of string network is proportional to Horizon scale... Can be still a subdominant component. expand 15/28

16 The key process to realise the scaling is reconnection. Reconnection takes place efficiently Loop-like strings are produced String energies (=length) are released via loops Possible to reach the scaling solution Scaling property has been found in numerical simulations Nambu-Goto : Abelian-Higgs : e.g. Allen, Shellard, PRL 64 (1990) 119 e.g. Moore, Shellard, PRD 65 (2001) /28

17 NOTE : It's unknown whether the reconnection process works well even in the case with superstrings, non-abelian gauge fields, gravity, and the coupling to matter. Superconducting string Matter field (another scalar field) flows along a string. This feature is common, for instance, in the Higgs mechanism. Matter field prevents the reconnection process? Witten, NPB 249 (1985) 557 Peter, PRD 45 (1990) 1091 Cosmic superstrings Two kinds of strings exists, F-string, D-string. A bound state, FD-strings, forms occasionally (~a few %). Each string length is not scaling in a mimetic model, double gauge field model. Urrestilla, Vilenkin, JHEP 0802 (2008) 037 Should we do higher-dimensional field-theoretic simulations? 17/28

18 Field-theoretic Simulations Stochastic Gravitational Wave Background Cosmic Strings Field-theoretic Simulations Summary 18/28

19 Collider simulation Simulation box : static box Typical number of grids : Initial conditions : Boundary conditions : Parameter : Initial conditions 19/28

20 Critical Type-I kink cusp can be a source of GW bursts m173a m175a 20/28

21 m73a m73a Salmi et al, PRD 77 (2008) (R) 21/28

22 m177a m176a Verbiest, Achucarro, PRD 84 (2011) /28

23 Loop collapsion Entangled loop collapsion tl3a tl7a Kinky loop collapsion Note We have no well established schemes to construct a loop configuration. Here we constructed it by force, so we do not consider... tl5a 23/28

24 Network simulation Simulation box : comiving box Typical number of grids : Initial conditions : Boundary conditions : themalised scalar field periodic Simulation time : Initial conditions Assumption - scalar field is well thermalised with the environment 24/28

25 String network (critical) String network (Type-I) Hiramatsu, Sendouda, Takahashi, Yamauchi, Yoo, PRD 88 (2013) /28

26 - Even in such a simple model, the physical properties of string networks - So far, we have no NG-like models incorporating the string interactions. Hiramatsu, Sendouda, Takahashi, Yamauchi, Yoo, PRD 88 (2013) /28

27 Summary Stochastic Gravitational Wave Background Cosmic Strings Field-theoretic Simulations Summary 27/28

28 Cosmic strings are still alive and still have a potential to explore the dark age of the Universe Field-theoretic approach is ready for practical use Main source of SGWB from strings is loops We should much more take care of GWs from loops Gravitational waves from a loop So far spectrum is computed from NG or VOS pulser DECIGO Loop (size) distirbution Loop size is really unknown - Extremely high resolution network simulation - Interpretation from Field-theoretic model to Nambu-Goto model Shape of a loop Time-evolution of the number of kinks/cusps on a loop is unknown Evolution of kinks/cusps on a loop taking the backreaction into account 28/28

Gravitational waves from Cosmic strings

Gravitational waves from Cosmic strings Sachiko Kuroyanagi Tokyo U. of Science 2013/12/6 62 References S. Kuroyanagi, K. Miyamoto, T. Sekiguchi, K. Takahashi, J. Silk, PRD 86, 023503 (2012) and PRD 87,