Gravitational Waves. Cosmic Strings

Transcription

1 Gravitational Waves from Cosmic Strings Jose J. Blanco-Pillado IKERBASQUE & UPV/EHU with: Jeremy Watcher (Bilbao) Ken Olum (Tufts) Ben Shlaer (Tufts) Xavier Siemens (UWM)

2 Outline of the talk Introduction to Cosmic Strings and their dynamics Cosmological Networks. Simulations. Cosmic String Loops. Stochastic Background of Gravitational Waves. Observational Implications Conclusions.

3 What is a cosmic string? Topological defects in field theory. Relativistic version of Abrikosov vortices. They exist in many extensions of the standard model. Cosmic Superstrings. Fundamental Strings can be stretched to cosmological sizes and behave basically as classical objects.

4 What is a cosmic string? Simplest model: S U(1) = Z d 4 µ V ( 2 ) V ( )= 4 ( 2 2 ) 2

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10 What is a cosmic string? Physical properties of the strings: They are topological stable objects, they have no ends. They are Lorentz invariant. Tension = Energy density per unit length They are not coupled to any massless mode, except gravity. (This is the simplest version of strings that we will consider here)

11 The String Scale Thickness, energy density and tension of the string are controlled by the symmetry breaking scale. For a Grand Unified Theory scale: GeV Thickness: = cm Linear mass density: µ = gr/cm Tension : T = N Gravitational effects depend on: Gµ = M Pl

12 Cosmological Formation Strings get formed at a cosmological phase transition. (Kibble 76). In order for strings to be cosmologically relevant this should happen at the end of inflation. They could be formed in models of hybrid inflation or during reheating. In String Theory they are produced at the end of brane inflation.

13 Initial Conditions (Vachaspati & Vilenkin 84).

14 Cosmic String Dynamics (Nambu, 71; Goto 70). A relativistic string dynamics has an action of the form, S NG = µ Z p d 2 The string is described by: X(, ) We use the gauge conditions: X Ẋ 2 = 1 The e.o.m. become: X 00 = Ẍ X 0 Ẋ = 0 X(, ) = 1 [a( )+b( + )] 2 a 0 = b 0 = 1

15 What about interactions? Strings interact by exchanging partners, creating loops. This mechanism produces kinks on strings. This builds up small scale structure on strings.

16 Cosmic String Dynamics (Loops) X(, ) = 1 2 [a( )+b( + )] The solutions for closed loops are periodic. The loops oscillate under their tension. The strings move typically relativistically. During its evolution a loop may have points where the string reaches the speed of light: A cusp Ẋ = 1 2 b0 a 0 b 0 = a 0

17 Cosmic String Cusps ( Turok 84). Loops will typically have a cusp in each oscillation. The string doubles back on itself. X Ẋ 2 = 1

18 The importance of Loops Without any mechanism for energy loss strings would dominate the energy density of the universe. Loops oscillate under their tension and lose energy by gravitational radiation. This mechanism allows strings to be subdominant part of the energy budget. No monopole problem for strings.

19 Gravitational Radiation by Loops The power of gravitational waves will affect the size of the loops: Ṁ G(... Q) 2 GM 2 L 4 w 6 Gµ 2 The total power has been calculated with several sets of loops: P Gµ Loops will therefore shrink in size so the rest mass of the loop will be: m(t) m(t 0 ) Gµ 2 (t t 0 ) L(t) L(t 0 ) Gµ(t t 0 )

20 Gravitational Waves from the Network There are 2 different contributions to gravitational waves from a network of strings: Stochastic background generated by all the modes in the loop. (Vilenkin 81, Hogan and Rees 84, Caldwell et al. 92, Siemens et al.; Battye et al., Sanidas et al., Binetruy et al.; and many more ). Burst signals from individual cusps. ( Damour & Vilenkin 01).

21 Stochastic background of Gravitational Waves The whole network of strings contributes to the stochastic background of GW. gw (ln f) = 8 G 3H 2 o f Z t0 0 dt 3 Z a(t) mmax a(t 0 ) 0 dm n(t, m) dp df n(t, m) It depends directly on the number of loops. dp df It also depends on the spectrum of gw emission by the surviving loops.

22 Cosmic String Networks As the string network evolves it reaches a scaling solution where the energy density of strings is a constant fraction of the energy density in the universe. 1 = constant All statistical properties scale with the horizon distance.

23 Cosmic String Simulations We take the V.V. initial conditions and evolving them forward in time. We use the Nambu-Goto dynamics taking care of the intercommutation of strings. We removed the loops after they have oscillated for a while without any intersection. We stop the simulation before the boundary conditions become important.

24 Nambu-Goto Cosmic String Networks (B-P., Olum and Shlaer 12).

25 The Scaling of Cosmic String Networks Long strings seem to scale relatively fast. This was also found earlier by smaller simulations: Albrecht & Turok, 89 Bennet and Bouchet, 89 Allen & Shellard, 90 And more recently: Ringeval, Sakellariadou and Bouchet, 05 Vanchurin, Olum and Vilenkin, 05. Martins and Shellard, 06 (B-P., Olum and Shlaer 12). Also from field theory simulations. Bevis, Hindmarsh, Kunz and Urrestilla, 10. = 1 d h r µ 1 On the other hand, the properties of loops and small scale structure on the strings approach scaling much slower.

26 The number of cosmic string loops There is a scaling population of loops being produced at large sizes. l 0.1d h (B-P., Olum and Shlaer 13). It takes a long time to find this scaling regime for loops. They become the dominant contribution to the number density of loops. We can extract the normalization of the number of loops from simulations.

27 The number of cosmic string loops In the radiation era: (Dotted line from: Ringeval, Sakellariadou and Bouchet). n r ( ) 0.52 ( + Gµ/2) 5/2 = m µd h (B-P., Olum and Shlaer 13). Scaling units

28 Stochastic background of Gravitational Waves The whole network of strings contributes to the stochastic background of GW. gw (ln f) = 8 G 3H 2 o f Z t0 0 dt 3 Z a(t) mmax a(t 0 ) 0 dm n(t, m) dp df n(t, m) It depends directly on the number of loops. dp df It also depends on the spectrum of gw emission by the surviving loops.

29 Stochastic background of Gravitational Waves The whole network of strings contributes to the stochastic background of GW. gw (ln f) = 8 G 3H 2 o f Z t0 0 dt 3 Z a(t) mmax a(t 0 ) 0 dm n(t, m) dp df n(t, m) It depends directly on the number of loops. dp df It also depends on the spectrum of gw emission by the surviving loops.

30 Gravitational Radiation by Loops Loops are periodic sources so they emit at specific frequencies f n = 2n L We have to determine the amount of radiation at each frequency and it total power = 1X n=1 P n L(t) L(t 0 ) Gµ(t t 0 )

31 Gravitational Radiation by Loops The spectrum of radiation depends on the shape of the string. Different structures on the strings have different spectrum: (Vachaspati and Vilenkin 85). P cusps n Gµ 2 n 4/3 P kinks n Gµ 2 n 5/3

32 Loops from the Simulation (B-P., Olum and Shlaer 12).

33 Smoothing the loops (Toy model for backreaction) (B-P., Olum 15). How does the string shape changes with backreaction? We will simulate backreaction by smoothing the string at different scales over their lifetime. We evolve the new loop until it falls into a non-selfintersecting trajectory. We repeat these for many loops to get statistical results. We will use these results to compute the typical gw-spectrum.

34 Smoothing the loops (B-P., Olum 15).

35 Gravitational Radiation by Loops L(t) L(t 0 ) Gµ(t t 0 ) (B-P. and Olum 17) Step 7 Step 6 Step

36 A typical smoothed Loop

37 Gravity Waves from cusps Vachaspati and Vilenkin 85. P cusps n Gµ 2 n 4/3 This leads to a slow decline of the power. High frequencies

38 Gravitational Radiation by Loops (B-P. and Olum 17) Angular distribution is typically highly anisotropic This makes the computation of the spectrum a hard problem.

39 Gravitational Radiation by Loops Averaging over more than 1000 loops we get a spectrum of the form. 18 Radiation Spectrum Step n 4/3 P n (B-P. and Olum 17) x10 6 1x10 7 1x10 8 1x10 9 n

40 Stochastic background of Gravitational Waves The whole network of strings contributes to the stochastic background of GW. gw (ln f) = 8 G 3H 2 o f Z t0 0 dt 3 Z a(t) mmax a(t 0 ) 0 dm n(t, m) dp df n(t, m) It depends directly on the number of loops. dp df It also depends on the spectrum of gw emission by the surviving loops.

41 Stochastic Background of GWs (B-P. and Olum 17) Gµ = Gµ = 10-9 h 2 Ω gw (ln f) Gµ = Gµ = Gµ = Gµ = Gµ = f(hz)

42 Observational Implications (B-P., Olum and Siemens 17). The spectrum of gravitational waves covers a wide range of frequencies Pulsar Timing arrays (PTAs) 3-5 nhz. Space-based interferometers: LISA, DECIGO, BBO, 10 mhz -1 Hz LIGO/VIRGO interferometers in the Hz.

43 Observational Implications (B-P., Olum and Siemens 17) PTA aligo O1 SMBBH aligo design GWh LISA BBO f[hz]

44 Observational Implications Current limit from Parkes PTA (Australia) Gµ < (B-P., Olum and Siemens 17). Similar results from NANOGrav and European Pulsar Timing. Gµ < few If strings are not detected by PTAs, LISA would be the relevant instrument for strings Gµ < These strings would not be seen in the CMB.

45 Conclusions We are entering an era of precision cosmology in cosmic string simulations. Loop number density in obtained from simulations. Actual loops from simulation, no guess work on shapes. All known effects taken into account except real backreaction. We can impose important constraints on the scale of the string from current PTA observations. Future observatories like LISA could detect or constrained this scenarios. Impact on high energy physics of the early universe.

46 Thank you