Forecast constraints on cosmic strings from future CMB, pulsar - PowerPoint PPT Presentation

Forecast constraints on cosmic strings from future CMB, pulsar timing and gravitational wave direct detection experiments Sachiko Kuroyanagi Univ. of Tokyo RESCEU (RESearch Center for the Early Universe) 12 Nov 2012 Based on S. Kuroyanagi, K. Miyamoto, T. Sekiguchi, K. Takahashi, J. Silk, PRD 86, 023503 (2012) + arXiv:1210.2829 [astro-ph]

Cosmic string ？ One dimensional topological defect generated in the early universe Generation mechanism spontaneous symmetry breaking 1: Phase transition 2: Cosmic superstrings Cosmological size D-strings or F-strings remains after inflation → could provide some insight into fundamental physics

Evolution of cosmic strings The energy density of cosmic strings ∝ a -2 ? Scaling law Cosmic String Networks approach a self- similar solution, which always looks same at the Hubble scale. energy density ∝ a -4 X ∝ a -2 Cosmic strings become loops via reconnection . ∝ a -3 Loops lose energy Cosmic strings by emitting gravitational waves. a: scale factor

Observational Probe 1. Direct detection Ground ： Advanced-LIGO 、 KAGRA 、 Virgo 、 IndIGO (2017-) KAGRA image (http://gwcenter.icrr.u-tokyo.ac.jp/) Space ： eLISA/NGO (2022?) 、 DECIGO (2027) 2. Pulsar timing : SKA (2020) 3. CMB temperature fluctuation +B-mode polarization : Planck, CMBpol eLISA image (http://elisa-ngo.org/) DECIGO image, S. Kawamura et al, PTA image (NRAO) J. Phys.: Conf. Ser. 122, 012006 (2006)

Current constraints on cosmic string parameters 3 parameters to characterize cosmic string ・ G μ( = μ /M pl2 )： tension (line density) ・α： initial loop size L ～α H -1 Phase transition origin: p=1 ・ p ： reconnection probability Cosmic superstring: p<<1 ・ CMB temperature fluctuation: G μ <~10 -7 for infinite strings ・ Gravitational lensing: G μ <~10 -6 ・ Gravitational waves for loops α =0.1, p=1 Pulsar timing: G μ <~10 -9 Direct detection (LIGO GWB): G μ <~10 -6 What about future constraints ？

Gravitational wave signals Strong GW emission from singular points called kinks and cusps kink cusp Rare Burst: GWs with large amplitude coming from close loops → direct detection Gravitational wave background (GWB): superposition of small GWs coming from the early epoch → direct detection + pulsar timing

How many cosmic string bursts are coming to the earth per year? (plotted as a function of the amplitude for the fixed frequency @220Hz) G μ =10 -7 , α =10 -16 , p=1 rate (per year) → ← amplitude

How many cosmic string bursts are coming to the earth per year? (plotted as a function of the amplitude for the fixed frequency @220Hz) G μ =10 -7 , α =10 -16 , p=1 LIGO ～ 220Hz 220 oscillations per second = 7 × 10 9 oscillations per year rate (per year) → ← amplitude

How many cosmic string bursts are coming to the earth per year? (plotted as a function of the amplitude for the fixed frequency @220Hz) G μ =10 -7 , α =10 -16 , p=1 G μ =10 -7 , α =10 -16 , p=1 LIGO ～ 220Hz 220 oscillations per second = 7 × 10 9 oscillations per year GWB small amplitude rate (per year) → but numerous ← amplitude

How many cosmic string bursts are coming to the earth per year? (plotted as a function of the amplitude for the fixed frequency @220Hz) G μ =10 -7 , α =10 -16 , p=1 G μ =10 -7 , α =10 -16 , p=1 LIGO h ～ 10 -25 @ f ～ 220Hz GWB rate (per year) → ← amplitude

How many cosmic string bursts are coming to the earth per year? (plotted as a function of the amplitude for the fixed frequency @220Hz) G μ =10 -7 , α =10 -16 , p=1 LIGO h ～ 10 -25 @ f ～ 220Hz GWB rate (per year) → rare burst ← amplitude

How many cosmic string bursts are coming to the earth per year? (plotted as a function of the amplitude for the fixed frequency @220Hz) G μ =10 -7 , α =10 -16 , p=1 LIGO h ～ 10 -25 @ f ～ 220Hz GWB distant (old) rate (per year) → rare burst near (new) ← amplitude

＝ Parameter dependences of the rate amplitude of GWs ↑ p ↓ number density ↑ G μ↑ lifetime ↓ number density ↓ lifetime ↓ number density ↓ α↓ GW power Γ : numerical constant ～ 50-100 （ initial loop energy ） Lifetime of loops ＝ （ energy release rate per time ）

Parameter dependences of the rate p G μ rare burst GWB α The parameter dependences of the large burst (rare burst) and small burst (GWB) are different because they are looking at different epoch of the Universe → give different information on cosmic string parameters

Spectrum of the GWB p G μ frequency frequency frequency α frequency

Accessible parameter region (for p=1) dotted ： Burst solid ： GWB

★ Advanced-LIGO can detect both rare bursts and GWB G μ =10 -7 , α =10 -16 , p=1 dotted ： Burst solid ： GWB

Constraint from Example: G μ =10 -7 , α =10 -16 , p=1 direct detection experiments Adv-LIGO 3year Kuroyanagi et. al. PRD 86, 023503 (2012) different parameter dependence = different constraints on black ： Burst only parameters red ： Burst + GWB

Constraint from Example: G μ =10 -7 , α =10 -16 , p=1 direct detection experiments Adv-LIGO 3year Kuroyanagi et. al. PRD 86, 023503 (2012) Kuroyanagi et. al. arXiv:1202.3032 -6.95 black ： Burst only Before marginalized over dotted: GWB only log 10 G µ -7 red ： Burst + GWB Strong degeneracy seen in -7.05 constraint from GWB since the observable is only Ω GW -16.2 -16 -15.8 log 10 � -15.8 -6.95 log 10 G µ -7 log 10 � -16 -7.05 -16.2 -0.08 -0.06 -0.04 -0.02 0 -0.08 -0.06 -0.04 -0.02 0 log 10 p log 10 p

Signals in the CMB temperature fluctuation B-mode polarization G μ G μ p p

If we combine CMB constraints... G μ =10 -7 , α =10 -16 , p=1 Adv-LIGO 3year + CMB B-mode Kuroyanagi et al. arXiv:1210.2829 black : LIGO Burst only red : LIGO Burst + GWB blue: LIGO +Planck green: LIGO+CMBpol orange: CMB pol only

Constraints from pulsar timing and space direct detection mission pulsar direct detection timing amplitude of GWB cusps on loops kinks on infinite strings inflation cosmic string observing GWs from different epochs frequency old new

Pulsar timing (SKA) + Advanced-LIGO burst search ★ G μ =10 -9 , α =10 -9 , p=1 dotted ： Burst solid ： GWB

Direct detection + Pulsar timing G μ =10 -9 , α =10 -9 , p=1 Adv-LIGO 3year (burst only) + SKA 10year Kuroyanagi et al. arXiv:1210.2829

Parameter constraint by eLISA G μ =10 -9 , α =10 -9 , p=1 eLISA 3year (burst only) Kuroyanagi et al. arXiv:1210.2829

Summary • Future CMB and GW experiments can be a powerful tool to probe cosmic strings. • If signals are detected, it would determine cosmic string parameters, which can provide us with hints of fundamental physics such as particle physics or superstring theory. • Two different kinds of GW observation (rare burst and GWB) provide different constraints on cosmic string parameters and lead to better accuracy in determining parameters. • Combination of different experiments (CMB, Pulser timing, direct detection) also helps to get stronger constraints. • Space GW missions are more powerful to prove cosmic strings.

＝ Estimation of the GW burst rate Initial number density of loops depends on α and p （ length of infinite string discarded to loops ） (initial length of loops = α t i ） Evolution of infinite strings random walk of ・ velocity-dependent one-scale model straight strings length L, velocity v energy conservation energy discarded to loops for small p: c → cp damping due to the expansion acceleration due to the curvature of the strings momentum parameter:

＝ Estimation of the GW burst rate depends on G μ and α loop evolution Initial loop length ＝ t i ： time when the loop formed Γ : numerical constant ～ 50-100 GW power From the energy conservation law （ energy of loop at time t = μ l ） ＝（ initial energy of the loop = μα t i ）ー（ enegry released to GWs =P Δ t ） Loop length at time t （ initial loop energy ） Lifetime of the loop ＝ （ energy release rate per time ） i i

Estimation of the GW burst rate GW burst rate emitted at t ～ t+dt from loops formed at t i ～ t i +dt i Beaming Loop number Time interval of GW emission ∝ ( loop length at t ) -1 θ m ∝ ( loop length at t ) 1/3 GW amplitude from loop of length l

Generation mechanism 1: phase transition The Universe has experienced symmetry breakings. If you consider U(1) symmetry breaking... 3 π /2 0 0 π 3 π /2 3 π /2 0 π /2 π /2 π π 3 π /2 π /2 π Hubble volume = causal region High energy vacuum remains at the center Tension G μ ~ the energy scale of the phase transition

Generation mechanism 2: Cosmic superstrings Cosmological size D-strings or F-strings remains after inflation in superstring theory Difference from phase transition origin ・ low reconnection probability (p) because of the extra dimension D-string: p=0.1-1 Phase transition origin: p=1 F-string: p=10 -3 -1 ・ broad values of G μ depending on the inflation scale and the extra internal degrees of freedom ( ・ Y-junction ・ mixed strings with different G μ ) → Cosmic strings could give some insight into fundamental physics