Projected constraints on the cosmic (super)string tension with future gravitational wave detection experiments

0.22 MB·English

by  Sotirios A. Sanidas

Draftversion January31,2013
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
PROJECTEDCONSTRAINTS ON THE COSMIC (SUPER)STRING TENSION WITH FUTURE
GRAVITATIONAL WAVE DETECTION EXPERIMENTS
Sotirios A. Sanidas, Richard A. Battye and Benjamin W. Stappers
JodrellBankCentreforAstrophysics,UniversityofManchester,Manchester,M139PL,UnitedKingdom;
[email protected],[email protected],[email protected]
(Dated: January 31, 2013)
Draft version January 31, 2013
3 ABSTRACT
1
Wepresentprojectedconstraintsonthe cosmicstringtension, Gµ/c2,thatcouldbeachievedbyfu-
0
turegravitationalwavedetectionexperimentsandexpressourresultsassemi-analyticrelationsofthe
2
formGµ(Ω h2)/c2,toallowfordirectcomputationofthetensionconstraintsforfutureexperiments.
gw
n TheseresultscanbeappliedtonewconstraintsonΩ h2 astheyareimposed. Experimentsoperating
a gw
indifferentfrequencybandsprobedifferentpartsofthegravitationalwavespectrumofacosmicstring
J
networkandaresensitivetodifferentuncertaintiesinthe underlyingcosmicstringmodelparameters.
0
We compute the gravitational wave spectra of cosmic string networks based on the one-scale model,
3
coveringalltheparameterspaceaccessedbyeachexperimentwhichisstronglydependentonthebirth

scaleofloopsrelativetothe horizon,α. Theupperlimits onthestringtensionavoidanyassumptions
]
O on the model parameters. We perform this investigation for Pulsar Timing Array experiments of
different durations as well as ground-based and space-borne interferometric detectors.
C
Subjectheadings: earlyuniverse—gravitationalwaves—instrumentation: miscellaneous—methods:
.
h numerical
p
-
o 1. INTRODUCTION with the most dominantofthem expected to be gravita-
r Cosmicstringsareone-dimensionaltopologicaldefects tional waves(GWs) (Vilenkin (1981); see, Vincent et al.
st ofcosmologicalsize,expectedtoformeitherduringsym- (1997)foranalternative). TheGWemissionfromallthe
a loops created by the network creates a stochastic gravi-
metry breaking phase transitions in the early Universe
[ tational wave background(SGWB).
(field theory strings) (Kibble 1976) or at the end of
Recently, Sanidas et al. (2012) have studied in detail
2 inflation in brane-world scenarios (cosmic superstrings)
the properties of the cosmic string SGWB and set a
v (Sarangi & Tye 2002).
conservative upper limit on the cosmic string tension,
2 The energy scale of cosmic strings is defined by their
4 linear energy density or tension, µ, usually referenced Gµ/c2 < 5.3×10−7 for networks with α≥ 10−9, avoid-
0 through the dimensionless quantity Gµ/c2, where G is ing any assumption on the parameters describing the
5 Newton’s constant and c the speed of light. In the case GW emission mechanism. Our result is approximately
1. of field theory strings, the tension is directly related to one orderof magnitude weakerthan the equivalentlimit
found by the Damour & Vilenkin (2005) analytic rela-
21 tthheeme,neµrgy∼sηca2leinηnoaftuthraelpuhnaistes,tr~an=sitcion=thkat=cr1e.ateInd tion, Gµ/c2 < 1.2 × 10−8 (van Haasteren et al. 2011,
1 the case of cosmic superstrings, their tension is directly 2012), which is due to the strong assumptions made for
: related to the fundamental string coupling g and the the latter (see also discussion in Shlaer et al. (2012)).
v compactification or warping scales. Therefores, the de- As part of the common effort of the European Pulsar
Xi tection, or at least the constraining of the cosmic string Timing Array (EPTA1, Ferdman et al. (2010)) collabo-
tension,providesa unique laboratoryfor physicsathigh rationtodetectGWswithpulsartiming,wepresenthere
r
a energies. an expansion of our previous work to evaluate the ten-
A cosmic string network consists of infinite strings sion constraints that will be achieved by future Pulsar
which stretch beyond our horizon and string loops Timing Array (PTA) experiments of different durations
(Vilenkin & Shellard 1994). After its creation, the net- andground-based/space-borneinterferometers. Thisnot
work evolves along with the expansion of the Universe onlyallowsustopredictfutureconstraints,butthesemi-
and is expected to settle into a scaling regime where all analytic formulae we deduce can be used when the lim-
its fundamental properties scale along with the horizon its on Ωgwh2 become available. First, we establish the
radius ∼ t, which is called the one-scale model. The parameter space accessible by each of these detectors.
scaling evolution of the network is attained through the Then, we discuss how the exclusion curves on the pa-
creation of loops. When two cosmic strings intersect, rameter space evolve relative to Ωgwh2. Using this in-
they intercommute with a probability p and exchange formation, we will evaluate the tension constraints as a
partners, chopping off loops from the network (Shellard function of Ωgwh2 for a range of experiments. We will
1987;Jackson et al.2005). In the one-scalemodel, loops alsoderivesemi-analyticformulaeforeaseofuseinfuture
are born with a size ℓ equal to a fraction of the parti- investigations. Additionally,wediscusshowtheradiative
b
cle horizond at the time of their birth, ℓ (t)=αd (t), efficiency parameter Γ, affects these constraints.
H b H
whereαisaconstant. Theseloopssubsequentlydecayby
emitting alloftheir energyinvariousforms ofradiation,
1 http://www.epta.eu.org
2
2. CONSTRAININGTHESTRINGTENSION parameter at the present time t0, is then given by
2.1. The cosmic string SGWB 2Gµ2c2 n∗ t0
Ω (f)= jP a5(t′)n (f,t′)dt′,
In the one-scale model, the basic parameters that de- gw ρ a5(t )f jZ j
terminetheGWspectrumare: thecosmicstringtension, crit 0 Xj=1 tf
Gµ/c2; the birth scale of loops relative to the horizon, (4)
α; and the intercommutation probability, p. In order to where ρcrit =3H02c2/8πG is the critical energy density.
compute the SGWB, we also need to model the spec- Acorrectionhastobe appliedinEq.(4)duetothe an-
trum of radiation emitted by a cosmic string loop. This nihilation of massive particles during the radiation era.
is quantified by: its spectral index q, with q = 4/3 for WhenthetemperatureoftheUniverse,T,dropsbelowa
cusps and q = 2 for kinks (Vilenkin & Shellard 1994); a specific particle mass threshold, the relevant family be-
cut-off on the number of emission modes, n∗ = 1 → ∞, comes non-relativistic, changing the number of relativis-
whichisusedtomodeltheeffectsofgravitationalbackre- tic degrees of freedom, g∗. This will result in a faster
action(Caldwell et al.1996);andtheradiativeefficiency expansionoftheUniverseeverytimesuchamassthresh-
Γ ≈ 50, which describes the efficiency of the GW emis- oldis crossed,affecting the valueofa(t)(Kolb & Turner
sionmechanism(Casper & Allen1995). InSanidas et al. 1990). Although these changes will not significantly af-
(2012)wehavedescribedindetailthecomputationofthe fect the evolution of the cosmic string network, which
cosmic string SGWB which we will only briefly recap it will quickly adapt to the new expansion rate and con-
here. vergetoits scalingevolution,they willhavea significant
From the energy-momentum tensor for cosmic strings effect on the energy density of the GWs emitted by the
wefindtheenergylostintoloopsinorderforthenetwork network.
to maintain scaling, These effects can be included with the use of a multi-
plicative factor for ρ , and therefore Ω h2, which has
gw gw
dE a˙(t) the form (g∗/g∗′)1/3, where g∗′ and g∗ are the relativistic
loop,cr =−V(t) ρ˙∞(t)+2 ρ∞(t) 1+hυ2i/c2 , degrees of freedom before and after the transition, and
dt (cid:20) a(t) (cid:21) acts to decrease the amplitude of the SGWB (Bennett
(cid:0) (cid:1)
(1) 1986;Caldwell & Allen1992;Bin´etruy et al.2012). This
where ρ∞(t) = Aµd−2(t)c2 is the energy density of in- correction is applied at time t = (32πGρ/3)−1/2,
H cor
finite strings, A is the number of infinite strings within where ρ = π2g∗T4/30 and its effects are observed at
the horizon, hυ2i is the mean squared velocity of cosmic a frequency f ≈ 2a(t )c[f αd (t )a(t )]−1, which
strings,a(t)thescalefactorandV =a3(t)isthecompu- depends stroncgolry on α.coPrTAsr, pHrobicnorg nH0z GWs, are
tation volume. We have considered A and hυ2i as fixed not significantly affected by these corrections, and that
parameters, using their most recently published values onlyinthe casewhereαis large. Thesecorrectionswere
(Blanco-Pillado et al. 2011), quoted in Table 1. Assum- notconsideredinSanidas et al.(2012),butthisdoesnot
ing that loops have a length ℓb(t) = αdH(t) when they affecttherobustnessoftheresultspresentedintheafore-
are born, from Eq. (1) we can find the loop formation mentioned paper. However, when considering GW de-
rate, tectors operating at the Hz and mHz bands significant
corrections are expected. We have computed these cor-
rections for every particle in the Standard Model using
dNloop = 2V(t)ρ∞(t) c − a˙(t)hυ2i , (2) the mass values in Beringer et al. (2012) and incorpo-
dt µαdH(t)c2 (cid:20)dH(t) a(t)c2 (cid:21) ratedthemtothecomputedspectra. InFig.1wepresent
a typical cosmic string GW spectrum for α = 0.1 with
thecharacteristicpeakandflatpartoriginatingfromthe
where N is the total number of loops within V(t)
loop looppopulationsinthematterandradiationerasrespec-
created since the creation of the network at t =
t c4/(Gµ)2, with t the Planck time. Since the rafte of tively,alongwith the correctionsto the spectrum due to
Pl Pl particle annihilation.
decay of length for loops is ΓGµ/c, we are able to com-
pute the number density n(ℓ,t)dℓ of loops with length
2.2. Exclusion Curves
between ℓ and ℓ+dℓ present at time t.
In our GW emission model, each loop emits into a The computation of the tension exclusion curves and
series of harmonics n, with frequency upper bounds for a SGWB limit is done using the pro-
ceduredescribedinSanidas et al.(2012). First,wecom-
putetheGWspectraofcosmicstringmodelscoveringall
2nc
the accessible parameter space. Second, we find which
f = , (3)
n
ℓ configurationsarecompliantwiththeSGWBlimit,both
in terms of amplitude and assuming a flat local slope2.
Finally, we plot these configurations in the Gµ−α pa-
and power dE /dt = P Gµ2c with P =
Γn−q/ n∗ m−gqw.,looTphen, using Enq. (3) and carnefully rameter space and the maximum tension allowed for a
redshiftinmg=t1he frequencies to the present time we can given Ωgwh2 limit will provide the tension upper limit.
P Foraparticularexperiment,itisessentialtodetermine
construct n (f,t) that provides the number density of
j the range of α values which are accessible to it. The
loops, which at the jth mode and at time t, emit GWs
detected at frequency f. The computation of the en- 2 Since we are only considering projected constraints by future
ergy density of GWs per logarithmic frequency interval experiments,anassumptionforthespectralslopeisnecessary. We
Ω h2, where H = 100hkms−1Mpc−1 is the Hubble willdiscussourchoicelater.
gw 0
3
-6 -5
GΜ=10-7
Α=0.1 -6 Wgwh2=10-8
p=1
n*=1 -7
2h q=4(cid:144)3
w
g -8
Wg10-7 2(cid:144)Μc Wgwh2=10-10
o G -9
l g10
o
l-10
-11 Wgwh2=10-12
-8
-10 -5 0 5
log f HHzL -12
10
Fig.1.— The SGWB of a cosmic string network before (solid -13
line) and after (dashed line) the particle annihilation corrections -9 -8 -7 -6 -5 -4 -3 -2 -1
areapplied. log Α
10
SGWB of cosmic strings can span a wide range of fre-
-5
quencies, from below the nHz regime to beyond a THz,
which depends on the size of the loops created by the Wgwh2=10-8
-6
network. The minimum frequency f of the SGWB is
min
provided by the first emission mode of the loops which
-7
are born at t , and hence α =f f d (t )/2c.
In this wor0k, we will notmtinreat tmhien Gr WH d0etectors as Wgwh2=10-10
-8
broadband,butinsteadwewilldesignateeachoneafidu- 2c
cial frequency; the one at which maximum sensitivity is (cid:144)Μ
G -9
achieved. For ground-based interferometers (hereafter, g10 Wgwh2=10-12
“Hz-detectors”) and space-borne interferometers (here- o
l-10
after, “mHz-detectors”), we have assumed fiducial fre-
quencies of f = 100Hz and f = 0.01Hz respectively.
-11
For PTA experiments, the fiducial frequency is the in-
verse of the elapsed time over which observations were
-12
taken: f = 6.3nHz, f = 3.2nHz and f = 1.6nHz
for 5-, 10-, and 20-year PTA experiments respectively.
-13
They can only detect GW emission for α≥αmin, where -20 -18 -16 -14 -12 -10 -8 -6 -4 -2
log α = −9.5 for a 5-year PTA, log α = −9.2 log Α
10 min 10 min 10
fora10-yearPTA,log α =−8.9fora20-yearPTA,
10 min Fig.2.—Exclusionlimitsforcosmicstringnetworkswithp=1
log10αmin = −15.7 for mHz-detectors and log10αmin = and various values for the upper limit on Ωgwh2 at f = 6.3nHz
−19.7 for Hz-detectors. Of course, real detectors are (upperpanel)andf =100Hz(lowerpanel).
broadband and can observe at higher frequencies than thatcasethe spectrumhasapositiveslope,ourassump-
the one that maximumsensitivity is achieved, but, since tion for a flat spectrum leads to an underestimation of
theyaretypicallyonlysensitiveforafewordersofmagni- the tension constraints. These two effects are expected
tude in frequency, α provides a useful rule-of-thumb. to be similar and cancel out, preserving the robustness
min
In Fig. 2 we present the exclusion curves for net- of our results.
works with p=1 for three projected limits on Ω h2 at The shape of the exclusion curves for Hz- and mHz-
gw
f =6.3nHzandf =100Hz. Inthe caseofPTAs(upper detectorsexhibitamuchlessprominentmid-αpeak(see,
panel), for Ω h2 & 10−10, the upper limit on Gµ/c2 is for example, Fig. 2, lower panel). The whole mid-α re-
gw
provided by the peak in the mid-α region. The rise in gion would be flat if we had not considered the mas-
the exclusion curve for α ∼ α is expected, since in sive particle annihilation corrections;a result of the fact
min
thatregionthe detectorprobesthespectrumatfrequen- that such detectors probe only the flat part of the spec-
cies lowerthanthe peakfrequency, withhigher valuesof trum originating from the radiation era. Moreover, the
Gµ/c2 required for a fixed Ω h2. For Ω h2 ≪ 10−10, upper limits on the tension are always provided by the
gw gw
the characteristic peak disappears and the upper limit mid-α peak since the peak created by the networkswith
onthe tension is providedby the models with α=αmin. α∼αmin never gets higher.
The Ω h2 value at the low frequency cut-off is pro-
gw
videdbytheloopswhicharebornatthepresenttimeand 3. PROJECTEDCONSTRAINTS
therefore,itwillnotbe stochastic. Inreality,the SGWB We computed the spectra for ∼ 32000 different pa-
isexpectedtostartfromafrequencyf &f ,wherethe rametersets (∼1.3×105 CPUhours),using anupdated
min
individual loop emission becomes unresolvable, reducing version of the code used in Sanidas et al. (2012). Most
the height of the secondarypeak and overestimatingthe changes concern numerical accuracy improvements and
tensionconstraintsforΩ h2 .10−10. However,sincein the use of the recently published values for the infinite
gw
4
For 5-year PTA experiments,
TABLE 1
Parameter values 0.0959x3+2.292x2+19.23x+50.31
used/investigated in thiswork.
for −10<x≤−7,
Quantity Value(s) log10(Gµ/c2)≤0.0917x2+2.85x+10.5
A(radiationera) 45
hυhυ2i2A/ic/2c(m2(ra(amtdteaiarttteeiorrane)reara)) 003..43505 for −12.5≤x≤−10. (5)
For 10-yearPTA experiments,
fr 0.71
Gµ/c2 [10−13,10−4]
α [10−19.7,0.1] 0.126x3+2.972x2+24.36x+63.22
q −4/3,−2 for −9.8<x≤−7,
nΓ∗ 50,1[1,01,01400] log10(Gµ/c2)=0.0794x2+2.53x+8.52
slitsrtinogf paallratmheesteerpsafrraommetBerlavnaclou-ePsillaaldonogetwaitl.h(2th0e11v)a.luAe for −12.5≤x≤−9.8. (6)
For 20-yearPTA experiments,
ranges we covered for the fundamental cosmic string
modelparametersis presentedinTable 1. Itis onlynec- 0.1565x3+3.629x2+29.05x+74.31
essarytouseasmallnumberofspectralparameters,since
thetensionconstraintsforanyαintheGµ/c2−αparam- for −9.5<x≤−7,
eotfeeristhpearcethweillqa=lwa4y/s3,bne∗pr=ov1idoedr bthyethqe=ex4c/lu3s,ionn∗c=ur1v0e4s log10(Gµ/c2)=0.074x2+2.37x+7.46
models as shown in Sanidas et al. (2012). Additionally,
we only considered networks with p = 1 since the final for −12.5≤x≤−9.5. (7)
results can be easily rescaled for networks with p 6= 1.
For mHz-detectors,
For the core results of this paper we used Γ = 50
(Casper & Allen 1995). log (Gµ/c2)=1.09x+3.16 for −12.5≤x≤−7. (8)
10
We have investigated SGWB amplitudes in the range
Ω h2 ∈[10−12.5,10−7], with ∆log (Ω h2)=0.1. For For Hz-detectors,
gw 10 gw
each value for Ωgwh2, we have computed the exclusion log (Gµ/c2)=1.03x+2.83 for −12.5≤x≤−7. (9)
curves as a function of α and located the highest pos- 10
sible Gµ/c2 value. In Fig. 3 (left panel) we present the These formulae can be easily adapted to describe cos-
projected tension constraints as a function of Ω h2. mic string networks with p 6= 1. In Sanidas et al.
gw
For PTAs, the constraints on the tension are almost (2012) we have pointed out that a non-zero intercom-
independentofthefrequencyofmaximumsensitivityex- mutation probability only rescales the GW spectrum,
cept in the region 10−10 . Ωgwh2 . 10−9. Longer du- Ωgwh2 ∝p−k,wherek isanindexdescribinghowthein-
ration experiments are preferred in that region3, which tercommutationprobabilityaffectsthepopulationstatis-
tics of infinite strings, and whose value is discussed in
is the expected sensitivity to the SGWB for LEAP
Sakellariadou (2005) and Avgoustidis & Shellard (2005,
(Kramer & Stappers 2010). The change in the slope of
the curve at Ω h2 ∼ 10−10 signifies the point at which 2006). Therefore, Eqs. (5), (6), (7), (8) and (9) can pro-
gw videconstraintsforanypossiblecombinationofpsimply
thetensionupperlimitisnolongerprovidedbythemid- by multiplying the polynomials with p−k.
αpeakbutinsteadfromtheα∼α models. ThemHz-
min Additionally, we have investigated the effects of vary-
detectors will provide weaker constraints on the tension
ingΓonthetensionconstraints. ThevalueofΓdepends
for all Ω h2 values investigated. The same applies for
gw onthetrajectoryofeachloopandisexpectedtobeinthe
Hz-detector, which will provide weaker constraints than
range∼50−100(Allen & Casper 1994;Casper & Allen
both PTAs and mHz-experiments.
1995; Boh´e 2011; Copi & Vachaspati 2011). We have
The relatively simple origin of the constraint curves
computed the tension constraints for networks with Γ∈
makes it possible to describe them with fitting formulae
[10,100]and we presentsome typical results in the right
Gµ(Ω h2)/c2. This will allow any future constraint on
gw panel of Fig. 3. In the case of Hz- and mHz detectors
Ω h2 by any experiment operating in the relevant fre-
gw the effects of varying Γ do not significantly change the
quency range to be directly connected to a robust con-
tension constraints. The same holds true for PTAs, ex-
straint on the string tension. Using least squares fitting cept in the region 10−10.5 . Ω h2 . 10−9 where low
and setting x=log (Ω h2), we find that: gw
10 gw values of Γ are equivalent to decreasing the frequency of
maximum sensitivity.
3 Longerdurationexperimentswilleventuallycollectmoredata
andsetmorestringentconstraints onΩgwh2 thantheshorterdu- We will conclude this section by discussing the con-
ration ones. However, if two such experiments manage to set the sequences of our assumption of a locally flat spectrum.
same constraint on Ωgwh2, the longer duration one will provide For Hz- and mHz-detectors, this assumption holds true
better constraints on the string tension in that region. The bet- since these detectors probe the flat part of the spectrum
ter performance of longer duration experiments stems from the
for most of the Gµ−α parameter space. In the case of
lower frequency that they probe with maximum sensitivity, plac-
ing them “deeper” in the high amplitude, matter era peak of the PTAs, the slope will be negative when Ωgwh2 & 10−10
cosmicstringGWspectrum. (upper limit provided by the mid-α peak) and positive
5
Hz-detectors Hz-detectors,G=10
-5 mHz-detectors -5 HHzz--ddeetteeccttoorrss,,GG==51000
PTA5-year mHz-detectors,G=10
PTA10-year mHz-detectors,G=50
-6 PTA20-year -6 mPTHAz5--deyteeacrt,orGs,=G1=0100
PTA5-year,G=30
2c-7 2c-7 PPTTAA55--yyeeaarr,,GG==5700
(cid:144)Μ (cid:144)Μ PTA5-year,G=100
G G
g10-8 g10-8
o o
l l
-9 -9
-10 -10
-11 -11
-13 -12 -11 -10 -9 -8 -7 -13 -12 -11 -10 -9 -8 -7
log10Wgwh2 log10Wgwh2
Fig.3.—Cosmicstringtensionupperlimitsfornetworkswithp=1asafunctionofΩgwh2 forvariousGWdetection experiments(left
panel)andtheeffects ofvaryingΓ(rightpanel).
when Ω h2 .10−10 (upper limit provided by the peak different properties. PTAs, probing the high amplitude
gw
atα∼α ). Inthefirstcase,theflatspectrumassump- matter era peak of the spectrum for most cosmic string
min
tion will lead to an underestimation of the constraint. modelparametercombinationsandonlypartiallysuffer-
For example, the EPTA limit on the string tension of ing from the massive particle annihilation corrections in
Sanidas et al. (2012) will provide a hint on the expected thecaseoflargeloops,provideanexcellenttooltodetect
discrepancy. Reworkingthatanalysisunderthe assump- strings,or at least, set the most stringentconstraints on
tion of a flat spectrum we find Gµ/c2 < 5.6 × 10−7 their tension. On the other side, ground-based interfer-
whereas the limit we acquired using the extra slope in- ometersprobeamuchwiderareaoftheparameterspace
formation was Gµ/c2 < 5.3×10−7, a 5.6% discrepancy. (α ≈10−20)makingthemtheonlytoolabletodetect
min
Weanticipatethattheprojectedconstraintsinthewhole emission from very small loops, and they are not sensi-
range where Ω h2 & 10−10 will be higher by a similar tive to the, unknown, details of the radiation spectrum
gw
percentage,somethingthatdoesnotaffecttherobustness (q and n∗). Space-borne interferometers, operating in
of our approach since we are interested in conservative a frequency range between PTAs and ground-based in-
constraints. In the case where, Ω h2 . 10−10 the con- terferometers, share advantages and disadvantages from
gw
straints are expected to be overestimated by a similar both.
percentage. However, expect that this will be canceled PTAs already set the most stringent constraints on
by a similar order underestimation of the constraints in the amplitude of the SGWB when compared to LIGO,
thisregionduetotheassumptionofthestochasticnature and Advanced LIGO which is expected to become op-
of the background at f , as discussed in Sec. 2.2. erational in 2015 will achieve a similar performance
min
(Harry & the LIGO Scientific Collaboration 2010). The
4. DISCUSSION further increase in the sensitivity of PTAs expected in
In this paper, we have presented fitting formulae for the near future (LEAP is expected to set upper lim-
the upper limits on the cosmic string tension which can its on Ω h2 . 10−10), will lead to constraints on
gw
beusedinfutureGWdetectionexperiments. Thesecon- Gµ/c2 . 2×10−9, with a SKA4-scale PTA experiment
straints are free of any assumption on model parame- improving this by two orders of magnitude.
ters within the one-scale model. These formulae provide
a conservative alternative to the approach discussed in
Damour & Vilenkin (2005) which is basedoncusp emis-
sion and an approximate loop number density, assump- 5. ACKNOWLEDGEMENTS
tions which are much stronger. The authors would like to thank Michael Kramer,
The GW spectum of cosmic strings, being extremely Mark Hindmarsh, and acknowledge the support of the
broadband is potentially accessed by every GW detec- colleagues in the EPTA during the preparation of this
tion experiment, with each of them probing bands with paper.
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