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because the gravitational interaction is so weak , a stochastic background of gravitational radiation ( the graviton background ) decouples from the matter in the universe at very early times .
for this reason , the stochastic background of gravitational radiation , which is in principle observable at the present time , carries with it a picture of the state of the universe at very early times , when energy densities and temperatures were very large .
the most interesting features of string theory are associated with its behavior at very high energies , near the planck scale .
such high energies are unobtainable in present - day laboratories , and are unlikely to be reached for quite some time .
they were , however , available during the very early history of the universe , so string theory can be probed by the predictions which it makes about that epoch .
recent work has shown how the early universe might behave , if superstring theories are a correct description of nature @xcite .
one of the robust predictions of this  string cosmology " is that our present - day universe would contain a stochastic background of gravitational radiation @xcite , with a spectrum which is quite different than that predicted by many other early - universe cosmological models @xcite . in particular , the spectrum of gravitational waves predicted by string cosmology has rising amplitude with increasing frequency .
this means that the radiation might have large enough amplitude to be observable by ground - based gravity - wave detectors , which operate at frequencies above @xmath0 .
this also allows the spectrum to be consistent with observational bounds arising at @xmath1 from observations of the cosmic background radiation and at @xmath2 from observation of millisecond pulsar timing residuals .    in this short paper
, we examine the spectrum of radiation produced by string cosmology , and determine the region of parameter space for which this radiation would be observable by the ( initial and advanced versions of the ) ligo detectors @xcite .
in models of string cosmology @xcite , the universe passes through two early inflationary stages . the first of these
is called the  dilaton - driven " period and the second is the  string " phase .
each of these stages produces stochastic gravitational radiation ; the contribution of the dilaton - driven phase is currently better understood than that of the string phase .    in order to describe the background of gravitational radiation
, it is conventional to use a spectral function @xmath3 which is determined by the energy density of the stochastic gravitational waves .
this function of frequency is defined by [ e : defomegagw ] _
gw(f ) = 1 _ critical d _
gw d f. here @xmath4 is the ( present - day ) energy density in stochastic gravitational waves in the frequency range @xmath5 , and @xmath6 is the critical energy - density required to just close the universe .
this is given by [ e : crit ] _
critical = 3 c^2 h_0 ^ 2 8 g 1.6 10 ^ -8 h_100 ^ 2 ergs / cm^3 , where the hubble expansion rate @xmath7 is the rate at which our universe is currently expanding , [ e : hubble ] h_0 = h_100 100 = 3.2 10 ^ -18h_100 1 sec .
because @xmath7 is not known exactly , it is defined in terms of a dimensionless parameter @xmath8 which is believed to lie in the range @xmath9 .
the spectrum of gravitational radiation produced in the dilaton - driven and string phase was discussed in @xcite . in the simplest model , which we will use in this paper ,
it depends upon four parameters .
the first pair of these are the frequency @xmath10 and the fractional energy density @xmath11 produced at the end of the dilaton - driven phase .
the second pair of parameters are the maximal frequency @xmath12 above which gravitational radiation is not produced and the maximum fractional energy density @xmath13 , which occurs at that frequency .
this is illustrated in fig .
[ f : spec ] .
an approximate form for the spectrum is @xcite [ e : approx ] _
gw(f)= where = is the logarithmic slope of the spectrum produced in the string phase .
if we assume that there is no late entropy production and make reasonable choices for the number of effective degrees of freedom , then two of the four parameters may be determined in terms of the hubble parameter @xmath14 at the onset of radiation domination immediately following the string phase of expansion @xcite , f_1= 1.3 10 ^ 10 ( h_r 5 10 ^ 17 ) ^1/2 and _ gw^max = 1 10 ^ -7 h_100 ^ -2 ( h_r 5 10 ^ 17 ) ^2 .
more complicated models and spectra were discussed in @xcite .
the ratios @xmath15 and @xmath16 are determined by the basic physical parameters of string cosmology models , the values of the hubble parameter and the string coupling parameter at the end of the dilaton - driven phase and the onset of the string phase @xcite .
a number of authors @xcite have shown how one can use a network of two or more gravitational wave antennae to detect a stochastic background of gravitational radiation .
the basic idea is to correlate the signals from separated detectors , and to search for a correlated strain produced by the gravitational - wave background , which is buried in the intrinsic instrumental noise .
it has been shown by these authors that after correlating signals for time @xmath17 ( we take @xmath18 ) the ratio of  signal " to  noise " ( squared ) is given by an integral over frequency @xmath19 : [ e : sovern ] ( s n ) ^2 = 9 h_0 ^ 4 50 ^4 t _ 0^df .    in order to detect a stochastic background with @xmath20 confidence the ratio @xmath21 needs to be at least @xmath22 . in this equation ,
several different functions appear , which we now define .
the instrument noise in the detectors is described by the one - sided noise power spectral densities @xmath23 .
the ligo project is building two identical detectors , one in hanford washington and one in livingston louisiana , which we will refer to as the  initial " detectors .
after several years of operation , these detectors will be upgraded to so - called  advanced " detectors . since the two detectors are identical in design , @xmath24 .
the design goals for the detectors specify these functions @xcite . they are shown in fig .  [
f : noise ] .
the next quantity which appears is the overlap reduction function @xmath25 .
this function is determined by the relative locations and orientations of the arms of the two detectors , and is identical for both the initial and advanced ligo detectors . for the pair of ligo detectors ( f ) = -0.124842 j_0(x ) - 2.90014 + 3.00837 , where the @xmath26 are spherical bessel functions .
the dimensionless frequency variable is @xmath27 with @xmath28 being the light - travel - time between the two ligo detector sites .
this function is shown in fig .
[ f : overlap ]
.    equation ( [ e : sovern ] ) allows us to assess the detectability ( using initial or advanced ligo ) of any particular stochastic background @xmath3 .
making use of the prediction from string cosmology , we may use equation ( [ e : sovern ] ) to assess the detectability of this stochastic background . for
any given set of parameters we may numerically evaluate the signal to noise ratio @xmath29 ; if this value is greater than @xmath22 then with at least 90% confidence , the background can be detected by ligo .
the regions of detectability in parameter space are shown in fig .
[ f : init ] for the initial ligo detectors , and in fig .
[ f : adva ] for the advanced ligo detectors . for these figures
we have assumed @xmath30 and @xmath31 .
the observable regions for different values of these parameters can be obtained by simple scaling of the presented results .    at the moment ,
the most restrictive observational constraint on the spectral parameters comes from the standard model of big - bang nucleosynthesis ( ns ) @xcite .
this restricts the total energy density in gravitons to less than that of approximately one massless degree of freedom in thermal equilibrium .
this bound implies that _
gw(f ) d f = _
gw^s < 0.7 10 ^ -5 h^-2_100 . [ nucleo ] where we have assumed an allowed @xmath32 at ns , and have substituted in the spectrum ( [ e : approx ] ) .
this bound is shown on figs .
[ f : init],[f : adva ] .
we also show the weaker  dilaton only " bound , assuming no stochastic background is produced during the ( more poorly - understood ) string phase of expansion : _
gw^s < 2.1 10 ^ -5 h^-2_100
. this is obtained by setting @xmath33 in the previous equation , i.e. assuming that @xmath34 vanishes for @xmath35 .
we note that if the  dilaton + string " spectrum is correct , then the ns bounds rule out any hopes of observation by initial ligo . on the other hand , in the  dilaton only " case , a detectable background is not ruled out by ns bounds ; it would be observable if the spectral peak falls into the detection bandpass between 50 and 200 hz ( figure 7 of @xcite ) .
because the function @xmath36 decays rapidly at high and low frequencies , the asymptotic behavior of the 90% confidence contours for the advanced ligo detector in the high and low @xmath37 regions can be estimated analytically as follows ( _ gw^s)_90%= 7.4 10 ^ -10 h_100 ^ -2 ( f_s/100 ) ^3 ,  f_s100 ( _ gw^s)_90%= 2.6 10 ^ -11  h_100 ^
-2  ( f_s/20 ) ^0.4 ,  f_s20 similar estimates may be obtained for the initial ligo detector .
in this short paper , we have shown how data from the the initial and advanced versions of ligo will be able to constrain string cosmology models of the early universe . in principle , this might also constrain the fundamental parameters of superstring theory .
the initial ligo is sensitive only to a narrow region of parameter space and is only marginally above the required sensitivity , while the advanced ligo detector has far better detection possibilities .
the simultaneous operation of other types of gravitational wave detectors which operate at higher frequencies , such as bar and resonant designs , ought to provide additional increase in sensitivity and therefore further constrain the parameter space .
-0.5 in g. veneziano , phys . lett . *
b265 * ( 1991 ) 287 . m. gasperini and g. veneziano , astropart
* 1 * ( 1993 ) 317 ; mod .
a8 * ( 1993 ) 3701 .
r. brustein , m. gasperini , m. giovannini and g. veneziano phys .
b361 * ( 1995 ) 45 . m. gasperini and m. giovannini , phys . rev .
* d47 * ( 1993 ) 1519 .
grishchuk , sov .
jetp * 40 * ( 1975 ) 409 .
m. s. turner , _ detectability of inflation produced gravitational waves _ , preprint fermilab - pub-96 - 169-a ( astro - ph/9607066 ) .
b. allen , _ the stochastic gravity - wave background : sources and detection _ , in proceedings of the les houches school on astrophysical sources of gravitational radiation , springer - verlag , 1996 .
a. abramovici , et .
al . , science * 256 * ( 1992 ) 325 .
r. brustein , _ spectrum of cosmic gravitational wave background _ , preprint bgu - ph-96 - 08 ( hep - th/9604159 ) .
r. brustein , m. gasperini and g. veneziano , _ peak and endpoint of the relic graviton background in string cosmology _
, preprint cern - th-96 - 37 ( hep - th/9604084 ) .
m. gasperini , _ relic gravitons from the pre - big - bang : what we know and what we do not know _ , preprint cern - th-96 - 186 ( hep - th/9607146 ) .
a. buonanno , m. maggiore and c. ungarelli , _ spectrum of relic gravitational waves in string cosmology _ , preprint ifup - th-25 - 96 ( gr - qc/9605072 ) .
m. galluccio , m. litterio and f. occhionero , _ graviton spectra in string cosmology _ , rome preprint ( gr - qc/9608007 ) .
g. veneziano , _ string cosmology and relic gravitational radiation _ , preprint cern - th-96 - 37 ( hep - th/9606119 ) .
p. michelson , mon . not .
. soc . * 227 * ( 1987 ) 933 .
n. christensen , phys .
* d46 * ( 1992 ) 5250 .
e. flanagan , phys . rev .
* d48 * ( 1993 ) 2389 .
@xmath38 note that the second term on the right hand side of equation ( b6 ) should read @xmath39 rather than @xmath40 , and that the sliding delay function shown in figure 2 on page 2394 is incorrect .
v. f. schwartzmann , jetp lett .
* 9 * ( 1969 ) 184 ; t. walker et al .
, ap . j. * 376 * ( 1991 ) 51 .
a characteristic spectrum of relic gravitational radiation is produced by a period of  stringy inflation " in the early universe . 
 this spectrum is unusual , because the energy - density rises rapidly with frequency . 
 we show that correlation experiments with the two gravitational wave detectors being built for the laser interferometric gravitational observatory ( ligo ) could detect this relic radiation , for certain ranges of the parameters that characterize the underlying string cosmology model .    
 = = ==#1#2 # 1#2 ^ 2#1 ^ 2 2n^2 2    -0.1 in    preprint numbers : wisc - milw-96-th-34,bgu - ph-96/09