Accessibility of the pre-big-bang models to LIGO

The recent search for a stochastic background of gravitational waves with LIGO interferometers has produced a new upper bound on the amplitude of this background in the 100 Hz region. We investigate the implications of the current and future LIGO results on pre-big-bang models of the early Universe, determining the exclusion regions in the parameter space of the minimal pre-big-bang scenario. Although the current LIGO reach is still weaker than the indirect bound from big bang nucleosynthesis, future runs by LIGO, in the coming year, and by Advanced LIGO ($\sim 2009$) should further constrain the parameter space, and in some parts surpass the Big Bang nucleosynthesis bound. It will be more difficult to constrain the parameter space in nonminimal pre-big bang models, which are characterized by multiple cosmological phases in the yet not well understood stringy phase, and where the higher-order curvature and/or quantum-loop corrections in the string effective action should be included.

Figure 1

$h_{100}^2{\Omega }_{\mathrm{GW}}(f)$ vs $f$, as predicted by the PBB model with $f_s=100\mathrm{Hz}$, $f_1=4.3\times {10}^{10}\mathrm{Hz}$, and $\mu =1.5$.

Figure 2

The 90% UL on ${\Omega }_{\alpha }$ is shown as a function of the spectral slope $\alpha$ for the most recent LIGO result. Expected sensitivities of LIGO and of Advanced LIGO are also shown.

Figure 3

The 90% UL exclusion curves are shown in the $f_1-\mu$ plane for $f_s=30\mathrm{Hz}$ (the excluded regions are above the corresponding curves). We show the latest result from LIGO, and the future expected reach of LIGO and of Advanced LIGO. The limit from the BBN is also shown. The horizontal gray dashed line denotes the most natural value of $f_1$, given by Eq. (4).

Figure 4

The 90% UL exclusion curves are shown in the $t_1/{\lambda }_s$ vs $H_s/(0.15M_{\mathrm{Pl}})$ plane, for $\mu =1.5$ and $f_s=30\mathrm{Hz}$ (the excluded regions are above the corresponding curves). We show the latest result from LIGO, and the future expected reach of LIGO and of Advanced LIGO. The limit from the BBN is also shown. The black circle denotes the most natural point, as given in Eq. (4).

Figure 5

The 90% UL exclusion curves are shown in the $f_s-\mu$ plane, for $f_1=4.3\times {10}^{11}\mathrm{Hz}$ (the excluded regions are to the right from the corresponding curves). We show the latest result from LIGO, and the future expected reach of LIGO and of Advanced LIGO. The indirect limit from the BBN excludes the whole region shown in this plane.

Figure 6

The 90% UL exclusion curves are shown in the $z_s-g_s$ plane, for $f_1=4.3\times {10}^{11}\mathrm{Hz}$. We show the latest result from LIGO (thick solid), and the future expected reach of LIGO (thin solid for the H1L1 pair, dashed for the H1H2 pair) and of Advanced LIGO (dash-dotted). The two sets of curves correspond to positive (left) and negative (right) signs of ($2\beta -3$).

Figure 7

The 90% UL exclusion curves are shown in the $f_s-\mu$ plane for $f_1=4.3\times {10}^{11}\mathrm{Hz}$ and for $\delta s=0.5$ (the excluded regions are to the right of the corresponding curves). We show the latest result from LIGO, and the future expected reach of LIGO and of Advanced LIGO. The indirect BBN limit excludes all models shown in this plane.

Figure 8

The 90% UL on ${\Omega }_{\mathrm{DO}}$ is shown as a function of $f_s$ for the models where stochastic gravitational background is not produced during the string phase. The latest LIGO result and the BBN bound are shown.