Direct detection of the inflationary gravitational wave background

TL;DR

The paper addresses the problem of directly detecting the inflationary gravitational-wave background (IGWB) at deci-Hertz frequencies with BBO/DECIGO, within slow-roll inflation models constrained by CMB/LSS data.It goes beyond simple power-law extrapolations by solving inflationary dynamics for four representative potentials and computing the GW transfer to direct-detection scales, linking $P_s$, $n_s$, and $r$ at CMB/LSS to $\Omega_{\mathrm{GW}} h^2$ and $n_t$ at BBO/DECIGO scales.A key finding is that detectable IGWB amplitudes require a relatively high inflation scale ($V^{1/4}\gtrsim 10^{15}$ GeV) and can discriminate between models that share the same slow-roll parameters at CMB/LSS scales, though direct detection remains unlikely without a CMB polarization signal.

Abstract

Inflation generically predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO) or Japan's Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO), both currently under study. Here we investigate the detectability of the inflationary gravitational-wave background at BBO/DECIGO frequencies. To do so, we survey a range of slow-roll inflationary models consistent with constraints from the CMB and large-scale structure (LSS). We go beyond the usual assumption of power-law power spectra, which may break down given the 16 orders of magnitude in frequency between the CMB and direct detection, and solve instead the inflationary dynamics for four classes of inflaton potentials. Direct detection is possible in a variety of inflationary models, although probably not in any in which the gravitational-wave signal does not appear in the CMB polarization. However, direct detection by BBO/DECIGO can help discriminate between inflationary models that have the same slow-roll parameters at CMB/LSS scales.

Figures (4)

• Figure 1: Regions in the $n_s$--$r$ parameter space consistent with the CMB-only (orange/medium gray) Peiris03, CMB plus galaxy surveys (red/dark gray), and CMB plus galaxy surveys plus Lyman-alpha-forest constraints (green/light gray) Seljak04. Here, $r$ is the tensor-to-scalar ratio, and $n_s$ is the scalar spectral index at CMB scales. We plot on top of these regions the parameter space occupied by the four models of inflation we consider: power-law (solid black line), chaotic (dotted red), symmetry-breaking (dashed-dot purple) and hybrid (short-dashed dark-red). The right axis shows the energy scale $[V(k_c)]^{1/4}$ of inflaton.
• Figure 2:
• Figure 3: Regions in the $\Omega_{\rm GW} h^2$--$n_t$ parameter space for (a) power-law, (b) chaotic, (c) symmetry-breaking, and (d) hybrid inflation. The colored (shaded) regions map out the corresponding regions in Fig. \ref{['fig:nsr']}. Here, the gravitational-wave density $\Omega_{\rm GW} h^2$ and spectral index $n_t$ are both evaluated at DECIGO/BBO scales. Also shown are the sensitivity goals of BBO and DECIGO.
• Figure 4: Here we plot the inflationary gravitational-wave background amplitude $\Omega_{\mathrm{GW}}h^2$ obtained with the exact inflationary dynamics described in Section IV versus the amplitudes obtained with the power-law approximations (with slow-roll parameters fixed by CMB/LSS observations) given in Section IIb. The panels show results for (a) power-law, (b) chaotic, (c) symmetry-breaking, and (d) hybrid inflation. The regions are models taken from the $n_s$--$r$ parameter space in Fig. \ref{['fig:nsr']} (and shown in Fig. \ref{['fig:all']}) and the blue dashed curves indicate equality.