Detectability of inflation-produced gravitational waves

Introduction Inflation addresses most of the fundamental problems in cosmology – the origin of the flatness, large-scale smoothness, and small density inhomogeneities needed to seed all the structure seen in the Universe today. If correct, it would extend our understanding of the Universe to as early as 10−32 sec and open a window on physics at energies of order 10 GeV. However, at the moment there is little evidence to confirm or to contradict inflation and no standard model of inflation. The key to testing inflation is to focus on its three basic predictions [1]: spatially flat Universe (total energy density equal to the critical energy density); almost scaleinvariant spectrum of gaussian density perturbations [2]; and almost scale-invariant spectrum of stochastic gravitational waves [3]. The first two predictions have important implications: the existence of nonbaryonic dark matter, as big-bang nucleosynthesis precludes baryons from contribution more than about 10% of the critical density [4], and the cold dark matter scenario for structure formation, based upon the idea that the nonbaryonic dark matter is slowly moving elementary particles left over from the earliest moments [5,6]. A host of cosmological observations are now beginning to sharply test the first two predictions [6]. Gravity waves are a telling test and probe of inflation: They provide a consistency check (see below); they are essential to learning about the scalar potential that drives inflation [7]; and they are a compelling signature of inflation – both a flat Universe and scale-invariant density perturbations were advocated before inflation. Detecting inflation-produced gravity waves presents a great experimental challenge [8]. In this Letter we discuss the potential of CBR anisotropy or polarization and of direct detection by the laser-interferometers to test this key prediction of inflation. Quantum Fluctuations The (Fourier) spectra of metric fluctuations excited during inflation are characterized by power laws in wavenumber k, k for density perturbations (scalar metric fluctuations) and knT−3 for gravity waves (tensor metric fluctuations). Scale invariance for density perturbations (n = 1) corresponds to fluctuations in the Newtonian potential that are independent of wavenumber; scale invariance for gravity waves (nT = 0) corresponds to dimensionless horizon-crossing strain amplitudes that are independent of wavenumber. The power-law indices are related to the scalar field potential, V (φ), that drives inflation: