Near comoving wavenumber k, the gravitational-wave background (GWB) from inflation carries information about the physical conditions near two moments in cosmic history: the moment when k "left the horizon" during inflation, and the moment when it "re-entered the horizon" after inflation. We investigate the extent to which this information can be extracted if the GWB is measured by a combination of cosmic-microwave-background (CMB) polarization experiments on large scales and space-based laser-interferometer experiments on small scales. To disentangle this information, we derive a new gravitational-wave transfer function that incorporates a number of physical effects that were treated less accurately, less generally, or were missing altogether in previous treatments. In particular, it incorporates: (i) dark energy with time-varying equation-of-state w(z); (ii) tensor anisotropic stress due to free-streaming relativistic particles in the early universe; and (iii) a variety of physical effects that cause deviations from the standard equation-of-state w = 1/3 during the radiation era. Based on this transfer function, we consider the degree to which the GWB can be used to test inflation and to probe the "primordial dark age" between the end of inflation and the electroweak phase transition.

We reconsider the predictions of inflation for the spectral index of scalar (energy density) fluctuations (ns) and the tensor/scalar ratio (r) using a discrete, model-independent measure of the degree of fine-tuning required to obtain a given combination of (ns, r ). We find that, except for cases with numerous unnecessary degrees of fine-tuning, ns is less than 0.98, measurably different from exact Harrison-Zel'dovich. Furthermore, if ns >or= 0.95, in accord with current measurements, the tensor/scalar ratio satisfies r >or= 10(-2), a range that should be detectable in proposed cosmic microwave background polarization experiments and direct gravitational wave searches.

Inflation predicts a primordial gravitational wave spectrum that is slightly "red," i.e. nearly scale-invariant with slowly increasing power at longer wavelengths. In this paper, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The spectrum is exponentially suppressed compared to inflation on long wavelengths, and the strongest constraint emerges from the requirement that the energy density in gravitational waves should not exceed around 10 per cent of the energy density at the time of nucleosynthesis.The recently-proposed cyclic model[1, 2] differs radically from standard inflationary cosmology [3,4], while retaining the inflationary predictions of homogeneity, flatness, and nearly scale-invariant density perturbations. It has been suggested that the cosmic gravitational wave background provides the best experimental means for distinguishing the two models. Inflation predicts a nearly scale-invariant (slightly red) spectrum of primordial tensor perturbations, whereas the cyclic model predicts a blue spectrum.[1] The difference arises because inflation involves an early phase of hyper-rapid cosmic acceleration, whereas the cyclic model does not.In this paper, we compute the gravitational wave spectrum for cyclic models to obtain both the normalization and spectral shape as a function of model parameters, improving upon earlier heuristic estimates. We find that the spectrum is strongly blue. The amplitude is too small to be observed by currently proposed detectors on all scales. Hence, the discovery of a stochastic background of gravitational waves would be evidence in favor of inflation, and would rule out the cyclic model.Readers unfamiliar with the cyclic model may consult [5] for an informal tour, and [6] for a recent analysis of phenomenological constraints. Cyclic cosmology draws strongly on earlier ideas associated with the "ekpyrotic universe" scenario. [7,8,9] Briefly, the scenario can be described in terms of the periodic collision of orbifold planes moving in an extra spatial dimension, or, equivalently, in terms of a four-dimensional theory with an evolving (modulus) field φ rolling back and forth in an effective potential V (φ). The field theory description is the long wavelength approximation to the brane picture in which the potential represents the interbrane interaction and the modulus field determines the distance between branes. For the purposes of this paper, the field theoretic description is more useful.The potential (Fig. 1) is small and positive for large φ, falling steeply negative at intermediate φ, and increasing again for negative φ. Each cycle consists of the following stages: (1) φ large and decreasing: the universe expands at an accelerated rate as V (φ) > 0 acts as dark energy; (2) φ intermediate and decreasing: the universe is dominated by a combination of scalar kinetic and potential energy, leading to slow contraction and to the generation of fluctuations; (3) φ negative and decreasing (beginning at conformal...

For a 4-dimensional spatially-flat Friedmann-Robertson-Walker universe with a scalar field φ(x), potential V (φ) and constant equation of state w = p/ρ, we show that an expanding solution characterized by ǫ = 3(1 + w)/2 produces the same scalar perturbations as a contracting solution with ǫ = 1/ǫ. The same symmetry applies to both the dominant and subdominant scalar perturbation modes. This result admits a simple physical interpretation and generalizes to d spacetime dimensions if we define ǫ ≡ [(2d − 5) + (d − 1)w]/(d − 2).