We study the primordial gravitational wave background produced in models of single field inflation. Using the inflationary flow approach, we investigate the amplitude of gravitational wave spectrum, ωgw, in the frequency range 1 mHz -1 Hz pertinent to future space-based laser interferometers. For models that satisfy the current observational constraint on the tensor-to-scalar ratio, r 0.36, we derive a strict upper bound of ωgw 1.6 × 10 −15 independent of the form of the inflationary potential. Applying, in addition, the observational constraints on the spectral index ns and its running, ωgw is expected to be considerably lower than this bound unless the shape of the potential is finely tuned. We contrast our numerical results with those based on simple power-law extrapolation of the tensor power spectrum from CMB scales. In addition to single field inflation, we summarise a number of other possible cosmological sources of primordial gravitational waves and assess what might be learnt from direct detection experiments such as LISA, Big Bang Observer and beyond.
We present a dynamical analysis of the inflationary flow equations. Our technique uses the Hubble 'jerk' parameter ξ ≡ (m 4 Pl /16π 2 )H −2 (dH/dφd 3 H/dφ 3 ) (where H is the Hubble parameter and φ the inflaton) as a discriminant of stability of fixed points. The results of the analysis are used to explain qualitatively the distribution of various observable parameters (e.g. the tensor-scalar ratio, r, and scalar spectral index, ns) seen in numerical solutions of the flow equations using stochastic initial conditions. Finally, we give a physical interpretation of the flow in phase-space in terms of slow-roll motion of the inflaton.
Abstract.We investigate the accuracy of the slow-roll approximation for calculating perturbation spectra generated during inflation. The Hamilton-Jacobi formalism is used to evolve inflationary models with different histories. Models are identified for which the scalar power spectra P R computed using the Stewart-Lyth slowroll approximation differ from exact numerical calculations using the Mukhanov perturbation equation. We then revisit the problem of primordial black holes generated by inflation. Hybrid-type inflationary models, in which the inflaton is trapped in the minimum of a potential, can produce blue power spectra and an observable abundance of primordial black holes. However, this type of model can now be firmly excluded from observational constraints on the scalar spectral index on cosmological scales. We argue that significant primordial black hole formation in simple inflation models requires contrived potentials in which there is a period of fast-roll towards the end of inflation. For this type of model, the Stewart-Lyth formalism breaks down. Examples of such inflationary models and numerical computations of their scalar fluctuation spectra are presented.PACS numbers: 98.80.CqAccuracy of slow-roll formulae: implications for primordial black hole formation.
The statistical meaning of the local non-Gaussianity parameters f NL and g NL is examined in detail. Their relations to the skewness and the kurtosis of the probability distribution of density fluctuations are shown to obey simple fitting formulae, accurate on galaxy-cluster scales. We argue that the knowledge of f NL and g NL is insufficient for reconstructing a well-defined distribution of density fluctuations. However, by weakening the statistical significance of f NL and g NL , it is possible to reconstruct a well-defined pdf by using a truncated Edgeworth series. We give some general guidelines on the use of such a series, noting in particular that 1) the Edgeworth series cannot represent models with nonzero f NL , unless g NL is nonzero also, 2) the series cannot represent models with g NL < 0, unless some higher-order non-Gaussianities are known. Finally, we apply the Edgeworth series to calculate the effects of g NL on the abundances of massive clusters and large voids. We show that the abundance of voids may generally be more sensitive to high-order non-Gaussianities than the cluster abundance. Subject headings: Cosmology: theory -large-scale structure of universe. siri@astro.ox.ac.uk
We review the prospects for detecting tensor modes generated during inflation by CMB polarization experiments and by searching for a stochastic gravitational wave background with laser interferometers in space. We tackle the following two questions: (i) what does inflation predict for the tensor fluctuations? (ii) is it really worth building experiments that can cover only a small range of tensor amplitudes? §1. IntroductionInflation is an extremely attractive idea that has gained widespread support. However, even a cursory glance at the literature will reveal a plethora of inflationary models. Inflation theory is mired in phenomenological model building (often involving 'unnatural' fine-tunings) rather than emerging in a compelling way from fundamental physics.From the observational point of view, inflation has received strong support from observations of the cosmic microwave background (CMB) anisotropies, and from studies of the large-scale distribution of galaxies. In particular, the beautiful CMB results from WMAP 1) are consistent with primordial adiabatic fluctuations with a nearly scale invariant spectrum, as expected in the simplest inflationary models. A key prediction of inflationary models is the existence of a stochastic background of gravitational waves. Such a background has not yet been observed, but its detection would provide incontrovertible evidence that inflation actually occurred and would set strong constraints on the dynamics of inflation. It is therefore no surprise that a vigorous effort is underway to detect tensor modes from inflation.In this article, we will first review what can be learned about inflationary models from the detection of tensor modes. We will then discuss the prospects for detecting tensor modes from observations of the polarization of the CMB and by direct detection using interferometers in space. We will then tackle the following thorny questions:(i) What does inflation predict for the amplitude of the tensor fluctuations?(ii) If theory does not constrain the amplitude of the tensor mode to within many orders of magnitude, is it really worth the effort to build experiments that can only cover a small range? Our perspective on point (i) is very different to that presented in a recent paper 2) . Point (ii) is clearly important in assessing the case for a post-Planck satellite dedicated to CMB polarization measurements 3) . Unless otherwise stated, we will assume the 'concordance' Λ-dominated cold dark matter cosmology, with cosmic typeset using PTPT E X.cls Ver.0.9
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