Classicality of the primordial perturbations
We show that during inflation, a quantum fluctuation becomes classical at all orders if it becomes classical at first order. Implications are discussed.
astro-ph↗
arXiv subjects
David Seery
Publications and source records attributed to David Seery.
Different approaches to the second order Klein-Gordon equation
We derive the Klein--Gordon equation for a single scalar field coupled to gravity at second order in perturbation theory and leading order in slow-roll. This is done in two ways: we derive the Klein--Gordon equation first using the Einstein field equations, and then directly from the action after integrating out the constraint equations. We also point out an unexpected result regarding the treatment of the field equations.
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Primordial Non-Gaussianity and Gravitational Waves: Observational Tests of Brane Inflation in String Theory
We study brane inflation scenarios in a warped throat geometry and show that there exists a consistency condition between the non-Gaussianity of the curvature perturbation and the amplitude and scale-dependence of the primordial gravitational waves. This condition is independent of the warping of the throat and the form of the inflaton potential. We find that such a relation could be tested by a future CMB polarization experiment if the Planck satellite is able to detect both a gravitational wave background and a non-Gaussian statistic. In models where the observable stage of inflation occurs when the brane is in the tip region of the throat, we derive a further consistency condition involving the scalar spectral index, the tensor-scalar ratio and the curvature perturbation bispectrum. We show that when such a relation is combined with the WMAP3 results, it leads to a model-independent bound on the gravitational wave amplitude given by 0.001 < r < 0.01. This corresponds to the range of sensitivity of the next generation of CMB polarization experiments.
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The inflationary trispectrum
We calculate the trispectrum of the primordial curvature perturbation generated by an epoch of slow-roll inflation in the early universe, and demonstrate that the non-gaussian signature imprinted at horizon crossing is unobservably small, of order tau_NL < r/50, where r < 1 is the tensor-to-scalar ratio. Therefore any primordial non-gaussianity observed in future microwave background experiments is likely to have been synthesized by gravitational effects on superhorizon scales. We discuss the application of Maldacena's consistency condition to the trispectrum.
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Non-gaussianity from the inflationary trispectrum
We present an estimate for the non-linear parameter τ_NL, which measures the non-gaussianity imprinted in the trispectrum of the comoving curvature perturbation, ζ. Our estimate is valid throughout the inflationary era, until the slow-roll approximation breaks down, and takes into account the evolution of perturbations on superhorizon scales. We find that the non-gaussianity is always small if the field values at the end of inflation are negligible when compared to their values at horizon crossing. Under the same assumption, we show that in Nflation-type scenarios, where the potential is a sum of monomials, the non-gaussianity measured by τ_NL is independent of the couplings and initial conditions.
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Non-Gaussian corrections to the probability distribution of the curvature perturbation from inflation
We show how to obtain the probability density function for the amplitude of the curvature perturbation, R, produced during an epoch of slow-roll, single-field inflation, working directly from n-point correlation functions of R. These n-point functions are the usual output of quantum field theory calculations, and as a result we bypass approximate statistical arguments based on the central limit theorem. Our method can be extended to deal with arbitrary forms of non-Gaussianity, appearing at any order in the n-point hierarchy. We compute the probability density for the total smoothed perturbation within a Hubble volume, ε, and for the spectrum of ε. When only the two-point function is retained, exact Gaussian statistics are recovered. When the three-point function is taken into account, we compute explicitly the leading slow-roll correction to the Gaussian result.
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Non-Gaussian Inflationary Perturbations from the dS/CFT Correspondence
We use the dS/CFT correspondence and bulk gravity to predict the form of the renormalized holographic three-point correlation function of the operator which is dual to the inflaton field perturbation during single-field, slow-roll inflation. Using Maldcaena's formulation of the correspondence, this correlator can be related to the three-point function of the curvature perturbation generated during single-field inflation, and we find exact agreement with previous bulk QFT calculations. This provides a consistency check on existing derivations of the non-Gaussianity from single-field inflation and also yields insight into the nature of the dS/CFT correspondence. As a result of our calculation, we obtain the properly renormalized dS/CFT one-point function, including boundary contributions where derivative interactions are present in the bulk. In principle, our method may be employed to derive the n-point correlators of the inflationary curvature perturbation within the context of (n-1)th-order perturbation theory, rather than nth-order theory as in conventional approaches.
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An Observational Test of Holographic Inflation
Observational consequences of inflationary cosmology in the holographic dual of the Randall-Sundrum type II braneworld scenario, as motivated by the AdS/CFT correspondence, are investigated. High energy corrections to the standard four-dimensional Friedmann equation induce a corresponding modification to the form of the single-field inflationary consistency equation based on Einstein gravity. The degree of departure from the standard expression is determined by the ratio, r, of the primordial tensor and scalar perturbation amplitudes and the coefficient, c, of the conformal anomaly in the dual gauge theory. It is found that a necessary condition for detecting such a correction with the next generation of cosmic microwave background (CMB) polarization experiments is that r >= 0.06. The bound is tightened to r > 0.3 for values of the central charge that are compatible with known compactifications of type IIB string theory as parametrized in terms of F-theory compactification on Calabi-Yau four-folds. This is close to the present upper bounds inferred from combined observations of the CMB anisotropy power spectrum and high redshift surveys. We conclude that if such modifications to the inflationary consistency equation are to be observable, the gravitational wave background should be detected in the near future. A further consequence of the non-standard dynamics at high energies is that the initial state of the universe is a quiescent singularity with a finite density and pressure.
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Cosmic No Hair for Braneworlds with a Bulk Dilaton Field
Braneworld cosmology supported by a bulk scalar field with an exponential potential is developed. A general class of separable backgrounds for both single and two-brane systems is derived, where the bulk metric components are given by products of world-volume and bulk coordinates and the world-volumes represent any anisotropic and inhomogeneous solution to an effective four-dimensional Brans-Dicke theory of gravity. We deduce a cosmic no hair theorem for all ever expanding, spatially homogeneous Bianchi world-volumes and find that the spatially flat and isotropic inflationary scaling solution represents a late-time attractor when the bulk potential is sufficiently flat. The dependence of this result on the separable nature of the bulk metric is investigated by applying the techniques of Hamilton-Jacobi theory to five-dimensional Einstein gravity. We employ the spatial gradient expansion method to determine the asymptotic form of the bulk metric up to third-order in spatial gradients. It is found that the condition for the separable form of the metric to represent the attractor of the system is precisely the same as that for the four-dimensional world-volume to isotropize. We also derive the fourth-order contribution to the Hamilton-Jacobi generating functional. Finally, we conclude by placing our results within the context of the holographic approach to braneworld cosmology.
hep-th↗
Primordial non-gaussianities from multiple-field inflation
We calculate the three-point correlation function evaluated at horizon crossing for a set of interacting scalar fields coupled to gravity during inflation. This provides the initial condition for the three-point function of the curvature perturbation in the Sasaki--Stewart δN formulation. We find that the effect is small, of the order of a slow-roll parameter, and that the non-gaussianity can be determined on large scales once the unperturbed background evolution is known. As an example of the use of our formalism, we calculate the primordial non-gaussianity arising in a model of assisted inflation.
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Primordial non-gaussianities in single field inflation
We calculate the three-point function for primordial scalar fluctuations in a single field inflationary scenario where the scalar field Lagrangian is a completely general function of the field and its first derivative. We obtain an explicit expression for the three-point correlation function in a self-consistent approximation scheme where the expansion rate varies slowly, analogous to the slow-roll limit in standard, single-field inflation. The three-point function can be written in terms of the familiar slow-roll parameters and three new parameters which measure the non-trivial kinetic structure of the scalar field, the departure of the sound speed from the speed of light, and the rate of change of the sound speed.
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Radiative constraints on brane quintessence
We investigate the constraints on quintessence arising from both renormalisable and non-renormalisable couplings where the 5d Planck mass is around the TeV scale. The quintessence field vacuum expectation value is typically of order the 4d Planck mass while non-renormalisable operators are expected to be suppressed by the 5d Planck mass. Non-renormalisable operators are therefore important in computing the 4d effective quintessence potential. We then study the quantum corrections to the quintessence potential due to fermion and graviton loops. The tower of Kaluza-Klein modes competes with the TeV-scale cut-off, altering the graviton contribution to the vacuum polarization of quintessence. Nevertheless we show that, as in four dimensions, the classical potential is stable to such radiative corrections.
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The consistency relation in braneworld inflation
The braneworld cosmology, in which our universe is imbedded as a hypersurface in a higher dimensional bulk, has the peculiar property that the inflationary consistency relation derived in a four-dimensional cosmology persists. This consistency condition relates the ratio of tensor and scalar perturbation amplitudes to the tensor spectral index produced during an epoch of slow-roll scalar field inflation. We attempt to clarify this surprising degeneracy. Our argument involves calculating the power spectrum of scalar field fluctuations around geometries perturbed away from the exact de Sitter case. This calculation is expected to be valid for perturbations which would not cause a late-time acceleration of the universe. We use these results to argue that the emergence of the same consistency relation in the braneworld can be connected with a specific property, that five-dimensional observables smoothly approach their four-dimensional counterparts as one takes the brane to infinite tension. We exhibit an explicit example where this does not occur, and in which a consistency relation does not persist.
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