Magnetogenesis and the primordial non-gaussianity

The primordial density fluctuation inevitably couples to all forms of matter via loop corrections and depends on the ambient conditions while inflation was ongoing. This gives us an opportunity to observe processes which were in progress while the universe was inflating, provided they were sufficiently dramatic to overcome suppression by powers of (H/MP)^2 ~ 10^(-9), where H is the Hubble scale during inflation and MP is the Planck mass. As an example, if a primordial magnetic field was synthesized during inflation, as suggested by some interpretations of the apparently universal 10^(-6) gauss field observed on galactic scales, then this could leave traces in inflationary observables. In this paper, I compute corrections to the spectrum and bispectrum generated by a varying electromagnetic coupling during inflation, assuming that the variation in this coupling is mediated by interaction with a collection of light scalar fields. If the mass scale associated with this interaction is too far below the Planck scale then the stability of perturbation theory can be upset. For the mass-scale which is relevant in the standard magnetogenesis scenario, however, the theory is stable and the model is apparently consistent with observational constraints.Comment: 37 pages, uses feynmp.sty and iopart.cls. v2: minor improvements in comparison with version submitted to (and accepted by) JCAP. Improves v1 with a more refined discussion of cutoffs and Lorentz invariance in Sections 4-5, but calculations are unchanged. Minor textual improvements throughou

Relics of spatial curvature in the primordial non-gaussianity

We study signatures in the Cosmic Microwave Background (CMB) induced by the presence of strong spatial curvature prior to the epoch of inflation which generated our present universe. If inflation does not last sufficiently long to drive the large-scale spatial curvature to zero, then presently observable scales may have left the horizon while spatial slices could not be approximated by a flat, Euclidean geometry. We compute corrections to the power spectrum and non-gaussianity of the CMB temperature anisotropy in this scenario. The power spectrum does not receive significant corrections and is a weak diagnostic of the presence of curvature in the initial conditions, unless its running can be determined with high accuracy. However, the bispectral non-gaussianity parameter f_NL receives modifications on the largest observable scales. We estimate that the maximum signal would correspond to f_NL ~ 0.3, which is out of reach for present-day microwave background experiments.Comment: 23 pages, uses ioplatex.sty. v2: only bibliographic change

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 \delta N 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.Comment: 24 pages, JCAP LaTeX style; replaced with version accepted by JCAP. Some corrections to Sections 2 and 5, conclusions unchange

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.Comment: 7 pages, uses RevTeX4. v2, replaced with version accepted by Phys. Rev.

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.Comment: 26 pages, uses iopart.cls. Updated to match version published in JCA

General CMB bispectrum analysis using wavelets and separable modes

In this paper we combine partial-wave (`modal') methods with a wavelet analysis of the CMB bispectrum. Our implementation exploits the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain the amplitude of arbitrary primordial bispectra. This will be particularly important for upcoming surveys such as \emph{Planck}. A key advantage is the computational efficiency of calculating the inverse covariance matrix in wavelet space, producing an error bar which is close to optimal. We verify the efficacy and robustness of the method by applying it to WMAP7 data, finding \fnllocal=38.4 \pm 23.6 and \fnlequil=-119.2 \pm 123.6

Quantum brane cosmology

This thesis deals with the interaction of quantum mechanical models and cosmologies based on brane universes, an area of active theoretical speculation over the last five years.For convenience, the material has been split into two parts. Part 1 deals with a selection of background topics which are necessary and relevant to the original research. This research is presented in Part 2. In addition, some auxiliary topics, both more elementary and more advanced, are described in the appendices. The selection of background topics has been influenced by the various techniques, physical theories and mathematical technologies which play a major role in the work presented in Part 2. Although the exposition is ad hoc, an attempt has been made to systematically develop portions where the technique (or use of it) may be unfamiliar.A fairly complete treatment of the necessary mathematical scaffolding is supplied. Although important, this material is familiar or strongly mathematical, and is deferred to the appendices. This includes an elementary survey of functional analysis in Appendix A, sufficient to support a discussion of the path integral. The path integral formalism is used extensively throughout this thesis, and, where available, constitutes our preferred representation of quantum mechanics. The discussion is limited to the relevant portions of the theory: functions in Banacli spaces, and the Sturm-Liouville basis (technology which appears many times in Part 2); direct evaluation of Gaussian functional integrals, ubiquitous in field theory calculations; and ((-function regularization of the operator determinants to which such Gaussian integrals give rise, which has a direct application in Chapter 9. In Appendix B we describe the necessary framework of differential geometry which supports general relativity, and low-energy discussions of string theory. All calculations in metric gravity are based on differential geometry, together with a good proportion of the technology which buttresses quantum field theory on curved space time, string theory, and some more advanced representations of quantum mechanics (see below). All of this is used extensively throughout both parts of the thesis. We include some more advanced topological technology which supports the discussion of string compactification. General results from compactification theory, when appropriately interpreted in the brane context, contribute important stability results for zero-modes of the Kaluza—Klein fields, and provide a natural home for the spectral KK technology used (in one form or another) throughout Part 2, but most especially in Chapter 7 and Chapter 8. Einstein gravity and Yang-Mills theory are set in context as examples of connexions on fibre bundles

The curvature perturbation at second order

We give an explicit relation, up to second-order terms, between scalar-field fluctuations defined on spatially-flat slices and the curvature perturbation on uniform-density slices. This expression is a necessary ingredient for calculating observable quantities at second-order and beyond in multiple-field inflation. We show that traditional cosmological perturbation theory and the `separate universe' approach yield equivalent expressions for superhorizon wavenumbers, and in particular that all nonlocal terms can be eliminated from the perturbation-theory expressions

Transport equations for the inflationary trispectrum

We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, tauNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.Comment: 24 pages, plus references and appendix. v2: matches version published in JCAP; typo fixed in Eq. (54