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David Wands

Publications and source records attributed to David Wands.

At least 109 records · Page 6Linked to original sources
arXiv2009

Cosmological perturbations

We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear and curvature of constant-time hypersurfaces and the orthogonal timelike vector field. We give the gauge transformation rules for metric and matter variables at first and second order. We show how gauge invariant variables are constructed by identifying geometric or matter variables in physically-defined coordinate systems, and give the relations between many commonly used gauge-invariant variables. In particular we show how the Einstein equations or energy-momentum conservation can be used to obtain simple evolution equations at linear order, and discuss extensions to non-linear order. We present evolution equations for systems with multiple interacting fluids and scalar fields, identifying adiabatic and entropy perturbations. As an application we consider the origin of primordial curvature and isocurvature perturbations from field perturbations during inflation in the very early universe.

astro-ph↗
arXiv2009

Scale-dependent bias from primordial non-Gaussianity in general relativity

In this note we examine the derivation of scale-dependent bias due to primordial non-Gaussianity of the local type in the context of general relativity. We justify the use of the Poisson equation in general relativistic perturbation theory and thus the derivation of scale-dependent bias as a test of primordial non-Gaussianity, using the spherical collapse model. The corollary is that the form of scale-dependent bias does not receive general relativistic corrections on scales larger than the Hubble radius. This leads to a formally divergent correlation function for biased tracers of the mass distribution which we discuss.

astro-ph.CO↗
arXiv2009

Non-Gaussianities from ekpyrotic collapse with multiple fields

We compute the non-Gaussianity of the curvature perturbation generated by ekpyrotic collapse with multiple fields. The transition from the multi-field scaling solution to a single-field dominated regime converts initial isocurvature field perturbations to an almost scale-invariant comoving curvature perturbation. In the specific model of two fields, $ϕ_1$ and $ϕ_2$, with exponential potentials, $-V_i \exp (-c_i ϕ_i)$, we calculate the bispectrum of the resulting curvature perturbation. We find that the non-Gaussianity is dominated by non-linear evolution on super-Hubble scales and hence is of the local form. The non-linear parameter of the curvature perturbation is given by $f_{NL} = 5 c_j^2 /12$, where $c_j$ is the exponent of the potential for the field which becomes sub-dominant at late times. Since $c_j^2$ must be large, in order to generate an almost scale invariant spectrum, the non-Gaussianity is inevitably large. By combining the present observational constraints on $f_{\rm NL}$ and the scalar spectral index, the specific model studied in this paper is thus ruled out by current observational data.

hep-th↗
arXiv2009

CMBPol Mission Concept Study: Probing Inflation with CMB Polarization

We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters.

astro-ph↗
arXiv2009

Curvature perturbations from ekpyrotic collapse with multiple fields

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in the ekpyrotic scaling solution in models where multiple fields have steep negative exponential potentials. The scale invariance of the spectrum is realized by a tachyonic instability in the isocurvature field. This instability drives the scaling solution to the late time attractor that is the old ekpyrotic collapse dominated by a single field. We show that the transition from the scaling solution to the single field dominated ekpyrotic collapse automatically converts the initial isocurvature perturbations about the scaling solution to comoving curvature perturbations about the late-time attractor. The final amplitude of the comoving curvature perturbation is determined by the Hubble scale at the transition.

hep-th↗
arXiv2009

Gravitational waves from an early matter era

We investigate the generation of gravitational waves due to the gravitational instability of primordial density perturbations in an early matter-dominated era which could be detectable by experiments such as LIGO and LISA. We use relativistic perturbation theory to give analytic estimates of the tensor perturbations generated at second order by linear density perturbations. We find that large enhancement factors with respect to the naive second-order estimate are possible due to the growth of density perturbations on sub-Hubble scales. However very large enhancement factors coincide with a breakdown of linear theory for density perturbations on small scales. To produce a primordial gravitational wave background that would be detectable with LIGO or LISA from density perturbations in the linear regime requires primordial comoving curvature perturbations on small scales of order 0.02 for Advanced LIGO or 0.005 for LISA, otherwise numerical calculations of the non-linear evolution on sub-Hubble scales are required.

astro-ph.CO↗
arXiv2008

Singularities in loop quantum cosmology

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of Loop Quantum Cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of singularities.

gr-qc↗
arXiv2008

Non-linear isocurvature perturbations and non-Gaussianities

We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended delta N-formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum of primordial isocurvature perturbations may be large and comparable to the bispectrum of adiabatic curvature perturbations.

astro-ph↗
arXiv2008

Cosmological perturbations through the big bang

Several scenarios have been proposed in which primordial perturbations could originate from quantum vacuum fluctuations in a phase corresponding to a collapse phase (in an Einstein frame) preceding the Big Bang. I briefly review three models which could produce scale-invariant spectra during collapse: (1) curvature perturbations during pressureless collapse, (2) axion field perturbations in a pre big bang scenario, and (3) tachyonic fields during multiple-field ekpyrotic collapse. In the separate universes picture one can derive generalised perturbation equations to describe the evolution of large scale perturbations through a semi-classical bounce, assuming a large-scale limit in which inhomogeneous perturbations can be described by locally homogeneous patches. For adiabatic perturbations there exists a conserved curvature perturbation on large scales, but isocurvature perturbations can change the curvature perturbation through the non-adiabatic pressure perturbation on large scales. Different models for the origin of large scale structure lead to different observational predictions, including gravitational waves and non-Gaussianity.

astro-ph↗
arXiv2008

Generalised perturbation equations in bouncing cosmologies

We consider linear perturbation equations for long-wavelength scalar metric perturbations in generalised gravity, applicable to non-singular cosmological models including a bounce from collapse to expansion in the very early universe. We present the general form for the perturbation equations which follows from requiring that the inhomogeneous universe on large scales obeys the same local equations as the homogeneous Friedmann-Robertson-Walker background cosmology (the separate universes approach). In a pseudo-longitudinal gauge this becomes a homogeneous second-order differential equation for adiabatic perturbations, which reduces to the usual equation for the longitudinal gauge metric perturbation in general relativity with vanishing anisotropic stress. As an application we show that the scale-invariant spectrum of perturbations in the longitudinal gauge generated during an ekpyrotic collapse are not transferred to the growing mode of adiabatic density perturbations in the expanding phase in a simple bounce model.

hep-th↗
arXiv2008

Primordial non-gaussianity from multiple curvaton decay

We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, and solve them in a sudden-decay approximation. We calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. Not surprisingly, we find large positive values of fNL if the energy densities of the curvatons are sub-dominant when they decay, as in the single curvaton case. But we also find a novel effect, which can be present only in multi-curvaton models: fNL becomes large even if the curvatons dominate the total energy density in the case when the inhomogeneous radiation produced by the first curvaton decay is diluted by the decay of a second nearly homogeneous curvaton. The minimum value min(fNL)=-5/4 which we find is the same as in the single-curvaton case. Using (non-)Gaussianity observations, Planck can be able to distinguish between single-field inflation and curvaton model. Hence it is important to derive theoretical predictions for curvaton model. From particle physics point of view it is more natural to assume multiple scalar fields (rather than just one ``curvaton'' in addition to inflaton). Our work updates the theoretical predictions of curvaton model to this case.

astro-ph↗
arXiv2007

Diagrammatic approach to non-Gaussianity from inflation

We present Feynman type diagrams for calculating the n-point function of the primordial curvature perturbation in terms of scalar field perturbations during inflation. The diagrams can be used to evaluate the corresponding terms in the n-point function at tree level or any required loop level. Rules are presented for drawing the diagrams and writing down the corresponding terms in real space and Fourier space. We show that vertices can be renormalised to automatically account for diagrams with dressed vertices. We apply these rules to calculate the primordial power spectrum up to two loops, the bispectrum including loop corrections, and the trispectrum.

hep-th↗
arXiv2007

Brane-world inflation: slow-roll corrections to the spectral index

We quantify the slow-roll corrections to primordial density perturbations arising from inflation driven by a four-dimensional scalar field with a monomial potential in a five-dimensional non-compact bulk spacetime. Although the difference between the classical brane-world solutions and standard four-dimensional solutions is large at early times, the change to the amplitude at late times of perturbations generated from quantum fluctuations is first-order in slow-roll parameters, leading to second-order slow-roll corrections to the spectral index. This confirms that the leading-order effects are correctly given by previous work in the literature.

astro-ph↗
arXiv2007

Primordial non-Gaussianity from two curvaton decays

We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. We find large positive values of fNL if the energy densities of the curvatons are sub-dominant when they decay, as in the single curvaton case. But we also find a large fNL even if the curvatons dominate the total energy density in the case when the inhomogeneous radiation produced by the first curvaton decay is diluted by the decay of a second nearly homogeneous curvaton. The minimum value min(fNL)=-5/4 which we find is the same as in the single-curvaton case.

hep-ph↗
arXiv2007

Low-energy effective theory for a Randall-Sundrum scenario with a moving bulk brane

We derive the low-energy effective theory of gravity for a generalized Randall-Sundrum scenario, allowing for a third self-gravitating brane to live in the 5D bulk spacetime. At zero order the 5D spacetime is composed of two slices of anti-de Sitter spacetime, each with a different curvature scale, and the 5D Weyl tensor vanishes. Two boundary branes are at the fixed points of the orbifold whereas the third brane is free to move in the bulk. At first order, the third brane breaks the otherwise continuous evolution of the projection of the Weyl tensor normal to the branes. We derive a junction condition for the projected Weyl tensor across the bulk brane, and combining this constraint with the junction condition for the extrinsic curvature tensor, allows us to derive the first-order field equations on the middle brane. The effective theory is a generalized Brans-Dicke theory with two scalar fields. This is conformally equivalent to Einstein gravity and two scalar fields, minimally coupled to the geometry, but nonminimally coupled to matter on the three branes.

hep-th↗
arXiv2007

Coupled bulk and brane fields about a de Sitter brane

We consider the evolution of a bulk scalar field in anti-de Sitter (AdS) spacetime linearly coupled to a scalar field on a de Sitter boundary brane. We present results of a spectral analysis of the system, and find that the model can exhibit both bound and continuum resonant modes. We find that zero, one, or two bound states may exist, depending upon the masses of the brane and bulk fields relative to the Hubble length and the AdS curvature scale and the coupling strength. In all cases, we find a critical coupling above which there exists a tachyonic bound state. We show how the 5-dimensional spectral results can be interpreted in terms of a 4-dimensional effective theory for the bound states. We find excellent agreement between our analytic results and the results of a new numerical code developed to model the evolution of bulk fields coupled to degrees of freedom on a moving brane. This code can be used to model the behaviour of braneworld cosmological perturbations in scenarios for which no analytic results are known.

hep-th↗
arXiv2007

Ekpyrotic collapse with multiple fields

A scale invariant spectrum of isocurvature perturbations is generated during collapse in the scaling solution in models where two or more fields have steep negative exponential potentials. The scale invariance of the spectrum is realised by a tachyonic instability in the isocurvature field. We show that this instability is due to the fact that the scaling solution is a saddle point in the phase space. The late time attractor is identified with a single field dominated ekpyrotic collapse in which a steep blue spectrum for isocurvature perturbations is found. Although quantum fluctuations do not necessarily to disrupt the classical solution, an additional preceding stage is required to establish classical homogeneity.

hep-th↗
arXiv2007

Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion

We calculate the power spectra of primordial curvature and isocurvature perturbations from a general two field inflation model at next-to-leading order correction in a slow-roll expansion. In particular we calculate the spectral indices to second order in slow-roll parameters. We show that the cross-correlation of the curvature and isocurvature perturbations at the time of Hubble-exit during inflation is non-zero at first-order in slow-roll parameters. We apply our results to different classes of inflation, including inflaton and curvaton scenarios. The spectrum of primordial gravitational waves, curvature and isocurvature perturbations obey generalised consistency relations in two-field inflation models. We give the first two consistency relations in an infinite hierarchy.

astro-ph↗