arXiv subjects

Hael Collins

Publications and source records attributed to Hael Collins.

At least 19 recordsLinked to original sources

arXiv2017

The quantum Fokker-Planck equation of stochastic inflation

We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.

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arXiv2016

Entangled Scalar and Tensor Fluctuations during Inflation

We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the $T$, $E$, and $B$ modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.

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arXiv2014

A Cosmological Slavnov-Taylor Identity

We develop a method for treating the consistency relations of inflation that includes the full time-evolution of the state. This approach relies only on the symmetries of the inflationary setting, in particular a residual conformal symmetry in the spatial part of the metric, along with general properties which hold for any quantum field theory. As a result, the consistency relations that emerge, which are essentially the Slavnov-Taylor identities associated with this residual conformal symmetry, apply very generally: they are true of the full Green's functions, hold largely independently of the particular inflationary model, and can be used for arbitrary states. We illustrate these techniques by showing the form assumed by the standard consistency relation between the two and three-point functions for the primordial scalar fluctuations when they are in a Bunch-Davies state. But because we have included the full evolution of the state, this approach works for a general initial state as well and does not need to have assumed that inflation began in the Bunch-Davies state.

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arXiv2014

Renormalizing an initial state

The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it is rarely possible to solve for the eigenstates of an interacting theory exactly, a general state and its evolution can nonetheless be constructed perturbatively in terms of the propagators and structures defined with respect to the free theory. The detailed form of the initial state in this picture is fixed by imposing suitable `renormalization conditions' on the Green's functions. This technique is illustrated with an example drawn from inflation, where the presence of nonrenormalizable operators and where an expansion that naturally couples early times with short distances make the ability to start the theory at a finite initial time especially desirable.

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arXiv2014

Primordial non-Gaussianities from inflation

These notes present a detailed introduction to Maldacena's calculation of the three-point function generated by the simplest class of inflationary models: those with a single inflaton field whose potential satisfies the slow-roll conditions and whose quantum fluctuations start in the asymptotic Bunch-Davies vacuum state. The three-point function should be the most readily observed evidence for non-Gaussianities amongst the primordial fluctuations produced by inflation. In these inflationary theories the non-Gaussianities are predicted to be extremely small, being naturally suppressed by the small slow-roll parameters.

astro-ph.CO↗

arXiv2014

Do Mixed States save Effective Field Theory from BICEP?

The BICEP2 collaboration has for the first time observed the B-mode polarization associated with inflationary gravitational waves. Their result has some discomfiting implications for the validity of an effective theory approach to single-field inflation since it would require an inflaton field excursion larger than the Planck scale. We argue that if the quantum state of the gravitons is a mixed state based on the Bunch-Davies vacuum, then the tensor to scalar ratio r measured by BICEP is different than the quantity that enters the Lyth bound. When this is taken into account, the tension between effective field theory and the BICEP result is alleviated.

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arXiv2013

Initial state propagators

It is possible to define a general initial state for a quantum field by introducing a contribution to the action defined at an initial-time boundary. The propagator for this theory is composed of two parts, one associated with the free propagation of fields and another produced by the operators of this initial action. The derivation of this propagator is shown for the case of a translationally and rotationally invariant initial state. In addition to being able to treat more general states, these techniques can also be applied to effective field theories that start from an initial time. The eigenstates of a theory with interacting heavy and light fields are different from the eigenstates of the theory in the limit where the interactions vanish. Therefore, a product of states of the noninteracting heavy and light theories will usually contain excitations of the heavier state once the interactions are included. Such excitations appear as nonlocal effects in the effective theory, which are suppressed by powers of the mass of the heavy field. By appropriately choosing the initial action, these excitations can be excised from the state leaving just effects that would be produced by a local action of the lighter fields.

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arXiv2012

Effective field theory in time-dependent settings

We use the in-in or Schwinger-Keldysh formalism to explore the construction and interpretation of effective field theories for time-dependent systems evolving out of equilibrium. Starting with a simple model consisting of a heavy and a light scalar field taken to be in their free vacuum states at a finite initial time, we study the effects from the heavy field on the dynamics of the light field by analyzing the equation of motion for the expectation value of the light background field. New terms appear which cannot arise from a local action of an effective field theory in terms of the light field, though they disappear in the adiabatic limit. We discuss the origins of these terms as well as their possible implications for time dependent situations such as inflation.

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arXiv2010

The influence of inhomogeneities on the large-scale expansion of the universe

The evolution of an inhomogeneous universe composed entirely of matter is followed from an early, nearly uniform state until the time when the inhomogeneities have begun to grow large. The particular distribution of matter studied in this article is chosen to have a periodic variation in only one of the directions, which is simple enough to allow the behavior of the metric to be solved analytically, well beyond a linear approximation based on the initial smallness of the fluctuation. This example provides an illustration of a universe where the inhomogeneities can affect its average expansion rate; and its simplicity allows a condition to be derived that tells when their presence should begin to become important. Since the averages of the non-uniform parts of the metric and the matter density grow faster than their uniform parts, the average expansion rate accelerates with the advent of the era governed by the inhomogeneities.

astro-ph.CO↗

arXiv2009

Enhancing non-Gaussianities by breaking local Lorentz invariance

This talk briefly explains how the breaking of a Lorentz-invariant description of nature at tiny space-time intervals might affect the non-Gaussian character of the primordial fluctuations left by inflation. For example, a model that contains irrelevant operators that only preserve the spatial symmetries along constant-time surfaces can generate a larger non-Gaussian component in the pattern of primordial fluctuations than is ordinarily predicted by inflation. This property can be useful for constraining models that allow some Lorentz violation at short distances, beyond the constraints possible from the power spectrum alone.

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arXiv2009

Trans-Planckian enhancements of the primordial non-Gaussianities

This article examines how breaking a Lorentz-invariant description of nature at tiny space-time intervals would affect the non-Gaussian character of the pattern of primordial perturbations left by inflation. We specifically study a set of irrelevant operators that preserve the spatial symmetries of the usual inflationary background. The non-Gaussian component in the primordial fluctuations can be much larger than the usual, small, inflationary prediction and can thus lead to much stronger constraints on the role of "trans-Planckian" physics in inflation than those from the measurements of the primordial power spectrum.

hep-ph↗

arXiv2008

Unparticles and inflation

We study some of the roles for unparticles in an inflationary universe. Unparticles by themselves are not appropriate for generating the primordial perturbations since their power spectrum does not match what has been inferred from observations. In fact, when the scaling dimension for the unparticles exceeds three-halves, the unparticle power spectrum diverges. However, when a unparticle couples to an ordinary inflaton particle, loop corrections can produce a slight enhancement of the inflaton's power spectrum at longer wavelengths. We examine these loop corrections from unparticles in some detail to learn how they scale in the wavelength of a perturbation and how they depend on the scaling dimension of the field.

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arXiv2008

Trans-Planckian relics in the scalar to tensor ratio

The physical properties of our universe at energy scales above the expansion rate during inflation can affect predictions for the ratio between the amplitudes of the primordial scalar and tensor fluctuations. In particular, we study here the effects of a breakdown of a locally Lorentz invariant description of nature at tiny space-time intervals. In some instances, these effects shift the amplitudes by a constant amount, altering the standard relation between this ratio and the slow-roll parameters. More generally, "trans-Planckian" effects introduce a modulation in the primordial power spectra which grows at shorter scales, making the value of the ratio sensitive to the scale at which it is defined. We also present a model where symmetries are broken at horizon scales during inflation. In this case, the power at large scales today could then be suppressed, relative to that at smaller scales.

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arXiv2007

Trans-Planckian signals from the breaking of local Lorentz invariance

This article examines how a breakdown of a locally Lorentz invariant, point-like description of nature at tiny space-time intervals would translate into a distinctive set of signals in the primordial power spectrum generated by inflation. We examine the leading irrelevant operators that are consistent with the spatial translations and rotations of a preferred, isotropically expanding, background. A few of the resulting corrections to the primordial power spectrum do not have the usual oscillatory factor, which is sometimes taken to be characteristic of a "trans-Planckian" signal. Perhaps more interestingly, one of these leading irrelevant operators exactly reproduces a correction to the power spectrum that occurs in effective descriptions of the state of the field responsible for inflation.

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arXiv2006

The energy-momentum tensor for an effective initial state and the renormalization of gravity

We renormalize the divergences in the energy-momentum tensor of a scalar field that begins its evolution in an effective initial state. The effective initial state is a formalism that encodes the signatures of new physics in the structure of the quantum state of a field; in an inflationary setting, these signatures could include trans-Planckian effects. We treat both the scalar field and gravity equivalently, considering each as a small quantum fluctuation about a spatially independent background. The classical gravitational equations of motion then arise as a tadpole condition on the graviton. The contribution of the scalar field to these equations contains divergences associated with the structure of the effective state. However, these divergences occur only at the initial time, where the state was defined, and they accompany terms depending solely upon the classical gravitational background. We define the renormalization prescription that adds the appropriate counterterms at the initial-time boundary to cancel these divergences, and illustrate it with several examples evaluated at one-loop order.

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arXiv2006

The renormalization of the energy-momentum tensor for an effective initial state

An effective description of an initial state is a method for representing the signatures of new physics in the short-distance structure of a quantum state. The expectation value of the energy-momentum tensor for a field in such a state contains new divergences that arise when summing over this new structure. These divergences occur only at the initial time at which the state is defined and therefore can be cancelled by including a set of purely geometric counterterms that also are confined to this initial surface. We describe this gravitational renormalization of the divergences in the energy-momentum tensor for a free scalar field in an isotropically expanding inflationary background. We also show that the back-reaction from these new short-distance features of the state is small when compared with the leading vacuum energy contained in the field.

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arXiv2005

An effective theory of initial conditions in inflation

We examine the renormalization of an effective theory description of a general initial state set in an isotropically expanding space-time, which is done to understand how to include the effects of new physics in the calculation of the cosmic microwave background power spectrum. The divergences that arise in a perturbative treatment of the theory are of two forms: those associated with the properties of a field propagating through the bulk of space-time, which are unaffected by the choice of the initial state, and those that result from summing over the short-distance structure of the initial state. We show that the former have the same renormalization and produce the same subsequent scale dependence as for the standard vacuum state, while the latter correspond to divergences that are localized at precisely the initial time hypersurface on which the state is defined. This class of divergences is therefore renormalized by adding initial-boundary counterterms, which render all of the perturbative corrections small and finite. Initial states that approach the standard vacuum at short distances require, at worst, relevant or marginal boundary counterterms. States that differ from the vacuum at distances below that at which any new, potentially trans-Planckian, physics becomes important are renormalized with irrelevant boundary counterterms.

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arXiv2005

Renormalization of initial conditions and the trans-Planckian problem of inflation

Understanding how a field theory propagates the information contained in a given initial state is essential for quantifying the sensitivity of the cosmic microwave background to physics above the Hubble scale during inflation. Here we examine the renormalization of a scalar theory with nontrivial initial conditions in the simpler setting of flat space. The renormalization of the bulk theory proceeds exactly as for the standard vacuum state. However, the short distance features of the initial conditions can introduce new divergences which are confined to the surface on which the initial conditions are imposed. We show how the addition of boundary counterterms removes these divergences and induces a renormalization group flow in the space of initial conditions.

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