90 research outputs found
Non-Gaussianity as a Particle Detector
We study the imprints of massive particles with spin on cosmological
correlators. Using the framework of the effective field theory of inflation, we
classify the couplings of these particles to the Goldstone boson of broken time
translations and the graviton. We show that it is possible to generate
observable non-Gaussianity within the regime of validity of the effective
theory, as long as the masses of the particles are close to the Hubble scale
and their interactions break the approximate conformal symmetry of the
inflationary background. We derive explicit shape functions for the scalar and
tensor bispectra that can serve as templates for future observational searches.Comment: 55 pages, 10 figure
Vacuum Decay in CFT and the Riemann-Hilbert problem
We study vacuum stability in 1+1 dimensional Conformal Field Theories with
external background fields. We show that the vacuum decay rate is given by a
non-local two-form. This two-form is a boundary term that must be added to the
effective in/out Lagrangian. The two-form is expressed in terms of a
Riemann-Hilbert decomposition for background gauge fields, and its novel
"functional" version in the gravitational case.Comment: 16 pages, 3 figure
Partially Massless Fields During Inflation
The representation theory of de Sitter space allows for a category of
partially massless particles which have no flat space analog, but could have
existed during inflation. We study the couplings of these exotic particles to
inflationary perturbations and determine the resulting signatures in
cosmological correlators. When inflationary perturbations interact through the
exchange of these fields, their correlation functions inherit scalings that
cannot be mimicked by extra massive fields. We discuss in detail the squeezed
limit of the tensor-scalar-scalar bispectrum, and show that certain partially
massless fields can violate the tensor consistency relation of single-field
inflation. We also consider the collapsed limit of the scalar trispectrum, and
find that the exchange of partially massless fields enhances its magnitude,
while giving no contribution to the scalar bispectrum. These characteristic
signatures provide clean detection channels for partially massless fields
during inflation.Comment: 48 pages, 5 figures. v2: references added, published versio
The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities
Scattering amplitudes at weak coupling are highly constrained by Lorentz
invariance, locality and unitarity, and depend on model details only through
coupling constants and particle content. In this paper, we develop an
understanding of inflationary correlators which parallels that of flat-space
scattering amplitudes. Specifically, we study slow-roll inflation with weak
couplings to extra massive particles, for which all correlators are controlled
by an approximate conformal symmetry on the boundary of the spacetime. After
classifying all possible contact terms in de Sitter space, we derive an
analytic expression for the four-point function of conformally coupled scalars
mediated by the tree-level exchange of massive scalars. Conformal symmetry
implies that the correlator satisfies a pair of differential equations with
respect to spatial momenta, encoding bulk time evolution in purely boundary
terms. The absence of unphysical singularities completely fixes this
correlator. A spin-raising operator relates it to the correlators associated
with the exchange of particles with spin, while weight-shifting operators map
it to the four-point function of massless scalars. We explain how these de
Sitter four-point functions can be perturbed to obtain inflationary three-point
functions. We reproduce many classic results in the literature and provide a
complete classification of all inflationary three- and four-point functions
arising from weakly broken conformal symmetry. The inflationary bispectrum
associated with the exchange of particles with arbitrary spin is completely
characterized by the soft limit of the simplest scalar-exchange four-point
function of conformally coupled scalars and a series of contact terms. Finally,
we demonstrate that the inflationary correlators contain flat-space scattering
amplitudes via a suitable analytic continuation of the external momenta.Comment: 110 pages, 13 figures, 1 table; V3: minor corrections and references
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A de Sitter -matrix for the masses
We define an -matrix for massive scalar fields on a fixed de Sitter
spacetime, in the expanding patch co-ordinates relevant for early Universe
cosmology. It enjoys many of the same properties as its Minkowski counterpart,
for instance: it is insensitive to total derivatives and field redefinitions in
the action; it can be extracted as a particular "on-shell" limit of
time-ordered correlation functions; and for low-point scattering, kinematics
strongly constrains its possible structures. We present explicit formulae
relating the usual observables - in-in equal-time correlators and wavefunction
coefficients at the conformal boundary - to -matrix elements. Finally, we
discuss some of the subtleties in extending this -matrix to light fields (in
the complementary series).Comment: 14 pages, 2 figure
The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
We extend the cosmological bootstrap to correlators involving massless
particles with spin. In de Sitter space, these correlators are constrained both
by symmetries and by locality. In particular, the de Sitter isometries become
conformal symmetries on the future boundary of the spacetime, which are
reflected in a set of Ward identities that the boundary correlators must
satisfy. We solve these Ward identities by acting with weight-shifting
operators on scalar seed solutions. Using this weight-shifting approach, we
derive three- and four-point correlators of massless spin-1 and spin-2 fields
with conformally coupled scalars. Four-point functions arising from tree-level
exchange are singular in particular kinematic configurations, and the
coefficients of these singularities satisfy certain factorization properties.
We show that in many cases these factorization limits fix the structure of the
correlators uniquely, without having to solve the conformal Ward identities.
The additional constraint of locality for massless spinning particles manifests
itself as current conservation on the boundary. We find that the four-point
functions only satisfy current conservation if the s, t, and u-channels are
related to each other, leading to nontrivial constraints on the couplings
between the conserved currents and other operators in the theory. For spin-1
currents this implies charge conservation, while for spin-2 currents we recover
the equivalence principle from a purely boundary perspective. For multiple
spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply
our methods to slow-roll inflation and derive a few phenomenologically relevant
scalar-tensor three-point functions.Comment: 128 pages, 15 figures; V3: minor corrections and references adde
Bootstrapping Multi-Field Inflation: non-Gaussianities from light scalars revisited
Primordial non-Gaussianities from multi-field inflation are a leading target
for cosmological observations, because of the possible large correlations
generated between long and short distances. These signatures are captured by
the local shape of the scalar bispectrum. In this paper, we revisit the
nonlinearities of the conversion process from additional light scalars into
curvature perturbations during inflation. We provide analytic templates for
correlation functions valid at any kinematical configuration, using the
cosmological bootstrap as a main computational tool. Our results include the
possibility of large breaking of boost symmetry, in the form of small speeds of
sound for both the inflaton and the mediators. We consider correlators coming
from the tree-level exchange of a massless scalar field. By introducing a
late-time cutoff, we identify that the symmetry constraints on the correlators
are modified. This leads to anomalous conformal Ward identities, and
consequently the bootstrap differential equations acquire a source term that
depends on this cutoff. The solutions to the differential equations are scalar
seed functions that incorporate these late-time growth effects. Applying
weight-shifting operators to auxiliary "seed" functions, we obtain a systematic
classification of shapes of non-Gaussianity coming from massless exchange. For
theories with de Sitter symmetry, we compare the resulting shapes with the ones
obtained via the formalism, identifying missing contributions away
from the squeezed limit. For boost-breaking scenarios, we derive a novel class
of shape functions with phenomenologically distinct features. Specifically, the
new shape provides a simple extension of equilateral non-Gaussianity: the
signal peaks at a geometric configuration controlled by the ratio of the sound
speeds of the mediator and the inflaton.Comment: 65 pages, 8 figure
The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
A key insight of the bootstrap approach to cosmological correlations is the
fact that all correlators of slow-roll inflation can be reduced to a unique
building block---the four-point function of conformally coupled scalars,
arising from the exchange of a massive scalar. Correlators corresponding to the
exchange of particles with spin are then obtained by applying a spin-raising
operator to the scalar-exchange solution. Similarly, the correlators of
massless external fields can be derived by acting with a suitable
weight-raising operator. In this paper, we present a systematic and highly
streamlined derivation of these operators (and their generalizations) using
tools of conformal field theory. Our results greatly simplify the theoretical
foundations of the cosmological bootstrap program.Comment: 53 pages, 5 figures; V2: minor corrections and references adde
Linking the Singularities of Cosmological Correlators
Much of the structure of cosmological correlators is controlled by their
singularities, which in turn are fixed in terms of flat-space scattering
amplitudes. An important challenge is to interpolate between the singular
limits to determine the full correlators at arbitrary kinematics. This is
particularly relevant because the singularities of correlators are not directly
observable, but can only be accessed by analytic continuation. In this paper,
we study rational correlators, including those of gauge fields, gravitons, and
the inflaton, whose only singularities at tree level are poles and whose
behavior away from these poles is strongly constrained by unitarity and
locality. We describe how unitarity translates into a set of cutting rules that
consistent correlators must satisfy, and explain how this can be used to
bootstrap correlators given information about their singularities. We also
derive recursion relations that allow the iterative construction of more
complicated correlators from simpler building blocks. In flat space, all energy
singularities are simple poles, so that the combination of unitarity
constraints and recursion relations provides an efficient way to bootstrap the
full correlators. In many cases, these flat-space correlators can then be
transformed into their more complex de Sitter counterparts. As an example of
this procedure, we derive the correlator associated to graviton Compton
scattering in de Sitter space, though the methods are much more widely
applicable.Comment: 69+29 pages, 6 figure
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