21 research outputs found
Hidden Universality in the Merger Rate Distribution in the Primordial Black Hole Scenario
It has been proposed that primordial black holes (PBHs) form binaries in the radiation dominated era. Once formed, some fraction of them may merge within the age of the universe by gravitational radiation reaction. We investigate the merger rate of the PBH binaries when the PBHs have a distribution of masses around O(10) M-circle dot, which is a generalization of the previous studies where the PBHs are assumed to have the same mass. After deriving a formula for the merger time probability distribution in the PBH mass plane, we evaluate it under two different approximations. We identify a quantity constructed from the mass distribution of the merger rate density per unit cosmic time and comoving volume R (m(1), m(2)), alpha = -(m(1)+ m(2))(2)partial derivative(2) In R/partial derivative m(1)partial derivative m(2),which universally satisfies 0.97 less than or similar to alpha less than or similar to 1.05 for all binary masses independently of the PBH mass function. This result suggests that the measurement of this quantity is useful for testing the PBH scenario
Non-gaussianity from the bispectrum in general multiple field inflation
We study the non-gaussianity from the bispectrum in multi-field inflation
models with a general kinetic term. The models include the multi-field
K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special
cases. We find that, in general, the sound speeds for the adiabatic and entropy
perturbations are different and they can be smaller than 1. Then the
non-gaussianity can be enhanced. The multi-field DBI-inflation is shown to be a
special case where both sound speeds are the same due to a special form of the
kinetic term. We derive the exact second and third order actions including
metric perturbations. In the small sound speed limit and at leading order in
the slow-roll expansion, we derive the three point function for the curvature
perturbation which depends on both adiabatic and entropy perturbations. The
contribution from the entropy perturbations has a different momentum dependence
if the sound speed for the entropy perturbations is different from the
adiabatic one, which provides a possibility to distinguish the multi-field
models from single field models. On the other hand, in the multi-field DBI
case, the contribution from the entropy perturbations has the same momentum
dependence as the pure adiabatic contributions and it only changes the
amplitude of the three point function. This could help to ease the constraints
on the DBI-inflation models.Comment: 16 pages, no figur
Classical approximation to quantum cosmological correlations
We investigate up to which order quantum effects can be neglected in
calculating cosmological correlation functions after horizon exit. As a toy
model, we study theory on a de Sitter background for a massless
minimally coupled scalar field . We find that for tree level and one loop
contributions in the quantum theory, a good classical approximation can be
constructed, but for higher loop corrections this is in general not expected to
be possible. The reason is that loop corrections get non-negligible
contributions from loop momenta with magnitude up to the Hubble scale H, at
which scale classical physics is not expected to be a good approximation to the
quantum theory. An explicit calculation of the one loop correction to the two
point function, supports the argument that contributions from loop momenta of
scale are not negligible. Generalization of the arguments for the toy model
to derivative interactions and the curvature perturbation leads to the
conclusion that the leading orders of non-Gaussian effects generated after
horizon exit, can be approximated quite well by classical methods. Furthermore
we compare with a theorem by Weinberg. We find that growing loop corrections
after horizon exit are not excluded, even in single field inflation.Comment: 44 pages, 1 figure; v2: corrected errors, added references,
conclusions unchanged; v3: added section in which we compare with stochastic
approach; this version matches published versio
Primordial Non-Gaussianities of General Multiple Field Inflation
We perform a general study of the primordial scalar non-Gaussianities in
multi-field inflationary models in Einstein gravity. We consider models
governed by a Lagrangian which is a general function of the scalar fields and
their first spacetime derivatives. We use formalism to relate scalar
fields and curvature perturbations. We calculate the explicit cubic order
perturbation action and the three-point function of curvature perturbation
evaluated at horizon-crossing. Under reasonable assumptions, in the limit of
small slow-varying parameters and a sound speed close to one, we find
that the non-Gaussianity is completely determined by these slow-varying
parameters and some other parameters determined by the structure of the
inflationary models. Our work generalizes previous results, and would be useful
to study non-Gaussianity in multi-field inflationary models that will be
constructed in the future.Comment: 26 pages, no figure; v2, minor revision; v3 minor misprints
corrected; v4 minor misprints correcte
Mathematical model for empirically optimizing large scale production of soluble protein domains
One-loop corrections to the curvature perturbation from inflation
An estimate of the one-loop correction to the power spectrum of the
primordial curvature perturbation is given, assuming it is generated during a
phase of single-field, slow-roll inflation. The loop correction splits into two
parts, which can be calculated separately: a purely quantum-mechanical
contribution which is generated from the interference among quantized field
modes around the time when they cross the horizon, and a classical contribution
which comes from integrating the effect of field modes which have already
passed far beyond the horizon. The loop correction contains logarithms which
may invalidate the use of naive perturbation theory for cosmic microwave
background (CMB) predictions when the scale associated with the CMB is
exponentially different from the scale at which the fundamental theory which
governs inflation is formulated.Comment: 28 pages, uses feynmp.sty and ioplatex journal style. v2: supersedes
version published in JCAP. Some corrections and refinements to the discussion
and conclusions. v3: Corrects misidentification of quantum correction with an
IR effect. Improvements to the discussio
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.Comment: 17 pages, 13 figures. v2: Comments and references added, v3:
Introduction expanded, subsection on evaluating loop diagrams added, minor
errors corrected, references adde
Enhanced Non-Gaussianity from Excited Initial States
We use the techniques of effective field theory in an expanding universe to
examine the effect of choosing an excited inflationary initial state built over
the Bunch-Davies state on the CMB bi-spectrum. We find that even for Hadamard
states, there are unexpected enhancements in the bi-spectrum for certain
configurations in momentum space due to interactions of modes in the early
stages of inflation. These enhancements can be parametrically larger than the
standard ones and are potentially observable in current and future data. These
initial state effects have a characteristic signature in -space which
distinguishes them from the usual contributions, with the enhancement being
most pronounced for configurations corresponding to flattened triangles for
which two momenta are collinear.Comment: 33 pages, 1 figure. Refs added and minor addition
Generation and Characterization of Large Non-Gaussianities in Single Field Inflation
Inflation driven by a single, minimally coupled, slowly rolling field
generically yields a negligible primordial non-Gaussianity. We discuss two
distinct mechanisms by which a non-trivial potential can generate large
non-Gaussianities. Firstly, if the inflaton traverses a feature in the
potential, or if the inflationary phase is short enough so that initial
transient contributions to the background dynamics have not been erased, modes
near horizon-crossing can acquire significant non-Gaussianities. Secondly,
potentials with small-scale structure may induce significant non-Gaussianities
while the relevant modes are deep inside the horizon. The first case includes
the "step" potential we previously analyzed while the second "resonance" case
is novel. We derive analytic approximations for the 3-point terms generated by
both mechanisms written as products of functions of the three individual
momenta, permitting the use of efficient analysis algorithms. Finally, we
present a significantly improved approach to regularizing and numerically
evaluating the integrals that contribute to the 3-point function.Comment: 29 pp, 8 fig
The separate universe approach to soft limits
We develop a formalism for calculating soft limits of -point inflationary
correlation functions using separate universe techniques. Our method naturally
allows for multiple fields and leads to an elegant diagrammatic approach. As an
application we focus on the trispectrum produced by inflation with multiple
light fields, giving explicit formulae for all possible single- and double-soft
limits. We also investigate consistency relations and present an infinite tower
of inequalities between soft correlation functions which generalise the
Suyama-Yamaguchi inequality.Comment: 28 pages, 7 figures. This is an author-created, un-copyedited version
of an article published in JCAP. IOP Publishing Ltd is not responsible for
any errors or omissions in this version of the manuscript or any version
derived from it. The Version of Record is available online at the DOI below.
v3: Updated to match version published in JCA