16 research outputs found
Separable and non-separable multi-field inflation and large non-Gaussianity
In this paper we provide a general framework based on formalism to
estimate the cosmological observables pertaining to the cosmic microwave
background radiation for non-separable potentials, and for generic \emph{end of
inflation} boundary conditions. We provide analytical and numerical solutions
to the relevant observables by decomposing the cosmological perturbations along
the curvature and the isocurvature directions, \emph{instead of adiabatic and
entropy directions}. We then study under what conditions large bi-spectrum and
tri-spectrum can be generated through phase transition which ends inflation. In
an illustrative example, we show that large and
can be obtained for the case of separable and
non-separable inflationary potentials.Comment: 21 pages, 6 figure
Effects of non-linearities on magnetic field generation
Magnetic fields are present on all scales in the Universe. While we
understand the processes which amplify the fields fairly well, we do not have a
"natural" mechanism to generate the small initial seed fields. By using fully
relativistic cosmological perturbation theory and going beyond the usual
confines of linear theory we show analytically how magnetic fields are
generated. This is the first analytical calculation of the magnetic field at
second order, using gauge-invariant cosmological perturbation theory, and
including all the source terms. To this end, we have rederived the full set of
governing equations independently. Our results suggest that magnetic fields of
the order of G can be generated (although this depends on the small
scale cut-off of the integral), which is largely in agreement with previous
results that relied upon numerical calculations. These fields are likely too
small to act as the primordial seed fields for dynamo mechanisms.Comment: 21 pages; v2: minor changes, added references; v3: version accepted
for publication in JCA
Inflationary signatures of single-field models beyond slow-roll
If the expansion of the early Universe was not close to de Sitter, the
statistical imprints of the primordial density perturbation on the cosmic
microwave background can be quite different from those derived in slow-roll
inflation. In this paper we study the inflationary signatures of all
single-field models which are free of ghost-like instabilities. We allow for a
rapid change of the Hubble parameter and the speed of sound of scalar
fluctuations, in a way that is compatible with a nearly scale-invariant
spectrum of perturbations, as supported by current cosmological observations.
Our results rely on the scale-invariant approximation, which is different from
the standard slow-roll approximation. We obtain the propagator of scalar
fluctuations and compute the bispectrum, keeping next-order corrections
proportional to the deviation of the spectral index from unity. These theories
offer an explicit example where the shape and scale-dependences of the
bispectrum are highly non-trivial whenever slow-roll is not a good
approximation.Comment: v1: 36 pages, including tables, appendices and references. v2:
abstract improved, references added, minor clarifications throughout the
text; matches version published in JCA
The inflationary bispectrum with curved field-space
We compute the covariant three-point function near horizon-crossing for a
system of slowly-rolling scalar fields during an inflationary epoch, allowing
for an arbitrary field-space metric. We show explicitly how to compute its
subsequent evolution using a covariantized version of the separate universe or
"delta-N" expansion, which must be augmented by terms measuring curvature of
the field-space manifold, and give the nonlinear gauge transformation to the
comoving curvature perturbation. Nonlinearities induced by the field-space
curvature terms are a new and potentially significant source of
non-Gaussianity. We show how inflationary models with non-minimal coupling to
the spacetime Ricci scalar can be accommodated within this framework. This
yields a simple toolkit allowing the bispectrum to be computed in models with
non-negligible field-space curvature.Comment: 22 pages, plus appendix and reference
Quantifying the behaviour of curvature perturbations during inflation
How much does the curvature perturbation change after it leaves the horizon,
and when should one evaluate the power spectrum? To answer these questions we
study single field inflation models numerically, and compare the evolution of
different curvature perturbations from horizon crossing to the end of
inflation. In particular we calculate the number of efolds it takes for the
curvature perturbation at a given wavenumber to settle down to within a given
fraction of their value at the end of inflation. We find that e.g. in chaotic
inflation, the amplitude of the comoving and the curvature perturbation on
uniform density hypersurfaces differ by up to 180 % at horizon crossing
assuming the same amplitude at the end of inflation, and that it takes
approximately 3 efolds for the curvature perturbation to be within 1 % of its
value at the end of inflation.Comment: Revtex4, 11 pages, 10 figures; v2: added results section E, added
references and acknowledgements; v3: clarification added to conclusions,
version to appear in CQ
The δN formula is the dynamical renormalization group
We derive the 'separate universe' method for the inflationary bispectrum,
beginning directly from a field-theory calculation. We work to tree-level in
quantum effects but to all orders in the slow-roll expansion, with masses
accommodated perturbatively. Our method provides a systematic basis to account
for novel sources of time-dependence in inflationary correlation functions, and
has immediate applications. First, we use our result to obtain the correct
matching prescription between the 'quantum' and 'classical' parts of the
separate universe computation. Second, we elaborate on the application of this
method in situations where its validity is not clear. As a by-product of our
calculation we give the leading slow-roll corrections to the three-point
function of field fluctuations on spatially flat hypersurfaces in a canonical,
multiple-field model.Comment: v1: 33 pages, plus appendix and references; 5 figures. v2:
typographical typos fixed, minor changes to the main text and abstract,
reference added; matches version published in JCA
Isocurvature initial conditions for second order Boltzmann solvers
We study how to set the initial evolution of general cosmological
fluctuations at second order, after neutrino decoupling. We compute approximate
initial solutions for the transfer functions of all the relevant cosmological
variables sourced by quadratic combinations of adiabatic and isocurvature
modes. We perform these calculations in synchronous gauge, assuming a Universe
described by the CDM model and composed of neutrinos, photons, baryons
and dark matter. We highlight the importance of mixed modes, which are sourced
by two different isocurvature or adiabatic modes and do not exist at the linear
level. In particular, we investigate the so-called compensated isocurvature
mode and find non-trivial initial evolution when it is mixed with the adiabatic
mode, in contrast to the result at linear order and even at second order for
the unmixed mode. Non-trivial evolution also arises when this compensated
isocurvature is mixed with the neutrino density isocurvature mode. Regarding
the neutrino velocity isocurvature mode, we show it unavoidably generates
non-regular (decaying) modes at second order. Our results can be applied to
second order Boltzmann solvers to calculate the effects of isocurvatures on
non-linear observables.Comment: 25+18 pages. No figure