16 research outputs found
Parametric Resonance in the Early Universe - A Fitting Analysis
Particle production via parametric resonance in the early Universe, is a
nonperturbative, non-linear and out-of-equilibrium phenomenon. Although it is a
well studied topic, whenever a new scenario exhibits parametric resonance, a
full re-analysis is normally required. To avoid this tedious task, many works
present often only a simplified linear treatment of the problem. In order to
surpass this circumstance in the future, we provide a fitting analysis of
parametric resonance through all its relevant stages: initial linear growth,
non-linear evolution, and relaxation towards equilibrium. Using lattice
simulations in an expanding grid in 3 + 1 dimensions, we parametrize the
dynamics outcome scanning over the relevant ingredients: role of the
oscillatory field, particle coupling strength, initial conditions, and
background expansion rate. We emphasize the inaccuracy of the linear
calculation of the decay time of the oscillatory field, and propose a more
appropriate definition of this scale based on the subsequent non-linear
dynamics. We provide simple fits to the relevant time scales and particle
energy fractions at each stage. Our fits can be applied to post-inflationary
preheating scenarios, where the oscillatory field is the inflaton, or to
spectator-field scenarios, where the oscillatory field can be e.g. a curvaton,
or the Standard Model Higgs.Comment: Extended discussion about the late-time dynamics of the system in
quadratic models. Minor changes in numerical fits with respect first version.
It matches version published in JCAP (30 pages + Appendices + Bibliography,
13 figures
Higgs-curvature coupling and post-inflationary vacuum instability
We study the post-inflationary dynamics of the Standard Model (SM) Higgs
field in the presence of a non-minimal coupling to gravity, both
with and without the electroweak gauge fields coupled to the Higgs. We assume a
minimal scenario in which inflation and reheating are caused by chaotic
inflation with a quadratic potential, and no additional new physics is relevant
below the Planck scale. By using classical real-time lattice simulations with a
renormalisation group improved effective Higgs potential and by demanding the
stability of the Higgs vacuum after inflation, we obtain upper bounds for
, taking into account the experimental uncertainty of the top-Yukawa
coupling. We compare the bounds in the absence and presence of the electroweak
gauge bosons, and conclude that the addition of gauge interactions has a rather
minimal impact. In the unstable cases, we parametrize the time when such
instability develops. For a top-quark mass , the
Higgs vacuum instability is triggered for , although a
slightly lower mass of pushes up this limit to
. This, together with the estimation
for stability during inflation, provides tight constraints to the
Higgs-curvature coupling within the SM.Comment: 15 pages, 13 figures. Minor changes to match version published in PR
The Decay of the Standard Model Higgs after Inflation
We study the nonperturbative dynamics of the Standard Model (SM) after
inflation, in the regime where the SM is decoupled from (or weakly coupled to)
the inflationary sector. We use classical lattice simulations in an expanding
box in (3+1) dimensions, modeling the SM gauge interactions with both global
and Abelian-Higgs analogue scenarios. We consider different post-inflationary
expansion rates. During inflation, the Higgs forms a condensate, which starts
oscillating soon after inflation ends. Via nonperturbative effects, the
oscillations lead to a fast decay of the Higgs into the SM species,
transferring most of the energy into and bosons. All species are
initially excited far away from equilibrium, but their interactions lead them
into a stationary stage, with exact equipartition among the different energy
components. From there on the system eventually reaches equilibrium. We have
characterized in detail, in the different expansion histories considered, the
evolution of the Higgs and of its dominant decay products, until equipartition
is established. We provide a useful mapping between simulations with different
parameters, from where we derive a master formula for the Higgs decay time, as
a function of the coupling constants, Higgs initial amplitude and
postinflationary expansion rate.Comment: Minor changes to match the PRD published version. Modulation of the
Higgs amplitude removed for in Sec. V, due to improving the time
resolution in the Higgs equation of motion. Results unaffecte
Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes
We reexamine the regularization of the two-point function of a scalar field
in a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. Adiabatic
regularization provides a set of subtraction terms in momentum space that
successfully remove its ultraviolet divergences at coincident points, but can
significantly distort the power spectrum at infrared scales, especially for
light fields. In this work we propose, by using the intrinsic ambiguities of
the renormalization program, a new set of subtraction terms that minimize the
distortions for scales , with an arbitrary mass scale. Our
method is consistent with local covariance and equivalent to general
regularization methods in curved spacetime. We apply our results to the
regularization of the power spectrum in de Sitter space: while the adiabatic
scheme yields exactly for a massless field, our
proposed prescription recovers the standard scale-invariant result
at super-horizon scales.Comment: Title changed with respect to first version. New section added on
renormalization conditions and coupling constants (Sect. 3). It matches the
published version in PLB. 6 pages + references, 1 figur
Energy distribution and equation of state of the early Universe: matching the end of inflation and the onset of radiation domination
We study the energy distribution and equation of state of the universe
between the end of inflation and the onset of radiation domination (RD),
considering observationally consistent single-field inflationary scenarios,
with a potential 'flattening' at large field values, and a monomial shape
around the origin. As a proxy for (p)reheating, we
include a quadratic interaction between the inflaton and
a light scalar 'daughter' field , with . We capture the
non-perturbative and non-linear nature of the system dynamics with lattice
simulations, obtaining that: the final energy transferred to depends
only on , not on , ; the final transfer of energy is always
negligible for , and of order for ;
the system goes at late times to matter-domination for , and always to
RD for . In the latter case we calculate the number of e-folds until RD,
significantly reducing the uncertainty in the inflationary observables
and .Comment: 7 pages + references, 5 figures. It matches published versio
Characterizing the post-inflationary reheating history, Part II: Multiple interacting daughter fields
We characterize the post-inflationary dynamics of an inflaton coupled
to multiple interacting daughter fields () through
quadratic-quadratic interactions . We assume a monomial
inflaton potential () around the minimum.
By simulating the system in 2+1-dimensional lattices, we study the
post-inflationary evolution of the energy distribution and equation of state,
from the end of inflation until a stationary regime is achieved. We show that
in this scenario, the energy transferred to the daughter field sector can be
larger than , surpassing this way the upper bound found previously for
single daughter field models. In particular, for the energy at very
late times is equally distributed between all fields, and only of the energy remains in the inflaton. We also consider scenarios in which
the daughter fields have scale-free interactions ,
including the case of quartic daughter field self-interactions (for ). We
show that these interactions trigger a resonance process during the non-linear
regime, which in the single daughter field case already allows to deplete more
than of the energy from the inflaton for .Comment: 23 pages + appendix, 15 figure
Physical scale adiabatic regularization in cosmological spacetimes
We propose a new scheme to regularize the stress-energy tensor and the
two-point function of free quantum scalar fields propagating in cosmological
spacetimes. We generalize the adiabatic regularization method by introducing
two additional mass scales not present in the standard program. If we set them
to the order of the physical scale of the problem, we obtain
ultraviolet-regularized quantities that do not distort the amplitude of the
power spectra at the infrared momentum scales amplified by the non-adiabatic
expansion of the universe. This is not ensured by the standard adiabatic
method. We also show how our proposed subtraction terms can be interpreted as
renormalization of coupling constants in the Einstein's equations. We finally
illustrate our proposed regularization method in two scenarios of cosmological
interest: de Sitter inflation and geometric reheating.Comment: 22 pages + references, 5 figure
The art of simulating the early Universe -- Part I
We present a comprehensive discussion on lattice techniques for the
simulation of scalar and gauge field dynamics in an expanding universe. After
reviewing the continuum formulation of scalar and gauge field interactions in
Minkowski and FLRW backgrounds, we introduce basic tools for the discretization
of field theories, including lattice gauge invariant techniques. Following, we
discuss and classify numerical algorithms, ranging from methods of
accuracy like and integration, to
methods up to accuracy, and the and
higher-order integrators, accurate up to . We adapt these methods
for their use in classical lattice simulations of the non-linear dynamics of
scalar and gauge fields in an expanding grid in dimensions, including the
case of `self-consistent' expansion sourced by the volume average of the
fields' energy and pressure densities. We present lattice formulations of
canonical cases of: Interacting scalar fields, Abelian gauge
theories, and Non-Abelian gauge theories. In all three cases we
provide symplectic integrators, with accuracy ranging from up to
. For each algorithm we provide the form of relevant observables,
such as energy density components, field spectra and the Hubble constraint.
Remarkably, all our algorithms for gauge theories respect the Gauss constraint
to machine precision, including when `self-consistent' expansion is considered.
As a numerical example we analyze the post-inflationary dynamics of an
oscillating inflaton charged under . The present manuscript
is meant as part of the theoretical basis for , a modern C++
MPI-based package for simulating the non-linear dynamics of scalar-gauge field
theories in an expanding universe, publicly available at www.cosmolattice.netComment: Minor corrections to match published version, and one more algorithm
added. Still 79 pages, 8 figures, 1 appendix, and many algorithm
CosmoLattice
This is the user manual for CosmoLattice, a modern package for lattice
simulations of the dynamics of interacting scalar and gauge fields in an
expanding universe. CosmoLattice incorporates a series of features that makes
it very versatile and powerful: it is written in C++ fully exploiting the
object oriented programming paradigm, with a modular structure and a clear
separation between the physics and the technical details, it is MPI-based
and uses a discrete Fourier transform parallelized in multiple spatial
dimensions, which makes it specially appropriate for probing scenarios with
well-separated scales, running very high resolution simulations, or simply very
long ones, it introduces its own symbolic language, defining field
variables and operations over them, so that one can introduce differential
equations and operators in a manner as close as possible to the continuum,
it includes a library of numerical algorithms, ranging from to methods, suitable for simulating global and gauge
theories in an expanding grid, including the case of `self-consistent'
expansion sourced by the fields themselves. Relevant observables are provided
for each algorithm (e.g.~energy densities, field spectra, lattice snapshots)
and we note that remarkably all our algorithms for gauge theories always
respect the Gauss constraint to machine precision. In this manual we explain
how to obtain and run CosmoLattice in a computer (let it be your laptop,
desktop or a cluster). We introduce the general structure of the code and
describe in detail the basic files that any user needs to handle. We explain
how to implement any model characterized by a scalar potential and a set of
scalar fields, either singlets or interacting with and/or gauge
fields. CosmoLattice is publicly available at www.cosmolattice.net.Comment: 111 pages, 3 figures and O(100) code file
Renormalized stress-energy tensor for spin-1/2 fields in expanding universes
We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-1/2 field in a spatially flat Friedmann-Lemaitre-Robertson-Walker universe. Its computation is based on the extension of the adiabatic regularization method to fermion fields introduced recently in the literature. The tensor is given in terms of UV-finite integrals in momentum space, which involve the mode functions that define the quantum state. As illustrative examples of the method efficiency, we see how to compute the renormalized energy density and pressure in two interesting cosmological scenarios: a de Sitter spacetime and a radiation-dominated universe. In the second case, we explicitly show that the late-time renormalized stress-energy tensor behaves as that of classical cold matter. We also check that, if we obtain the adiabatic expansion of the scalar field mode functions with a similar procedure to the one used for fermions, we recover the well-known WKB-type expansion