148 research outputs found
Hamiltonian approach to 2nd order gauge invariant cosmological perturbations
In view of growing interest in tensor modes and their possible detection, we
clarify the definition of tensor modes up to 2nd order in perturbation theory
within the Hamiltonian formalism. Like in gauge theory, in cosmology the
Hamiltonian is a suitable and consistent approach to reduce the gauge degrees
of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian
reduction. An appropriate set of gauge invariant variables that describe the
dynamical degrees of freedom may be obtained by suitable canonical
transformations in the phase space. We derive a set of gauge invariant
variables up to 2nd order in perturbation expansion and for the first time we
reduce the 3rd order action without adding gauge fixing terms. In particular,
we are able to show the relation between the uniform- and Newtonian
slicings, and study the difference in the definition of tensor modes in these
two slicings.Comment: Revised versio
Cosmological gravitational waves from isocurvature fluctuations
Gravitational waves induced by large primordial curvature fluctuations may result in a sizable stochastic gravitational wave background. Interestingly, curvature fluctuations are gradually generated by initial isocurvature fluctuations, which in turn induce gravitational waves. Initial isocurvature fluctuations commonly appear in multi-field models of inflation as well as in the formation of scattered compact objects in the very early universe, such as primordial black holes and solitons like oscillons and cosmic strings. Here, we provide a review on isocurvature induced gravitational waves and its applications to dark matter and the primordial black hole dominated early universe
GW Backgrounds associated with PBHs
PBH formation requires high-density regions in the (random) density field
filling the primordial universe. While only the largest (and so rarest)
overdensities collapse to form PBHs, the rest cause large anisotropic stresses,
which are the source of GWs. We provide an overview of the theoretical aspects
of the GW backgrounds associated with PBHs from large primordial fluctuations.
We consider GW backgrounds associated with PBH formation, PBH reheating and
unresolved PBH binaries. We present several graphical summaries and
illustrations for the busy reader.Comment: To appear [with updates] in the book "Primordial Black Holes", ed.
Chris Byrnes, Gabriele Franciolini, Tomohiro Harada, Paolo Pani, Misao
Sasaki; Springer (2024). I tried to show the generation of induced GWs with
new illustrations, two of them in real space. So, any comments are welcome,
especially about the illustration
Lectures on Gravitational Wave Signatures of Primordial Black Holes
We provide a pedagogical approach to gravitational waves in cosmology with
focus on gravitational wave signals related to primordial black holes. These
lectures notes contain more details than one is able to present in the two
two-hour lectures they are meant to and, as such, they should be thought as a
complementary material. The main aim of these lectures is that, by the end, one
obtains a certain degree of intuition on gravitational waves in cosmology and
understands the basic features of scalar induced gravitational waves. We also
highlight must-check properties of induced gravitational waves as well as
current issues regarding secondary gravitational waves in cosmology. Throughout
the lecture we provide exercises, supplementary information and activities with
public codes to be ready to derive your own results.Comment: Lectures notes prepared for the ICCUB School 2023 on Primordial Black
holes in the University of Barcelona. Comments and corrections are welcom
Cosmological disformal invariance
The invariance of physical observables under disformal transformations is
considered. It is known that conformal transformations leave physical
observables invariant. However, whether it is true for disformal
transformations is still an open question. In this paper, it is shown that a
pure disformal transformation without any conformal factor is equivalent to
rescaling the time coordinate. Since this rescaling applies equally to all the
physical quantities, physics must be invariant under a disformal
transformation, that is, neither causal structure, propagation speed nor any
other property of the fields are affected by a disformal transformation itself.
This fact is presented at the action level for gravitational and matter fields
and it is illustrated with some examples of observable quantities. We also find
the physical invariance for cosmological perturbations at linear and high
orders in perturbation, extending previous studies. Finally, a comparison with
Horndeski and beyond Horndeski theories under a disformal transformation is
made.Comment: 23 pages + Appendix, updated versio
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