23 research outputs found
On Inflation with Non-minimal Coupling
A simple realization of inflation consists of adding the following operators
to the Einstein-Hilbert action: (partial phi)^2, lambda phi^4, and xi phi^2 R,
with xi a large non-minimal coupling. Recently there has been much discussion
as to whether such theories make sense quantum mechanically and if the inflaton
phi can also be the Standard Model Higgs. In this note we answer these
questions. Firstly, for a single scalar phi, we show that the quantum field
theory is well behaved in the pure gravity and kinetic sectors, since the
quantum generated corrections are small. However, the theory likely breaks down
at ~ m_pl / xi due to scattering provided by the self-interacting potential
lambda phi^4. Secondly, we show that the theory changes for multiple scalars
phi with non-minimal coupling xi phi dot phi R, since this introduces
qualitatively new interactions which manifestly generate large quantum
corrections even in the gravity and kinetic sectors, spoiling the theory for
energies > m_pl / xi. Since the Higgs doublet of the Standard Model includes
the Higgs boson and 3 Goldstone bosons, it falls into the latter category and
therefore its validity is manifestly spoiled. We show that these conclusions
hold in both the Jordan and Einstein frames and describe an intuitive analogy
in the form of the pion Lagrangian. We also examine the recent claim that
curvature-squared inflation models fail quantum mechanically. Our work appears
to go beyond the recent discussions.Comment: 14 pages, 2 figures. Version 2: Clarified findings and improved
wording. Elaborated important sections and removed an unnecessary section.
Added references. Version 3: Updated towards JHEP version. Version 4: Final
JHEP versio
Inflation and dark matter in two Higgs doublet models
We consider the Higgs inflation in the extension of the Standard Model with
two Higgs doublets coupled to gravity non-minimally. In the presence of an
approximate global U(1) symmetry in the Higgs sector, both radial and angular
modes of neutral Higgs bosons drive inflation where large non-Gaussianity is
possible from appropriate initial conditions on the angular mode. We also
discuss the case with single-field inflation for which the U(1) symmetry is
broken to a Z_2 subgroup. We show that inflationary constraints, perturbativity
and stability conditions restrict the parameter space of the Higgs quartic
couplings at low energy in both multi- and single-field cases. Focusing on the
inert doublet models where Z_2 symmetry remains unbroken at low energy, we show
that the extra neutral Higgs boson can be a dark matter candidate consistent
with the inflationary constraints. The doublet dark matter is always heavy in
multi-field inflation while it can be light due to the suppression of the
co-annihilation in single-field inflation. The implication of the extra quartic
couplings on the vacuum stability bound is also discussed in the light of the
recent LHC limits on the Higgs mass.Comment: (v1) 28 pages, 8 figures; (v2) 29 pages, a new subsection 3.3 added,
references added and typos corrected, to appear in Journal of High Energy
Physic
Spectral action, Weyl anomaly and the Higgs-Dilaton potential
We show how the bosonic spectral action emerges from the fermionic action by
the renormalization group flow in the presence of a dilaton and the Weyl
anomaly. The induced action comes out to be basically the Chamseddine-Connes
spectral action introduced in the context of noncommutative geometry. The
entire spectral action describes gauge and Higgs fields coupled with gravity.
We then consider the effective potential and show, that it has the desired
features of a broken and an unbroken phase, with the roll down.Comment: 23 pages, 4 figure
f(R) theories
Over the past decade, f(R) theories have been extensively studied as one of
the simplest modifications to General Relativity. In this article we review
various applications of f(R) theories to cosmology and gravity - such as
inflation, dark energy, local gravity constraints, cosmological perturbations,
and spherically symmetric solutions in weak and strong gravitational
backgrounds. We present a number of ways to distinguish those theories from
General Relativity observationally and experimentally. We also discuss the
extension to other modified gravity theories such as Brans-Dicke theory and
Gauss-Bonnet gravity, and address models that can satisfy both cosmological and
local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in
Relativity, Published version, Comments are welcom
Higgs field in cosmology
The accelerated expansion of the early universe is an integral part of modern
cosmology and dynamically realized by the mechanism of inflation. The simplest
theoretical description of the inflationary paradigm is based on the assumption
of an additional propagating scalar degree of freedom which drives inflation -
the inflaton. In most models of inflation the fundamental nature of the
inflaton remains unexplained. In the model of Higgs inflation, the inflaton is
identified with the Standard Model Higgs boson and connects cosmology with
elementary particle physics. A characteristic feature of this model is a
non-minimal coupling of the Higgs boson to gravity. I review and discuss
several phenomenological and fundamental aspects of this model, including the
impact of quantum corrections and the renormalization group, the derivation of
initial conditions for Higgs inflation in a quantum cosmological framework and
the classical and quantum equivalence of different field parametrizations.Comment: 36 pages, 9 figures; references added, typos corrected. Invited
contribution to the Heraeus-Seminar "Hundred Years of Gauge Theory", 30 July
- 3 August 2018, Physikzentrum Bad Honnef, organized by Silvia De Bianchi and
Claus Kiefer. To appear in the proceedings "100 Years of Gauge Theory. Past,
present and future perspectives" in the series `Fundamental Theories of
Physics' (Springer
Entanglement entropy of black holes
The entanglement entropy is a fundamental quantity which characterizes the
correlations between sub-systems in a larger quantum-mechanical system. For two
sub-systems separated by a surface the entanglement entropy is proportional to
the area of the surface and depends on the UV cutoff which regulates the
short-distance correlations. The geometrical nature of the entanglement entropy
calculation is particularly intriguing when applied to black holes when the
entangling surface is the black hole horizon. I review a variety of aspects of
this calculation: the useful mathematical tools such as the geometry of spaces
with conical singularities and the heat kernel method, the UV divergences in
the entropy and their renormalization, the logarithmic terms in the
entanglement entropy in 4 and 6 dimensions and their relation to the conformal
anomalies. The focus in the review is on the systematic use of the conical
singularity method. The relations to other known approaches such as 't Hooft's
brick wall model and the Euclidean path integral in the optical metric are
discussed in detail. The puzzling behavior of the entanglement entropy due to
fields which non-minimally couple to gravity is emphasized. The holographic
description of the entanglement entropy of the black hole horizon is
illustrated on the two- and four-dimensional examples. Finally, I examine the
possibility to interpret the Bekenstein-Hawking entropy entirely as the
entanglement entropy.Comment: 89 pages; an invited review to be published in Living Reviews in
Relativit