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