QCD axion window and false vacuum Higgs inflation
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Springer
Received: January 20, Revised: March 15, Accepted: May 3, Published: May 28,
2020 2020 2020 2020
Hiroki Matsui,a Fuminobu Takahashia,b and Wen Yinc a
Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan b Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan c Department of Physics, KAIST, Yuseong-gu, Daejeon 34141, Korea
E-mail: [email protected], [email protected], [email protected] Abstract: The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, Hinf , is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, Hinf can be larger than 100 GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum to the electroweak vacuum. Keywords: Beyond Standard Model, Cosmology of Theories beyond the SM, Higgs Physics ArXiv ePrint: 2001.04464
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)154
JHEP05(2020)154
QCD axion window and false vacuum Higgs inflation
Contents 1
2 The QCD axion and the Bunch-Davies distribution
3
3 False vacuum Higgs inflation 3.1 A false vacuum in the Higgs potential 3.2 The effective QCD scale 3.3 The QCD axion window opened wider
5 5 9 9
4 False vacuum decay and slow-roll inflation 4.1 Thin-wall approximation (1011 GeV vfalse Mpl ) 4.2 Non-degenerate vacua (vfalse ∼ 1011 GeV) 4.3 Thick-wall regime (vfalse ∼ Mpl ) 4.4 Open bubble universe and the dynamics
10 12 14 15 16
5 Slow-roll inflation after the bubble nucleation
17
6 Discussion and conclusions
20
1
Introduction
The Peccei-Quinn (PQ) mechanism is the most plausible solution to the strong CP problem [1, 2]. It predicts the QCD axion, a pseudo Nambu-Goldstone boson, which arises as a consequence of the spontaneous breakdown of the global U(1) PQ symmetry [3, 4]. The QCD axion, a, is coupled to the standard model (SM) QCD as Laxion =
g32 a α ˜ µν F F , 32π 2 fa µν α
(1.1)
α the gluon field strength, where fa is the decay constant, g3 the strong gauge coupling, Fµν µν and F˜α its dual. The global U(1) PQ symmetry is explicitly broken by non-perturbative
effects of QCD through the above coupling. If there is no other explicit breaking, the axion acquires a mass χ(T ) ma (T )2 = , (1.2) fa2 where χ(T ) is the topological susceptibility. At T ΛQCD ' O(100) MeV, the topological susceptibility χ(T ) is vanishingly small, and so, the axion is almost massless. χ(T ) grows as the temperature decreases, and it approaches a constant value χ0 at T . ΛQCD . The detailed temperature dependence of χ(T ) was studied by using the lattice QCD [5–10]. When the axion mass becomes comparable to the Hubble param
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