Modiﬁed hybrid inﬂation reheating and stabilization of the electroweak vacuum

2025-05-06 0 0 1.47MB 24 页 10玖币

侵权投诉

Modiﬁed hybrid inﬂation, reheating

and stabilization of the electroweak

vacuum

Merna Ibrahim,a,1Mustafa Ashry,b,2

Esraa Elkhateeba,3Adel M. Awada,4and

Ahmad Moursyc,5

aDepartment of Physics, Faculty of Science, Ain Shams University, 11566, Cairo,

Egypt.

bDepartment of Mathematics, Faculty of Science, Cairo University, 12613, Giza, Egypt.

cDepartment of Basic Sciences, Faculty of Computers and Artiﬁcial Intelligence, Cairo

University, Giza 12613, Egypt.

E-mail: mernaibrahim_p@sci.asu.edu.eg,mustafa@sci.cu.edu.eg,

dr.esraali@sci.asu.edu.eg,a.awad@sci.asu.edu.eg,a.moursy@fci-cu.edu.eg

Abstract. We propose a modiﬁcation to the standard hybrid inﬂation model [1], that

connects a successful hybrid inﬂation scenario to the standard model Higgs sector, via

the electroweak vacuum stability. The proposed model results in an eﬀective inﬂation

potential of a hilltop-type, with both the trans-Planckian and sub-Planckian inﬂation

regimes consistent with the recent Planck/BICEP combined results. Reheating via

the inﬂation sector decays to right-handed neutrinos is considered. An upper bound

on the reheating temperature TR<

∼2×1011 (1 ×1013)GeV, for large (small) ﬁeld

inﬂation, will suppress contributions from one-loop quantum corrections to the inﬂation

potential. This may push the neutrino Yukawa couplings to be O(1) and aﬀect the

vacuum stability. We show that the couplings of the SM Higgs to the inﬂation sector

can guarantee the electroweak vacuum stability up to the Planck scale. The so-called

hybrid Higgs-inﬂaton model leads to a positive correction for the Higgs quartic coupling

at a threshold scale, which is shown to have a very signiﬁcant eﬀect in stabilizing

the electroweak vacuum. We ﬁnd that even with O(1) neutrino Yukawa couplings,

threshold corrections leave the SM vacuum stability intact.

arXiv:2210.03247v3 [hep-ph] 22 Feb 2023

Contents

1 INTRODUCTION 1

2 MODIFIED HYBRID INFLATION MODEL 3

3 INFLATION OBSERVABLES 7

4 REHEATING AND QUANTUM CORRECTIONS 11

5 HIGGS VACUUM STABILITY 13

5.1 Matching conditions 13

5.2 Renormalization group equations 15

6 CONCLUSIONS 20

1 INTRODUCTION

The Standard Model of cosmology (SMC), and the Standard Model of particle physics

(SM) are extremely successful in describing the observations of the Cosmic Microwave

Background (CMB), and the low-energy experimental results of particle colliders, re-

spectively. It turns out that elementary scalar particles play an important role in both

particle physics and the early universe. In fact, the detection of the SM Higgs boson in

2012 [2,3] was the ﬁrst successful signature of an elementary scalar playing a crucial

role in particle physics. However, this discovery left unanswered questions, indicating

that the SM is not the ultimate theory, such as the hierarchy problem and the problem

of stability of the electroweak (EW) vacuum.

On the other hand, a scalar ﬁeld (the inﬂaton φ) is believed to play another piv-

otal role in the early universe, where it may be responsible for the cosmic inﬂation.

The latter resolves the problems of ﬂatness and horizon of the SMC, and the absence

of early phase transition remnants can be justiﬁed. It is tempting to investigate pos-

sible connections between the two sectors of inﬂation and particle physics as well as

impacts on both high- and low-energy physics. One portal to such a connection is the

reheating process after the end of inﬂation, where the inﬂaton oscillates around its

true minimum and decays into the SM particles when the Hubble parameter and the

inﬂaton decay are of the same order, H∼Γφ. In nonoscillatory models [4–6], where

the inﬂaton keeps rolling in a runway direction, reheating after inﬂation is achieved via

diﬀerent mechanisms such as gravitational reheating, instant preheating, or curvaton

– 1 –

reheating for example. Other connections between the two sectors can be achieved via

a messenger that interacts with both sectors and inﬂuences physics in both of them as

studied in [7–11].

The SM Higgs vacuum stability is one of the issues that raises concerns in both

beyond standard model particle physics and cosmology of the early universe. The EW

vacuum is stable up to an instability scale ΛI∼1011, where for higher scales the SM

Higgs quartic coupling is driven to negative values by the dominant contribution of

the top quark Yukawa coupling to the RGEs. As a matter of fact, the EW vacuum

stability is very sensitive to the precision measurements of the top quark mass mtand

less sensitive to the strong coupling αs[12–14]. According to these uncertainties, the

instability scale lies between 109.ΛI.1012 GeV. However, in the presence of a deeper

minimum of the Higgs potential, at much larger ﬁeld value [15,16], the EW vacuum

may be metastable if its lifetime is larger than the age of the universe. The current

measurements of the top quark mass mtand the Higgs mass mhsupport the hypothesis

that the EW vacuum is metastable [12,17]. However, this situation may be subject to

change for more precise measurements of mt, and even considering new physics that

explains the neutrino masses. Accordingly, the EW vacuum may move to the instability

region. Moreover, quantum ﬂuctuations may push the Higgs over its barrier causing

destabilization of the Higgs during inﬂation [18–20]. If typical momentum, which is

of the same order as the hubble scale during inﬂation k∼Hinf , is greater than the

potential barrier, then the EW vacuum can decay. Therefore, considering the inﬂation

sector may even worsen the situation of the EW vacuum stability/metastability. These

problems can be avoided if new physics arises at the instability scale ΛIor by deﬁning

a direct coupling between the inﬂaton and the Higgs boson [11,18,21,22].

The hybrid inﬂation model (HI) [1] combines the inﬂation potential with a spon-

taneous symmetry breaking potential, where the inﬂation ends by a waterfall phase

triggered by the inﬂaton φ. In its simplest form, this class of models predicts a large

spectral index ns ∼1and very small tensor-to-scalar ratio rif the ﬁeld variations

are taken to be as small as sub-Planckian values [1,23]. On the other hand, if ﬁeld

variations are super-Planckian, we have r > 0.1. Both limits of the model are ruled out

by Planck observations [24,25]. In Ref. [23], it was indicated that including one-loop

quantum corrections to HI tree-level potential can improve the nsand rvalues. It was

assumed that the inﬂation scalars interact with right-handed neutrinos (RHN), that

acquire large masses through the waterfall scalar vev. In this case, the neutrino Yukawa

coupling with SM Higgs can be ∼ O(1), which worsens the EW vacuum stability [13]

and may even be dangerous for the metastability.

In this paper, we propose a connection between the SM Higgs sector and the

– 2 –

hybrid inﬂation sector. We introduce a new scalar ﬁeld χthat is interacting with

the hybrid inﬂation sector to improve the inﬂation observables for a tree-level scalar

potential on one hand, and on the other hand, stabilizes the EW vacuum up to the

Planck scale. We will make use of the threshold modiﬁcations to the running of the

SM Higgs coupling due to the inﬂation sector ﬁelds.

The paper is organized as follows. In Sec. 2, we provide the details of the modiﬁed

hybrid inﬂation model as well as the inﬂation dynamics and the eﬀective inﬂation

potential. In Sec. 3, we study the parameter space and the observables predictions of

the model. Then we explore constraints from reheating, neutrino masses, and quantum

corrections in Sec. 4. Section 5is devoted to investigate the low-energy consequences

such as the stability of the SM Higgs vacuum. Finally, we give our conclusions in

Sec. 6.

2 MODIFIED HYBRID INFLATION MODEL

We propose a modiﬁed version of the hybrid inﬂation model [1] (MHI). It consists of

three SM singlet real scalars, the inﬂaton φand the waterfall ﬁeld ψas well as an extra

scalar ﬁeld χ, with full scalar potential of the form

VMHI(φ, ψ, χ) = λψψ2−v2

22+m2

2φ2+ 2λφψφ2ψ2−2λφχφ2χ2

+λχχ2−v2

22+ 2λψχψ2−v2

2χ2−v2

2,(2.1)

where m, vψ, vχare mass dimensionful scales while λψ, λχ, λφψ, λφχ, λψχ are di-

mensionless couplings. The ﬁrst three terms correspond to the known hybrid inﬂation

model [1]. The last three terms give the modiﬁcation on the HI1. The negative coeﬃ-

cient in the fourth term of (2.1) can be justiﬁed in the context of the inverted hybrid

inﬂation (IHI) [27] and may be obtained in some contexts such as supersymmetry [27].

2We will work in Planck units where the reduced Planck mass MP= 1. The global

minimum of the potential (2.1) is located at

hφi= 0,hψi=vψ

√2,hχi=vχ

√2,(2.2)

1Similar modiﬁcations on chaotic inﬂation were also proposed in [10,26], based on a shift symmetry

arguments.

2In fact, we do not consider supersymmetry in this paper, and we focus on linking our modiﬁed

hybrid inﬂation model to the EW vacuum stability in a non-SUSY case. However, if supersymmetry is

considered as a UV completion to the SM, with a very large breaking scale, the EW vacuum stability

is still questionable.

– 3 –

at which V= 0. Since the inﬂaton φacquires a zero vev, it does not mix with the

other two ﬁelds ψ, χ in the mass matrix and it is separated with a squared mass

φ=m2+ 2λφψv2

ψ−2λφχv2

χ.(2.3)

On the other hand, the mass matrix in the basis (ψ, χ)is given by

ψχ = 4 λψv2

ψλψχvψvχ

λψχvψvχλχv2

χ!(2.4)

with the following squared masses

ψ,χ = 2hλψv2

ψ+λχv2

χ±q(λψv2

ψ−λχv2

χ)2+ 4λ2

ψχv2

ψv2

χi(2.5)

It is clear that in the absence of the mixing λψχ between ψand χ, the squared masses

are given by m2

ψ= 4λψv2

ψ, m2

χ= 4λχv2

χ.

The inﬂationary trajectory is obtained by minimizing the MHI potential (2.1)

with respect to the ψand χﬁelds. It turns out that during inﬂation, ψis frozen at

the origin while χis shifted to a nonzero value on the trajectory

(ψ, χ) = 0,sλφχ

λχ

φ2+λψχ

2λχ

ψ+1

2v2

χ!(2.6)

Using the ﬁeld-dependent squared mass matrix, a critical value φcthat triggers the

waterfall phase has the form

φc=vψ

√2sλψλχ−λ2

ψχ

λχλφψ +λφχλψχ

(λψχ →0)

−−−−−→ vψ

√2sλψ

λφψ

(2.7)

In that respect, the inﬂation eﬀective potential takes the form

Vinf (φ) = V0+αφ2−βφ4,(2.8)

with the following parameters

V0=v4

4λψ−λ2

ψχ

λχ, α =m2

2−λφχv2

χ+λψχ

λχ

ψ, β =λ2

φχ

λχ

.(2.9)

Here, the vacuum energy V0should be positive, hence λψλχ> λ2

ψχ. The latter

condition is consistent with the requirement of having a real value for φc. Since the

coeﬃcient βis positive, with the negative sign term in (2.8), there is a possibility that

the inﬂaton rolls down from a hilltop close to φ= 0, if αis negative as well. This case

will be similar to the inverted hybrid inﬂation [27]. However, the system, in this case, is

– 4 –

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Modiedhybridination,reheatingandstabilizationoftheelectroweakvacuumMernaIbrahim,a;1MustafaAshry,b;2EsraaElkhateeba;3AdelM.Awada;4andAhmadMoursyc;5aDepartmentofPhysics,FacultyofScience,AinShamsUniversity,11566,Cairo,Egypt.bDepartmentofMathematics,FacultyofScience,CairoUniversity,12613,Giza,Egypt.cD...

展开>> 收起<<

Modiﬁed hybrid inﬂation reheating and stabilization of the electroweak vacuum.pdf

共24页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Modiﬁed hybrid inﬂation reheating and stabilization of the electroweak vacuum

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: