超对称SO(10)模型中的非最小四次膨胀与重力耦合

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"超对称SO中的非最小四次膨胀（10）" 本文详细探讨了在超对称SO(10)理论框架下如何实现非最小四次膨胀（λϕ4 inflation），这是一种涉及宇宙早期膨胀阶段的物理现象。超对称SO(10)模型是一种被广泛研究的理论，因为它能够统一基本粒子物理学中的多种力，并且能够解释中微子质量的来源。在描述这一过程时，作者指出，16-16希格斯多重态在模型中扮演了关键角色。这些多重态能够将SO(10)群分解为更小的SU(5)群，同时生成右旋中微子的质量。中微子质量的产生是通过所谓的“重子-中微子对称性破缺”（leptogenesis）来实现的，这是一个解释宇宙中物质-反物质不对称性的可能机制。在这种情况下，膨胀场φ与16-16希格斯多重态相关联，自然地成为了膨胀的动力源。此外，文章还讨论了45-plet希格斯多重态的作用。在膨胀过程中，这个希格斯多重态需要获得大统一尺度（GUT scale）的能量，这有助于解决单极子问题。单极子是GUT理论中可能出现的不稳定粒子，它们的生成可能会导致宇宙中过量的能量密度。通过使45-plet希格斯在膨胀期间达到高能状态，可以抑制单极子的产生，从而使模型更加稳定。文章进一步分析了膨胀的物理性质，特别是标量谱指数ns和张量到标量比r的预测值。标量谱指数ns是衡量宇宙微波背景辐射(CMB)波动平滑程度的参数，其观测值对理解膨胀模型至关重要。文章指出，所提出的模型产生的ns值与实验观测非常吻合。同时，模型预测的r值落在10^-3到10^-2的范围内，这是对张量模式波动相对于标量模式波动强度的估计，也是CMB观测的重要目标之一。这篇研究展示了超对称SO(10)模型如何优雅地融合了宇宙膨胀、中微子质量生成以及大统一理论的元素。通过非最小耦合的四次膨胀机制，模型不仅解决了物理上的挑战，还给出了与实验数据相一致的宇宙学预测。这一工作为理解和探索宇宙的早期历史提供了一种新的、有潜力的理论视角。

Physics Letters B 765 (2017) 256–259

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Non-minimal quartic inﬂation in supersymmetric SO(10)

George K. Leontaris

a,b,∗

, Nobuchika Okada

, Qaisar Shaﬁ

Theory Department, CERN, CH-1211, Geneva 23, Switzerland

Physics Department, Theory Division, Ioannina University, GR-45110 Ioannina, Greece

Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA

Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, DE 19716, Newark, USA

a r t i c l e i n f o a b s t r a c t

Article history:

Received

4 December 2016

Accepted

12 December 2016

Available

online 16 December 2016

Editor:

M. Cveti

We describe how quartic (λφ

) inﬂation with non-minimal coupling to gravity is realized in realistic

supersymmetric SO(10) models. In a well-motivated example the 16 −16 Higgs multiplets, which break

SO(10) to SU(5) and yield masses for the right-handed neutrinos, provide the inﬂaton ﬁeld φ. Thus,

leptogenesis is a natural outcome in this class of SO(10) models. Moreover, the adjoint (45-plet) Higgs

also acquires a GUT scale value during inﬂation so that the monopole problem is evaded. The scalar

spectral index n

is in good agreement with the observations and r, the tensor to scalar ratio, is predicted

for realistic values of GUT parameters to be of order 10

−3

–10

−2

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

By incorporating a single right-handed neutrino per genera-

tion

to cancel new anomalies from gauging the accidental global

U(1)

B−L

symmetry of the Standard Model (SM), both SU(4) ×

SU(2)

× SU(2)

[1] and SO(10) [2] provide particularly com-

pelling

examples of unifying the strong and electroweak forces.

A non-supersymmetric model of SO(10) inﬂation [3], based on an

earlier SU(5) model [4], was proposed a longtime ago. In this class

of SO(10) inﬂation models, driven by a gauge singlet ﬁeld with

minimal coupling to gravity and utilizing the Coleman–Weinberg

potential [5], the scalar to tensor ratio r, a canonical measure of

gravity waves generated during inﬂation, is estimated to be  0.02,

for n

= 0.96–0.97 [6]. Depending on the SO(10) symmetry break-

ing

pattern, an observable number density of intermediate mass

magnetic monopoles may be present in our galaxy [7].

this letter we propose to implement primordial inﬂation in

realistic supersymmetric SO(10) models [8]. We do this with a

supergravity generalization of non-minimal λφ

inﬂation [9]. Re-

call

that λφ

inﬂation with a minimal coupling to gravity pre-

dicts

an r value close to 0.25–0.3, depending on the number of

e-foldings (N

= 60–50). This prediction for r lies well outside the

2-σ range allowed by Planck [10] and WMAP 9 [11]. In contrast,

λφ

inﬂation with a suitable non-minimal coupling to gravity is

in good agreement with the data regarding the key parameters

and r. The quantity r, in particular, can be as low as 0.003 or

Corresponding author.

E-mail

addresses: leonta@uoi.gr (G.K. Leontaris), okadan@ua.edu (N. Okada),

shaﬁ@bartol.udel.edu (Q. Shaﬁ).

so, for n

= 0.96–0.97. The discussion closely follows a previous

model [12] based on supersymmetric SU(5).

In order to retain perturbative uniﬁcation of the MSSM gauge

couplings in supersymmetric SO(10) we prefer to work with lower

dimensional SO(10) representations. We employ 16 − 16 Higgs

to break SO(10) to SU(5) while keeping supersymmetry unbro-

ken.

The 16 vacuum expectation value (VEV) also provides large

masses ( 10

GeV), via higher dimensional operators, to the

right-handed neutrinos. In addition, the adjoint 45-plet, in con-

junction

either with a 54-plet or using higher dimensional op-

erators,

is employed to complete the breaking of SO(10) to the

MSSM gauge symmetry. Finally, following [13], we can employ two

Higgs 10-plets to implement electroweak symmetry breaking and

accommodate the charged fermion masses and mixings as well as

neutrino oscillation data. This summarizes the basic structure of a

realistic supersymmetric SO(10) model.

Recall that a non-minimal λφ

inﬂation scenario is deﬁned by

the following action in the Jordan frame:



√

−g



−

(1 +ξ ϕ

) R +

μν

∂

ϕ∂

ϕ −



(1)

where we have set to unity the reduced Planck mass, M

= 2.44 ×

GeV. In the limit ξ → 0

the non-minimal gravitational cou-

pling

term ξ ϕ

R vanishes and we approach minimal λϕ

chaotic

inﬂation. In the Einstein frame with a canonical gravity sector, we

can describe the action with a new inﬂaton ﬁeld (σ ) which has a

canonical kinetic term. The relation between σ and ϕ is given by

http://dx.doi.org/10.1016/j.physletb.2016.12.038

0370-2693/

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