De Martini Francesco
Dipartimento di Fisica, Universita' la Sapienza, 00185 Roma, Italy
Accademia dei Lincei, via della Lungara 10, 00165 Roma, Italy.
Philos Trans A Math Phys Eng Sci. 2017 Nov 13;375(2106). doi: 10.1098/rsta.2016.0388.
The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of Weyl's differential geometry: the parallel displacement of vectors in curved space-time. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the (2) ⊗(1) as well as on the conformal groups of space-time Weyl's transformations is analysed within the framework of a general-relativistic, conformally covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An 'effective cosmological potential': is expressed in terms of the dark energy potential: [Formula: see text] via the 'mass reduction parameter': [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a 'free parameter' by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which accounts for the measured cosmological constant, i.e. the measured content of vacuum-energy in the Universe. The non-integrable application of Weyl's geometry leads to a Proca equation accounting for the dynamics of a -particle, a vector-meson proposed as an an optimum candidate for dark matter. On the basis of previous cosmic microwave background results our theory leads, in the condition of cosmological 'critical density', to the assessment of the average energy content of the -excitation. The peculiar mathematical structure of offers a clue towards a very general resolution of a most intriguing puzzle of modern quantum field theory, the 'Cosmological Constant Paradox' (here referred to as the '-Paradox'). Indeed, our 'universal' theory offers a resolution of the -Paradox for all exponential inflationary potentials: (,)∝ , and for all linear superpositions of these potentials, where belongs to the mathematical set of the 'real numbers'. An explicit solution of the -Paradox is reported for =2. The resolution of the -Paradox cannot be achieved in the context of Riemann's differential geometry.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
人们发现，负责宇宙暴胀的标量场的本质根植于外尔微分几何的最基本概念：弯曲时空中矢量的平行位移。在这种新颖的几何情形下，基于(2)⊗(1)以及时空外尔变换的共形群的轻子标准电弱理论，在包含电磁和杨 - 米尔斯场的广义相对论共形协变标量 - 张量理论框架内进行了分析。自发对称性破缺过程中的希格斯机制被确定，这为基本粒子的一些相关性质与宇宙暗能量含量之间提供了形式上的联系。一个“有效宇宙学势”：通过“质量约化参数”：[公式：见原文]，用暗能量势：[公式：见原文]表示，这是宇宙的一个普遍性质。希格斯玻色子的质量，在标准电弱理论中被视为一个“自由参数”，而我们的理论发现它与质量[公式：见原文]成正比，该质量解释了测得的宇宙学常数，即宇宙中测得的真空能量含量。外尔几何的不可积应用导致了一个普罗卡方程，该方程描述了一种 - 粒子的动力学，这种矢量介子被提议作为暗物质最合适的候选者。基于先前的宇宙微波背景结果，我们的理论在宇宙“临界密度”条件下，对 - 激发的平均能量含量进行了评估。的特殊数学结构为现代量子场论中一个极具吸引力的谜题——“宇宙学常数悖论”（这里称为“ - 悖论”）提供了一个非常普遍的解决方案线索。实际上，我们的“通用”理论为所有指数暴胀势：(,)∝ ，以及这些势的所有线性叠加提供了 - 悖论的解决方案，其中属于“实数”的数学集合。对于 =2，报告了 - 悖论的一个显式解。在黎曼微分几何的背景下无法实现 - 悖论的解决方案。本文是主题为“第二次量子革命：基础问题”的特刊的一部分。
