Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum gravity theory. The gravifield sided on both locally flat noncoordinate spacetime and globally flat Minkowski spacetime is an essential ingredient for gauging global spin and scaling symmetries. The locally flat gravifield spacetime spanned by the gravifield is associated with a noncommutative geometry characterized by a gauge-type field strength of the gravifield. A coordinate-independent and gauge-invariant action for the quantum gravity is built in the gravifield basis. In the coordinate basis, we derive equations of motion for all quantum fields including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for gravifield tensor is deduced in connection directly with the total energy-momentum tensor. When the spin and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we obtain exact solutions by solving equations of motion for the background fields in a unitary basis. The massless graviton and massive spinon result as physical quantum degrees of freedom. The resulting Lorentz-invariant and conformally flat background gravifield space-time is characterized by a cosmic vector with a nonzero cosmological mass scale. The conformal size of the Universe becomes singular at the cosmological horizon and turns out to be inflationary. A mechanism for quantum inflation is demonstrated to generate the inflation of the early Universe. Two types of gravity equation result, one is as the extension to Einstein's equation of general relativity, and the other is a new one that characterizes spinon dynamics.
We present two scale invariant models of inflation in which the addition of quadratic in curvature terms in the usual Einstein-Hilbert action, in the context of Palatini formulation of gravity, manages to reduce the value of the tensor-to-scalar ratio. In both models the Planck scale is dynamically generated via the vacuum expectation value of the scalar fields.
我们认为，涌现时空图像承认背景独立的宇宙暴胀的制定。在这幅图中，暴胀对应于时空的动力学涌现，而传统的暴胀只是由于暴胀子场携带的真空能量而使预先存在的时空（指数）膨胀。我们证明宇宙暴胀是描述真空中普朗克能量凝聚动力学过程的矩阵量子力学的含时解，而不需要引入任何暴胀子场和{ \it ad hoc}暴胀势.因此，突现时空图像实现了对暴胀宇宙的背景无关描述，它具有足够优雅和解释力，可以针对多重宇宙假设捍卫物理学的完整性。
The presence of a light vector field coupled to a scalar field during inflation makes a distinct prediction: the observed correlation functions of the cosmic microwave background (CMB) become statistically anisotropic. We study the implications of the current bound on statistical anisotropy derived from the Planck 2013 CMB temperature data for such a model. The previous calculations based on the attractor solution indicate that the magnitude of anisotropy in the power spectrum is proportional to $N^2$, where $N$ is the number of $e$-folds of inflation counted from the end of inflation. In this…
We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples…
We revisit the invariance of the curved spacetime Maxwell equations under conformal transformations. Contrary to standard literature, we include the discussion of the four-current, the wave equations for the four-potential and the field, and the behaviour of gauge conditions under the conformal transformation.
Classical scale invariance represents a promising framework for model building beyond the Standard Model. However, once coupled to gravity, any scale-invariant microscopic model requires an explanation for the origin of the Planck mass. In this paper, we provide a minimal example for such a mechanism and show how the Planck mass can be dynamically generated in a strongly coupled gauge sector. We consider the case of hidden SU(N_c) gauge interactions that link the Planck mass to the condensation of a scalar bilinear operator that is nonminimally coupled to curvature. The effective theory at ene…
The instability of (quasi) de Sitter spacetime from quantum gravitational effects has been discussed in many works. Especially, the gravitational backreaction from quantum energy momentum tensor is crucial for understanding the low-energy description of quantum gravity and sometimes destabilize the spacetime. In this paper we discuss the (quasi) de Sitter instability from gravitational backreaction involving quantum conformal anomaly. The conformal or trace anomaly corresponds to the quantum gravitational contributions of the massless conformal fields and affects the spacetime homogeneously. F…
Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratio $\dot{H}/a^2$ diverges at the boundary, where $\dot{H}$ and $a$ represent the time derivative of the Hubble parameter and the scale factor, respectively. On the other hand, if the ratio $\dot{H}/a^2$ converges, then the past boundary is regular and continuously extendible. We also develop a method to judge the continuous ($C^0$)extendibility of spacetime in the case of slow-ro…
We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the $R^2$ term and the tracker…
It is shown that the squeezed limit of inflationary expectation values follows from reparametrization invariance of the wavefunction of the universe. This translates into a constraint on the longitudinal modes of functional derivatives of the wavefunction. Thus, the local non-Gaussianity induced by single field inflation is purely a gauge artifact, and should not yield a physically measurable effect. We focus on Einstein gravity in de Sitter space and single field inflation, although the formalism only relies on the diffeomorphism invariance of the theory, and thus applies to any theory of gra…
Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime
最近，Kostelecky [V.A. Kostelecky，Phys. Lett. B 701，137（2011）]提出自发洛伦兹不变性破坏（sLIV）与Finsler几何有关。Finsler时空本质上是各向异性的，自然地导致了Lorentz不变性破坏（LIV）。本文研究了局部闵可夫斯基时空中的电磁场。拉格朗日是明确提出的电磁场。它与标准模型扩展（SME）中的一个兼容。我们给出了洛伦兹-破坏麦克斯韦方程组以及电磁波方程。得到了电磁波的形式平面波解。光的速度可以取决于光的方向，并且光锥可以扩大或缩小。LIV效应可以看作是各向异性介质对电磁波的影响。此外，在这个模型中，光的双折射不会出现在领先的顺序。通过对伽马射线暴的观测，得到了时空各向异性的一个约束条件。
Cosmological inflation provides the initial conditions for the structure formation. However, the origin of large-scale magnetic fields cannot be addressed in this framework. The key issue for this long-standing problem is the conformal invariance of the electromagnetic (EM) field in 4-D. While many approaches have been proposed in the literature for breaking conformal invariance of the EM action, here, we provide a completely new way of looking at the modifications to the EM action and generation of primordial magnetic fields during inflation. We explicitly construct a higher derivative EM act…
