The main results are reviewed of relating the scalar field of noncompactified Kaluza-Klein gravity to the Higgs field of particle physics. The embedding of 4D spacetime in a 5D manifold can result in a variable cosmological 'constant' and particle masses tiny compared to the Planck value.
We introduce gravity theories featuring spontaneously growing gauge fields where the growth is due to the Higgs mechanism. The underlying physics is inspired by the spontaneous scalarization phenomena in scalar-tensor theories. The tachyonic instability that causes the growth in spontaneous scalarization and its analog for vector fields is introduced not as an explicit potential term, but through a scalar coupling using a Higgs field. The resulting theories are distinct from previous examples of spontaneous tensorization in that they respect the gauge symmetry at the level of the action. Our r…
In this article, we intend to find a specific model which can satisfy the further refining dS swampland conjecture and scalar weak gravity conjecture (SWGC) simultaneously, in particular, Higgs inflation model and its two extensions: Higgs-Dilaton model and Palatini Higgs inflation. We find that although Higgs inflation model and Higgs-Dilaton model could satisfy the further refining dS swampland conjecture, the two models cannot satisfy SWGC and its strong version. While Palatini Higgs inflation could satisfy these conjectures simultaneously. Therefore Palatini Higgs inflation could be a "rea…
Presented is a quantum gravity theory that is a quantum mechanical generalization of Einstein's vierbein field-based approach, where the classical metric tensor field is promoted to a quantum mechanical metric tensor field operator. The quantum gravity theory derives from quantum information dynamics intrinsic to quantized space, which is taken to be a tensor product space on a qubit array. Hence, the metric tensor field operator is expressed as a product of two frame 4-vectors, which are anticommuting operators and naturally represented by Dirac matrices. The quantum gravity theory reduces to…
We study how higher-order gravity affects Higgs inflation in the Palatini formulation. We first review the metric and Palatini formulations in comparative manner and discuss their differences. Next cosmic inflation driven by a scalar field and inflationary observables are discussed. After this we review the Higgs inflation and compute the inflationary observables both in the metric and Palatini formulations. We then consider adding higher-order terms of the curvature to the action. We derive the equations of motion for the most general action quadratic in the curvature that does not violate pa…
Gravity as a Higgs Field. III. Nongravitional Deviations of Gravitational Fields
在第一和第二部分的工作（gr-qc/9405013，9407032），我们已经表明，重力是{ \it sui generis}一个希格斯场对应于自发对称性破缺时，费米子物质只允许洛伦兹子群的世界对称性的几何舞台。从数学的观点来看，引力的希格斯性质是由于不同的引力场导致旋量丛上的$γ$ -矩阵对世界流形的余切向量的不等价表示。由此可见，引力场不能形成一个仿射空间，而仿射空间是以某一背景场的偏差的线性空间为模型的。换句话说，即使是弱的引力场也不满足叠加原理，特别是不能用通常的方法量子化。同时，我们可以检验引力场$h$的叠加偏差$σ$，使得$h+σ$不是引力场。这些偏差在位错流形中的仿射群规范理论的框架下得到了充分的数学描述，它们的拉格朗日密度不同于我们熟悉的引力密度。它们对标准引力效应有贡献，例如，修正牛顿的引力势
We study a gravity model in 2+1 dimensions, arising from a generalized Chern-Simons (CS) density we call a Higgs-Chern-Simons (HCS) density. This generalizes the construction of gravitational systems resulting from non-Abelian CS densities in all odd dimensions. The new HCS densities employed here are arrived at by the usual one-step descent of new Higgs--Chern-Pontryagin (HCP) densities, the latter resulting from the dimensional reduction of Chern-Pontryagin (CP) densities in some even dimension, such that in any given dimension (including even) there is an infinite tower of such models. Here…
Starobinsky inflation and Higgs inflation in gravity, and their equivalence based on the common inflationary potential are extended to supergravity in the proper framework, where the Starobinsky and Higgs descriptions of inflation arise in two different gauges of the same supergravity model.
Models of inflation in which the Higgs field is non-minimally coupled to gravity lead, after a recaling of the metric, to a complicated expression for the potential of the inflaton field. Nevertheless, this potential produces the desired features, both theoretical and experimental, after some approximations are made. In this note, we also allow for a modification of the Higgs kinetic term in such a way that the resulting potential for the inflaton field is, without any approximation, of the simplest form after the rescaling of the metric.
This article investigates the effects of Tree Level Higgs Potential on reheating in $f(Q)$ gravity. We examine the formalism of tree level inflation in a modified $f(Q)$ model, finding that the slow roll and e-folds number during inflation depend on the $f(Q)$ model $α$ parameter. Additionally, we calculate the reheating as a function of the decay rate, constraining the inflationary parameters and reheating temperature. Our study reveals that the Tree Level Higgs Potential influences the reheating temperature and decay rate. We conclude that increasing the decay rate energy leads to higher reh…
Teleparallel gravity is a formulation of general relativity that is physically equivalent to metric gravity if the gravitational action has the Einstein-Hilbert form and matter is minimally coupled. However, scalar fields generally couple directly to the connection, breaking the equivalence. In particular, this happens for the Standard Model Higgs. We show that a teleparallel theory with a non-minimally coupled scalar field has no linear scalar perturbations, and therefore cannot give successful inflation, unless the non-minimal coupling functions satisfy a particular relation. If the relation…
We derive a Higgs inflationary model in the context of a complex geometrical scalar-tensor theory of gravity. In this model the Higgs inflaton scalar field has geometrical origin playing the role of the Weyl scalar field in the original non-riemannian background geometry. The energy scale enough to generate inflation from the Higgs energy scale is achieved due to the compatibility of the theory with its background complex Weyl-integrable geometry. We found that for a number of e-foldings $N=63$, a nearly scale invariant spectrum for the inflaton is obtained with an spectral index $n_s\simeq 0.…
We consider an extension of Higgs inflation in which the Higgs field is non-minimally coupled to gravity through its kinetic term. We analyzed power-law coupling functions with positive or negative integer power and found that the Higgs boson can drive a successful inflation only for the cases $n=2,1,0,-1$. Theoretical predictions for both tensor to scalar ratio $r$ and scalar spectral index $n_s$ are within the 2018 \textit{Planck} $95\%$ CL. The behavior of the self coupling $λ$ with respect to the scalar field at the horizon crossing was obtained, and It was found that it can take values in…
We present an updated review of Kraichnan's derivation of Einstein's equations from quantum field theory, including the period after the discovery of the Higgs mechanism. Gravitation in the Einstein sense is seen to be renormalizable and consistent with the Standard Model of Fundamental Interactions.
First, we propose a scale-invariant modified gravity interacting with a neutral scalar "inflaton" and a Higgs-like SU(2)xU(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes in the physical Einstein frame a quintessential inflationary scenario driven by the "inflaton" together with gravity-inflaton assisted dynamical spontaneous SU(2)xU(1) symmetry breaking in the post-inflationary universe, whereas SU(2)xU(1) symmetry remains intact in the inflationary epoch. Next, we find the explicit representation of the…
The Higgs effective potential becomes unstable at approximately $10^{11}$ GeV, and if only standard model interactions are considered, the lifetime $τ$ of the electroweak vacuum turns out to be much larger than the age of the Universe $T_U$. It is well known, however, that $τ$ is extremely sensitive to the presence of unknown new physics: the latter can enormously lower $τ$. This poses a serious problem for the stability of our Universe, demanding for a physical mechanism that protects it from a disastrous decay. We have found that there exists a universal stabilizing mechanism that naturally …
We consider a family of new Higgs-Chern-Simons (HCS) gravity models in 2n+1 dimensions (n=1,2,3). This provides a generalization of the (usual) gravitational Chern-Simons (CS) gravitaties resulting from non- Abelian CS densities in all odd dimensions, which feature vector and scalar fields in addition to the metric. The derivation of the new HCS gravitational (HCSG) actions follows the same method as in the usual-CSG case resulting from the usual CS densities. The HCSG result from the HCS densities, which result through a one-step descent of the Higgs-Chern-Pontryagin (HCP), the latter being d…
There are indications that an asymptotically safe UV completion of the Standard Model with gravity could constrain the Higgs self-coupling, resulting in a prediction of the Higgs mass close to the vacuum stability bound in the Standard Model. The predicted value depends on the top quark mass and comes out somewhat higher than the experimental value if the current central value for the top quark mass is assumed. Beyond the Standard Model, the predicted value also depends on dark fields coupled through a Higgs portal. Here we study the Higgs self-coupling in a toy model of the Standard Model wit…
We consider Weyl's conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a $\tilde R^2$ term in moving from the Jordan frame to the Einstein frame. A massless Nambu-Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent …
In this letter we investigate gauge invariant scalar fluctuations of the metric in a non-perturbative formalism for a Higgs inflationary model recently introduced in the framework of a geometrical scalar-tensor theory of gravity. In this scenario the Higgs inflaton field has its origin in the Weyl scalar field of the background geometry. We found a nearly scale invariance of the power spectrum for linear scalar fluctuations of the metric. For certain parameters of the model we obtain values for the scalar spectral index $n_s$ and the scalar to tensor ratio $r$ that fit well with the Planck 201…
In the framework of Higgs inflation, we consider the electromagnetic field nonminimally coupled to gravity via the parity-preserving $\propto RF^{2}$ and parity-violating $\propto RF\tilde{F}$ terms. Using the perturbation theory to the leading order in these couplings, we study the generation of the electromagnetic field during the inflation stage. We derive the effective kinetic and axial coupling functions arising in the Einstein frame in the usual metric as well as Palatini formulations of gravity. For both formulations, we determine the power spectrum, energy density, and helicality of th…
