During inflation, there is a preferred reference frame in which the expansion of the background spacetime is spatially isotropic. In contrast to Minkowski spacetime, observables can depend on the velocity of the system with respect to this cosmic rest frame. We derive new constraints from radiative stability and unitarity on effective field theories with such spontaneously broken Lorentz symmetry. In addition to a maximum energy scale, there is now also a critical velocity at which the theory breaks down. The theory therefore has different resolving power in time and in space, and we show that these can only coincide if cubic Lorentz-violating interactions are absent. Applying these bounds to the Effective Field Theory of Inflation, we identify the region of parameter space in which inflation can be both single-field and weakly coupled on subhorizon scales. This can be implemented as a theoretical prior, and we illustrate this explicitly using Planck observational constraints on the primordial bispectrum.
The concepts of Lorentz invariance of local (flat space) physics, and unitarity of time evolution and the S-matrix, are famously rigid and robust, admitting no obvious consistent theoretical deformations, and confirmed to incredible accuracy by experiments. But neither of these notions seem to appear directly in describing the spatial correlation functions at future infinity characterizing the "boundary" observables in cosmology. How then can we see them emerge as {\it exact} concepts from a possible ab-initio theory for the late-time wavefunction of the universe? In this letter we examine thi…
We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the linearised level we find that the trace of metric perturbations receives a positive or negative mass squared contribution. However, only for the Fierz-Pauli combination the theory is free of ghosts. The mass term for the trace of metric perturbations can be cancelled by explicitly breaking scale invariance. This reintroduces fine-tuning. Models based on four form fi…
It is shown that a spontaneously-broken gauge theory of the Lorentz group contains Ashtekar's chiral formulation of General Relativity accompanied by dust. From this perspective, gravity is described entirely by a connection $ω$ valued in the Lie algebra of the complexified Lorentz group and a Lorentz-charged scalar field $τ$. The model is "pre-geometric" in the sense that the spacetime metric may be constructed only in the symmetry-broken regime. We speculate on the extent to which this dust may account for dark matter and on the behaviour of the theory in regimes where the symmetry is not br…
Since Stephen Hawking discovered that black holes emit thermal radiation, black holes have become the theoretical laboratories for testing our ideas on quantum gravity. This dissertation is devoted to the study of singularities, the formation of black holes by gravitational collapse and the global structure of spacetime. All our investigations are in the context of a recently proposed approach to quantum gravity, which breaks Lorentz and diffeomorphism symmetries at very high energies.
We compute the $2\rightarrow 2$ gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass $m_{3/2}$) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as $κ^2 E^4/m_{3/2}^2$, signaling a potential breakdown of unitarity at a scale $Λ^2\sim m_{3/2}/κ\sim M_{\mathrm{SUSY}}^2$. As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (s…
In this paper, we revisit the issue of static hairs of black holes in gravitational theories with broken Lorentz invariance in the case that the speed $c_ϕ$ of the khronon field becomes infinitely large, $c_ϕ = \infty$, for which the sound horizon of the khronon field coincides with the universal horizon, and the boundary conditions at the sound horizon reduce to those given normally at the universal horizons. As a result, less boundary conditions are present in this extreme case in comparison with the case $c_ϕ = $ finite. Then, it would be expected that static hairs might exist. However, we …
In this paper, we show the existence of static and rotating universal horizons and black holes in gravitational theories with the broken Lorentz invariance. We pay particular attention on the ultraviolet regime, and show that universal horizons and black holes exist not only in low energy scales but also in the UV scales. This is realized by presenting various static and stationary exact solutions of the full theory of the projectable Hořava gravity with an extra U(1) symmetry in (2+1)-dimensions, which, by construction, is power-counting renormalizable.
We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability conditions are modified from those in relativistic theories. We show that for renormalizability, an extended version of the power counting condition is required in addition to the conventional one. The unitarity bound for S-matrix elements also gives stronger constraints on interaction terms because of the reference frame dependence of scattering amplitudes…
We study tree-unitarity and renormalizability in Lifshitz-scaling theory, which is characterized by an anisotropic scaling between the spacial and time directions. Due to the lack of the Lorentz symmetry, the conditions for both unitarity and renormalizability are modified from those in relativistic theories. For renormalizability, the conventional discussion of the power counting conditions has to be extended. Because of the dependence of $S$-matrix elements on the reference frame, unitarity requires stronger conditions than those in relativistic cases. We show that the conditions for unitari…
We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension. We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) model and the Standard-Model Extension. As part of the analysis,we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.
In the Penrose process and the Blandford-Znajek mechanism, the rotational energy of a black hole (BH) is extracted via particle fission and magnetic tension, respectively. Recently, inspired by a fundamental trait in plasma astrophysics known as magnetic reconnection (MR), a new energy extraction mechanism based on the fast reconnection of the magnetic field lines inside the ergosphere has been proposed by Comisso and Asenjo. In this paper, we investigate energy extraction caused by MR in the ergosphere of a rapidly spinning BH with broken Lorentz symmetry by a background bumblebee vector fiel…
Arnold Sommerfeld Center for Theoretical Physics, Ludwig–Maximilians–Universität München（慕尼黑路德维希-马克西米利安大学阿诺德·索末菲理论物理中心）；Kavli IPMU (WPI), UTIAS, The University of Tokyo, and Center for Data-Driven Discovery（东京大学 Kavli 宇宙粒子与宇宙学前沿研究所、UTIAS 及数据驱动发现中心）
In this paper, we first show that the definition of the universal horizons studied recently in the khrononmetric theory of gravity can be straightforwardly generalized to other theories that violate the Lorentz symmetry, by simply considering the khronon as a probe field and playing the same role as a Killing vector field. As an application, we study static charged ($D+1$)-dimensional spacetimes in the framework of the healthy (non-projectable) Horava-Lifshitz (HL) gravity in the infrared limit, and find various solutions. Some of them represent Lifshitz space-times with hyperscaling violation…
Instantons and unitarity in quantum cosmology with fixed four-volume
我们在所谓的广义相对论的幺模版本中找到了爱因斯坦方程的一些复解，并将它们解释为鞍点，从而在具有“无边界”型拓扑的时空流形上的几乎处处洛伦兹度规的空间上得到引力路径积分的估计。在这种情况下，无边界初始条件与量子测度的可定义性的相容性归结为无边界波函数的归一化性和幺正演化。我们考虑具有空间拓扑S^3的陶布小超空间模型中的时空拓扑R^4和RP^4 # R^4，以及具有空间拓扑T^3的比安基I型小超空间模型中的时空拓扑R^2 x T^2。在每种情况下，都存在一个复杂的鞍点（或鞍点的组合），它产生一个与正规化和幺正演化相容的波函数。这种鞍点的存在倾向于证明幺模理论比传统的爱因斯坦引力更少发散。在比安基I型的情况下，杰出的复杂的解决方案是近似真实的和洛伦兹在晚些时候，似乎描述了爆炸性膨胀从零尺寸在T=0。(In与此相反，在陶布的情况下，唯一具有近似洛伦兹晚期行为的复解产生一个波函数，它是可归一化的，但非幺正地演化，总概率在幺正模“时间”中呈指数增长，其方式表明在零体积下不断创造新的宇宙。）提出了包含更多自由度后这些结果的稳定性问题。
A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the "Vierbein" assuring local gauge invariance enters not as an independent dynamical field, but emerges as a functional of the Lorentz gauge field. The underlying geometry of the theory turns out to be a $SO(1,3)$ Banach bundle. The most general action which is renormalizable by power-counting is constructed in terms of the gauge field and its first derivatives. It contains no higher derivative terms in the gauge field which destroy unitarity in th…
