We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a BRST-exact formulation of the theory, which can be considered as a topological field theory.
Field theory models of axion monodromy have been shown to exhibit vacuum energy sequestering as an emergent phenomenon for cancelling radiative corrections to the cosmological constant. We study one loop corrections to this class of models coming from virtual axions using a heat kernel expansion. We find that the structure of the original sequestering proposals is no longer preserved at low energies. Nevertheless, the cancellation of radiative corrections to the cosmological constant remains robust, even with the new structures required by quantum corrections.
We carry out the Hamiltonian analysis of the local vacuum energy sequestering model - a manifestly local and diffeomorphism invariant extension of general relativity which has been shown to remove the radiatively unstable contribution to the vacuum energy generated by matter loops. We find that the degravitation of this UV sensitive quantity is enforced via global relations that are a consequence of the model's peculiar constraint structure. We also show that the model propagates the proper number of degrees of freedom and thus locally reduces to general relativity on-shell.
The sequestering mechanism has been proposed as a remedy to the old cosmological constant problem of the non-gravitating vacuum energy in the matter sector. Here it is shown that an extension of this global constraint mechanism arises naturally from an averaging condition for residual cosmological constants produced in different patches of the Universe. The new mechanism naturally yields the small observed value that gives rise to cosmic acceleration at late times, hence, addressing the new cosmological constant problem. Hereby the halo model picture is adopted with all matter content ultimate…
Vacuum energy sequestering is a mechanism for cancelling off the radiative corrections to vacuum energy. The most comprehensive low energy model, proposed in 1606.04958 [hep-th], has the ability to cancel off radiative corrections to vacuum energy for loops of both matter and gravitons, in contrast to earlier proposals. Here we explore the framework and cosmological consequences of this model, which we call Omnia Sequestra, owing to its ability to sequester all. A computation of historic integrals on a cosmological background reveals some subtleties with UV sensitivity not seen in earlier mode…
A formulation of Covariant Canonical Quantization is discussed, which works on an extended Hilbert space and reduces to conventional canonical quantization when constraining to the solution of the field equation a priori. From the formal point of view it may be seen as a formalism between the canonical operator and the functional integral approach. A covariant number operator and two symmetric vacua are constructed. By that means, certain well-known quantities like the LSZ formula are rederived via a projection limit. The time-ordering operator can be replaced by taking into account the mirror…
We consider a vacuum static spacetime in a finite size cavity. On the boundary, we specify a metric and a finite constant local temperature $T$. No spherical or any other spatial symmetry is assumed. We show that (i) inside a cavity, only a black hole or flat spacetime are possible, whereas a curved horizonless regular space-time is excluded, (ii) in the limit when the horizon area shrinks, the Hawking temperature diverges, (iii) for the existence of a black hole, $T$ should be high enough. When $T\rightarrow \infty $, a black hole phase is favorable thermodynamically. Our consideration essent…
We introduce a generalization of the usual vacuum energy, called `deformed vacuum energy', which yields anisotropic pressure whilst preserving zero inertial mass density. It couples to the shear scalar in a unique way, such that they together emulate the canonical scalar field with an arbitrary potential. This opens up a new avenue by reconsidering cosmologies based on canonical scalar fields, along with a bonus that the kinetic term of the scalar field is replaced by an observable, the shear scalar. We further elaborate the aspects of this approach in the context of dark energy.
Gravitational models of self-tuning are those in which vacuum energy has no observable effect on spacetime curvature, even though it is a priori unsuppressed below the cut-off. We complement Weinberg's no go theorem by studying field theoretic completions of self-adjustment allowing for broken translations as well as other generalisations, and identify new obstructions. Our analysis uses a very general Kallen-Lehmann spectral representation of the exchange amplitude for conserved sources of energy-momentum and exploits unitarity and Lorentz invariance to show that a transition from self-tuning…
We show that a pair of field theory monodromies in which the shift symmetry is broken by small, well motivated deformations, naturally incorporates a mechanism for cancelling off radiative corrections to the cosmological constant. The lighter monodromy sector plays the role of inflation as well as providing a rigid degree of freedom that acts as a dynamical counterterm for the cosmological constant. The heavier monodromy sector includes a rigid dilaton that forces a global constraint on the system and the cancellation of vacuum energy loops occurs at low energies via the sequestering mechanism…
We analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When $Λ>0$ the energy diverges, but a renormalised formula with well defined flux is obtained. We show that the renormalised energy in the asymptotically off-diagonal gauge coincides with the quadratisation of the generalisation of the Trautman-Bondi mass proposed in [13].
Canonical methods of quasiclassical dynamics make it possible to go beyond a strict background approximation for cosmological perturbations by including independent fields such as correlation degrees of freedom. New models are introduced and analyzed here for cosmological dynamics in the presence of quantum correlations between background and perturbations, as well as cross-correlations between different modes of a quantum field. Evolution equations for moments of a perturbation state reveal conditions required for inhomogeneity to build up out of an initial vacuum. A crucial role is played by…
The vacuum expectation values (VEVs) of the field squared and energy-momentum tensor for a massless scalar field are investigated in the Milne universe with general number of spatial dimensions. The vacuum state depends on the choice of the mode functions in the canonical quantization procedure and we assume that the field is prepared in the conformal vacuum. As the first step an integral representation for the difference of the Wightman functions corresponding to the conformal and Minkowski vacua is derived. The mean field squared and energy-momentum tensor are obtained in the coincidence lim…
Recently, the variation of the Planck mass in the General Relativistic Einstein-Hilbert action was proposed as a self-tuning mechanism of the cosmological constant, preventing Standard Model vacuum energy from freely gravitating and enabling an estimation of the magnitude of its observed value. We explore here new aspects of this proposal. We first develop an equivalent Einstein-frame formalism to the current Jordan-frame formulation of the mechanism and use this to highlight similarities and differences of self-tuning to the sequestering mechanism. We then show how with an extension of the lo…
In this article, I have considered a real scalar field theory and able to show that under Bogoliubov transformation in infinite volume limit or thermodynamic limit the transformed Hamiltonian no longer invariant under U(1) action defined appropriately as it was before doing transformation. We also have checked this fact by looking at the correlation functions under the action of U(1) group. We suitably defined field operators that are associated with particle production phenomena then we can also show that correlation functions of such field operators also don't follow U(1) invariance, shown i…
Consistent Canonical Quantization of Gravity: Recovery of Classical GR from BRST-invariant Coherent States
Max-Planck-Institut für Physik（马克斯·普朗克物理研究所）；Arnold Sommerfeld Center, Ludwig-Maximilians-Universität（慕尼黑大学阿诺德·索末菲中心）；Sydney Consortium for Particle Physics and Cosmology, School of Physics, The University of Sydney（悉尼大学物理学院粒子物理与宇宙学联盟）
We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples to the canonically transformed gravitational field. We find that a naive matter coupling to the transformed field leads to the appearance of an extra mode in the phase space, rendering the theory inconsistent. We then find a consistent and novel way of matter coupling: after imposing a gauge fixing condition, a matter field can minimally couple to gravity wi…
Within the premise of canonical quantisation, we re-examine the quantum structure of bosonic tensionless string theory. In the classical theory, the worldsheet metric degenerates and the Bondi-Metnzer-Sachs (BMS) algebra arises as the residual symmetries on fixing the tensionless equivalent of the conformal gauge. In the quantum regime, we find, on careful examination, that there are multiple ways to impose constraints to restrict the physical Hilbert space, which in turn lead to three distinct choices of tensionless vacua. We analyse these vacua in detail, commenting on various aspects like t…
A Self-gravitating Dirac-Born-Infeld Global Monopole
将整体引力场的场论推广到Dirac Born Infeld（DBI）场，研究了四维球对称时空中DBI整体引力场的引力性质.对度规场和DBI标量场的耦合方程进行了渐近数值求解。结果表明，DBI的引力效应相当于度规中的亏损立体角加上原点处的负质量。然而，与正则整体介子相比，在相同的假真空和对称破缺尺度下，DBI整体介子具有相对较小的核和较大的有效质量绝对值。这样，当光线经过时，它可以给出一个较大的偏转角。特别地，当翘曲因子的尺度足够小时，DBI整体介子的有效质量不明显依赖于虚真空的值，这与正则整体介子的有效质量有本质的不同.
A new formulation for obtaining the tunneling action for vacuum decay based on the so-called tunneling potential was developed recently. In the original derivation, the new action was obtained by requiring that its variation led to the correct equations of motion and the same value for the action as evaluated on the Euclidean bounce. We present an alternative derivation of the tunneling potential action via canonical transformations. We discuss both single-field and multi-field cases as well as the case with gravity. We also comment on the possible application of the new approach to the calcul…
An important yet perplexing result from work in the 90s and 00s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was done by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. In this paper we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temp…
We formulate the quantum field theory description of neutron-antineutron oscillations in the framework of canonical quantization, in analogy with the Bardeen--Cooper--Schrieffer (BCS) theory and the Nambu--Jona-Lasinio model. The physical vacuum of the theory is a condensate of pairs of {\it would-be neutrons and antineutrons} in the absence of the baryon-number violating interaction. The quantization procedure defines uniquely the mixing of massive Bogoliubov quasiparticle states which represent the neutron. In spite of not being mass eigenstates, neutron and antineutron states are defined on…
We investigate the $θ$-vacuum structure and the 't Hooft anomaly at $θ=π$ in a simple quantum mechanical system on $S^1$ to scrutinize the applicability of the functional renormalization group (fRG) approach. Even though the fRG is an exact formulation, a naive application of the fRG equation would miss contributions from the $θ$ term due to the differential nature of the formulation. We first review this quantum mechanical system on $S^1$ that is solvable with both the path integral and the canonical quantization. We discuss how to construct the quantum effective action including the $θ$ depe…
