Spherically symmetric geometrodynamics is studied for scalar–tensor theory and Einstein General Relativity minimally coupled to a scalar field. We discussed the importance of boundary terms for non-compact space-like foliations and derived the equations of motion in the Hamiltonian formalism both in the Jordan and Einstein frames. On the reduced phase space obtained by gauge-fixing the lapse and the radial shift functions, the two frames are connected through a Hamiltonian canonical transformation. We discussed the effects of the singularity of the Hamiltonian canonical transformation connecting Jordan and Einstein frames for two static solutions (Fisher, Janis, Newman and Winicour solution in the Einstein frame and Bocharova–Bronnikov–Melnikov–Bekenstein black hole solution in the Jordan frame).

Italy

Vatican

Matteo Galaverni

United States

Gabriele Gionti

Spherically symmetric geometrodynamics in Jordan and Einstein frames

It was recently suggested — based on general self-consistency arguments as well as results from the bootstrap [1–3] — that the CFT describing the -state Potts model is logarithmic for generic values of , with rank-two Jordan blocks for and $$ {\overline{L}}_0 $$ in many sectors of the theory. This is despite the well-known fact that the lattice transfer matrix (or Hamiltonian) is diagonalizable in (arbitrary) finite size. While the emergence of Jordan blocks only in the limit → ∞ is perfectly possible conceptually, diagonalizability in finite size makes the measurement of logarithmic couplings (whose values are analytically predicted in [2, 3]) very challenging. This problem is solved in the present paper (which can be considered a companion to [2]), and the conjectured logarithmic structure of the CFT confirmed in detail by the study of the lattice model and associated “emerging Jordan blocks.”

Lawrence Liu

France

Jesper Jacobsen

Hubert Saleur

Emerging Jordan blocks in the two-dimensional Potts and loop models at generic

A longstanding issue is the classical equivalence between the Jordan and the Einstein frames, which is considered just a field redefinition of the metric tensor and the scalar field. In this work, based on the previous result that the Hamiltonian transformations from the Jordan to the Einstein frame are not canonical on the extended phase space, we study the possibility of the existence of canonical transformations. We show that on the reduced phase space – defined by suitable gauge fixing of the lapse and shifts functions – these transformations are Hamiltonian canonical. Poisson brackets are replaced by Dirac’s brackets following the Bergman-Dirac’s procedure. The Hamiltonian canonical transformations map solutions of the equations of motion in the Jordan frame into solutions of the equations of motion in the Einstein frame.

On the canonical equivalence between Jordan and Einstein frames

We study the Hilbert space of the Class 5 model described in <inter-ref xmlns:ns0='http://www.w3.org/1999/xlink' ns0:role='http://www.elsevier.com/xml/linking-roles/preprint' ns0:href='arxiv:1904.12005' id='inf0010'>arXiv:1904.12005</inter-ref>. Despite being integrable, neither its transfer matrix nor its Hamiltonian are diagonalisable, meaning that the usual Algebraic Bethe Ansatz does not provide the full Hilbert space. Instead, we make use of the symmetries of the model to construct the Jordan blocks of the transfer matrix. We also show that the Hamiltonian and the transfer matrix, despite commuting, do not have the same Jordan block structure.

Germany

Juan Miguel Nieto García

Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries

The conformal correspondence between FLRW universes in the Einstein and Jordan frames allows for an expansion-collapse duality – an always expanding Einstein frame universe can have a dual Jordan frame description that is contracting forever. The scenario eventually runs into an apparent paradox. When the contracting Jordan frame universe becomes sufficiently small, the classical description becomes inadequate and the universe is expected to develop quantum characteristics. However, at this time, the corresponding Einstein frame universe is expected to behave classically, due to the arbitrarily large size it has grown to. The conformal map here appears to be providing a duality between a quantum effect-dominated universe and a classical universe. We investigate the status of the conformal map at the quantum level in such a scenario, focusing on addressing this paradox. The Einstein and Jordan frame universes are quantized using the Wheeler-DeWitt prescription. We show that the classical conformal map holds at the quantum level when compared through expectation values of scale factors. The relative quantum fluctuation in the scale factor becomes conformally invariant, it increases in both the past and future directions according to the internal clock. Expectedly, the quantum fluctuations in the collapsing Jordan frame increase as it shrinks towards singularity. More surprisingly, the quantum fluctuations in the expanding Einstein frame increase as well, even as its classical scale factor becomes larger. Despite having drastically different cosmological evolutions, the rise in quantum characteristics in a collapsing frame implies the same in its expanding counterpart, thereby resolving the apparent paradox.

India

Dipayan Mukherjee

Harkirat Sahota

Einstein and Jordan frame correspondence in quantum cosmology: expansion-collapse duality

We revisit the phenomenological predictions of the Universal Texture Zero (UTZ) model of flavour originally presented in [1], and update them in light of both improved experimental constraints and numerical analysis techniques. In particular, we have developed an in-house Markov Chain Monte Carlo (MCMC) algorithm to exhaustively explore the UTZ’s viable parameter space, considering both leading- and next-to-leading contributions in the model’s effective operator product expansion. We also extract – for the first time – reliable UTZ predictions for the (poorly constrained) leptonic CP-violating phases, and ratio observables that characterize neutrino masses probed by (e.g.) oscillation,  $$\beta $$  <math> <mi>β</mi> </math>  -decay, and cosmological processes. We therefore dramatically improve on the proof-in-principle phenomenological analysis originally presented in [1], and ultimately show that the UTZ remains a minimal, viable, and appealing theory of flavour. Our results also further demonstrate the potential of robustly examining multi-parameter flavour models with MCMC routines.

Jordan Bernigaud

Portugal

Ivo Medeiros Varzielas

Miguel Levy

United Kingdom

Jim Talbert

Revisiting the universal texture zero of flavour: a Markov chain Monte Carlo analysis

Unlike the minimally coupled gravity theory where matter is coupled with gravity in such a manner so that one can differentiate the matter and gravity sector uniquely, the non-minimally coupled theories (NMCT) are distinguished by the intermingling of two. As a consequence of this the calculation of the energy momentum tensor (EMT) in NMCT is beset with an arbitrariness. In this paper we provide an algorithm based on the well known equivalence between Jordan frame and Einstein frame formulations which enables us to construct the EMT for NMCT in a unique way.

Sk. Moinuddin

Pradip Mukherjee

Anirban Saha

Amit Roy

Energy momentum tensor of a non-minimally coupled scalar from the equivalence of the Einstein and Jordan frames

We demonstrate a spontaneous tendency of quantum wave packets to become quasi-classical, providing a classical limit for the Universe dynamics. However, this limit is not maintained in the future (after a critical value of the relational time) and a spreading process is turned on. We show that the onset of an inflationary scenario is not able to make this localization stable of the wave packets for the Bianchi I model. Instead, when we implement a perturbative inflationary scenario for the isotropic Universe a mechanism of stable classicalization of the Universe emerges. This result outlines a sharp difference between the standard relativistic cosmology and a modified f(R) paradigm.

Mariaveronica Angelis

Giovanni Montani

On the emergence of a classical isotropic universe from a quantum f(R) Bianchi cosmology in the Jordan frame

We continue the classification of the Jordan chains of the eclectic three state spin chain that we started in our previous article. Following the same steps, we construct the generalised eigenvectors of this spin chain by computing the strongly twisted limit of linear combinations of eigenvectors of a twisted XXX SU(3) spin chain. We show that this classification problem can be mapped to the computation of the number of positive integer solutions of a system of linear equations.

Juan García

Jordan blocks and the Bethe Ansatz II: The eclectic spin chain beyond K = 1

We consider the phenomenological signatures of Simplified Models of Flavourful Leptoquarks, whose Beyond-the-Standard Model (SM) couplings to fermion generations occur via textures that are well motivated from a broad class of ultraviolet flavour models (which we briefly review). We place particular emphasis on the study of the vector leptoquark ∆ μ  with assignments (3 , 1 , 2/3) under the SM’s gauge symmetry, SU(3) C  × SU(2) L  × U(1) Y , which has the tantalising possibility of explaining both   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {\mathcal{R}}_{K^{\left(\ast \right)}} $$  and   <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {\mathcal{R}}_{D^{\left(\ast \right)}} $$  anomalies. Upon performing global likelihood scans of the leptoquark’s coupling parameter space, focusing in particular on models with tree-level couplings to a single charged lepton species, we then provide confidence intervals and benchmark points preferred by low (er)-energy flavour data. Finally, we use these constraints to further evaluate the (promising) Large Hadron Collider (LHC) detection prospects of pairs of τ-flavoured ∆ μ , through their distinct (a)symmetric decay channels. Namely, we consider direct third-generation leptoquark and jets plus missing-energy searches at the LHC, which we find to be complementary. Depending on the simplified model under consideration, the direct searches constrain the ∆ μ  mass up to 1500-1770 GeV when the branching fraction of ∆ μ  is entirely to third-generation quarks (but are significantly reduced with decreased branching ratios to the third generation), whereas the missing-energy searches constrain the mass up to 1150-1700 GeV while being largely insensitive to the third-generation branching fraction.