arXiv subjects

Sebastian Zell

Publications and source records attributed to Sebastian Zell.

At least 37 records · Page 2Linked to original sources

arXiv2024

Einstein-Proca theory from the Einstein-Cartan formulation

We construct a theory of gravity in which a propagating massive vector field arises from a quadratic curvature invariant. The Einstein-Cartan formulation and a partial suppression of torsion ensure the absence of ghost and strong-coupling problems, as we prove with nonlinear Lagrangian and Hamiltonian analysis. Augmenting General Relativity with a propagating torsion vector, our theory provides a purely gravitational origin of Einstein-Proca models and constrains their parameter space. As an outlook to phenomenology, we discuss the gravitational production of fermionic dark matter.

hep-th↗

arXiv2024

Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions

General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity, we employ metric-affine gravity, which encompasses as special cases the metric, Palatini, Einstein-Cartan and Weyl formulations. We first discuss the interaction of fermions with torsion and non-metricity, also commenting on projective symmetry. With a view towards the Standard Model, we then construct a generic model of (complex) scalar, fermionic and gauge fields coupled to GR and derive an equivalent metric theory, which features numerous new interaction terms. As a first observable consequence, we point out that a gravitational mechanism for producing dark matter in the form of singlet fermions can be used to distinguish between metric gravity and other formulations of GR.

gr-qc↗

arXiv2023

Non-Polynomial Interactions as a Path Towards a Non-Renormalizable UV-Completion

We propose a new class of single-field scalar quantum field theories with non-polynomial interactions leading to a two-point Green's function that can be naturally continued beyond the naive cutoff scale. This provides a new prospect for self-completing theories in the UV-domain. In our approach, the formal power series for the scalar potential has a vanishing radius of convergence and is defined through Borel resummation. We discuss concrete examples, among others with a spectral function that vanishes at large momenta, potentially leading to an asymptotically free theory. Finally, we give an outlook on future research, with a view towards possible applications to inflation and gravity.

hep-th↗

arXiv2023

Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field

General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine gravity, which avoids any assumption about the vanishing of curvature, torsion or non-metricity. We use it to construct an action of a scalar field coupled non-minimally to gravity. It encompasses as special cases numerous previously studied models. Eliminating non-propagating degrees of freedom, we derive an equivalent theory in the metric formulation of GR. Finally, we give a brief outlook to implications for Higgs inflation.

hep-th↗

arXiv2023

Scale invariant Einstein-Cartan gravity and flat space conformal symmetry

We find the conditions under which scale-invariant Einstein-Cartan gravity with scalar matter fields leads to an approximate conformal invariance of the flat space particle theory up to energies of the order of the Planck mass. In the minimal setup, these models, in addition to the fields of the Standard Model and the graviton, contain only one extra particle -- a massless dilaton. Theories of this type can pave the way for a self-completion all the way up the Planck scale and lead to rather universal inflationary predictions, close to those of the simplest Higgs-inflation scenario in the metric theory of gravity.

hep-th↗

arXiv2023

Field redefinitions, perturbative unitarity and Higgs inflation

For inflation driven by the Higgs field coupled non-minimally to gravity, we study the cutoff energy scale above which perturbation theory breaks down. Employing the metric formulation, we first give an overview of known results and then provide a new way to calculate a lower bound on the cutoff. Our approach neither relies on a gauge choice nor does it require any calculation of amplitudes. Instead, it exploits the fact that the S-matrix is invariant under field redefinitions. In agreement with previous findings, we demonstrate that the cutoff is significantly higher during inflation than in vacuum, which ensures the robustness of semi-classical predictions. Along the way, we generalize our findings to the Palatini formulation and comment on a useful parametrization of the Higgs doublet in both scenarios.

hep-ph↗

arXiv2023

Critical Points in Palatini Higgs Inflation with Small Non-Minimal Coupling

We investigate inflation driven by the Higgs boson in the Palatini formulation of General Relativity. Our analysis primarily focuses on a small non-minimal coupling of the Higgs field to gravity in the range $0<ξ\lesssim 1$. We incorporate the renormalization group running of the relevant parameters as computed within the Standard Model and allow for small corrections. In addition to $ξ$, our model features two tunable parameters: the low-energy value of the top Yukawa coupling and an effective jump of the Higgs self-interaction. Our results indicate that critical points leading to a large enhancement of the power spectrum can be produced. However, the observed amplitude of perturbations in the CMB cannot be matched within this setting. On the one hand, this makes it difficult to generate a sizable abundance of primordial black holes. On the other hand, our finding can be viewed as further evidence that Palatini Higgs inflation has favourable high-energy properties due to robustness against quantum corrections.

hep-ph↗

arXiv2022

Black Hole Metamorphosis and Stabilization by Memory Burden

Systems of enhanced memory capacity are subjected to a universal effect of memory burden, which suppresses their decay. In this paper, we study a prototype model to show that memory burden can be overcome by rewriting stored quantum information from one set of degrees of freedom to another one. However, due to a suppressed rate of rewriting, the evolution becomes extremely slow compared to the initial stage. Applied to black holes, this predicts a metamorphosis, including a drastic deviation from Hawking evaporation, at the latest after losing half of the mass. This raises a tantalizing question about the fate of a black hole. As two likely options, it can either become extremely long lived or decay via a new classical instability into gravitational lumps. The first option would open up a new window for small primordial black holes as viable dark matter candidates.

hep-th↗

arXiv2022

$TimeEvolver$: A Program for Time Evolution With Improved Error Bound

We present $TimeEvolver$, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix $i H$, where $H$ is the Hamiltonian, with an initial vector $v$. The fact that $H$ is Hermitian makes it possible to provide an easily computable bound on the accuracy of the Krylov approximation. Apart from effects of numerical roundoff, the resulting a posteriori error bound is rigorous, which represents a crucial novelty as compared to existing software packages such as $Expokit$ (R. Sidje, ACM Trans. Math. Softw. 24 (1) 1998). On a standard notebook, $TimeEvolver$ allows to compute time evolution with adjustable precision in Hilbert spaces of dimension greater than $10^6$. Additionally, we provide routines for deriving the matrix $H$ from a more abstract representation of the Hamiltonian operator.

quant-ph↗

arXiv2021

Scale and Weyl Invariance in Einstein-Cartan Gravity

We show how Einstein-Cartan gravity can accommodate both global scale and local scale (Weyl) invariance. To this end, we construct a wide class of models with nonpropagaing torsion and a nonminimally coupled scalar field. In phenomenological applications the scalar field is associated with the Higgs boson. For global scale invariance, an additional field -- dilaton -- is needed to make the theory phenomenologically viable. In the case of the Weyl symmetry, the dilaton is spurious and the theory reduces to a sub-class of one-field models. In both scenarios of scale invariance, we derive an equivalent metric theory and discuss possible implications for phenomenology.

hep-th↗

arXiv2021

Einstein-Cartan Portal to Dark Matter

It is well-known since the works of Utiyama and Kibble that the gravitational force can be obtained by gauging the Poincaré group, which puts gravity on the same footing as the Standard Model fields. The resulting theory -- Einstein-Cartan gravity -- inevitably contains four-fermion and scalar-fermion interactions that originate from torsion associated with spin degrees of freedom. We show that these interactions lead to a novel mechanism for producing singlet fermions in the Early Universe. These fermions can play the role of dark matter particles. The mechanism is operative in a large range of dark matter particle masses: from a few keV up to $\sim 10^8~$GeV. We discuss potential observational consequences of keV-scale dark matter produced this way, in particular for right-handed neutrinos. We conclude that a determination of the primordial dark matter momentum distribution might be able to shed light on the gravity-induced fermionic interactions.

hep-ph↗

arXiv2021

Higgs inflation in Einstein-Cartan gravity

We study inflation driven by the Higgs field in the Einstein-Cartan formulation of gravity. In this theory, the presence of the Holst and Nieh-Yan terms with the Higgs field non-minimally coupled to them leads to three additional coupling constants. For a broad range of parameters, we find that inflation is both possible and consistent with observations. In most cases, the spectral index is given by $n_s=1-2/N_\star$ (with $N_\star$ the number of e-foldings) whereas the tensor-to-scalar ratio $r$ can vary between about $10^{-10}$ and $1$. Thus, there are scenarios of Higgs inflation in the Einstein-Cartan framework for which the detection of gravitational waves from inflation is possible in the near future. In certain limits, the known models of Higgs inflation in the metric and Palatini formulations of gravity are reproduced. Finally, we discuss the robustness of inflationary dynamics against quantum corrections due to the scalar and fermion fields.

hep-ph↗

arXiv2021

Matter matters in Einstein-Cartan gravity

We study scalar, fermionic and gauge fields coupled nonminimally to gravity in the Einstein-Cartan formulation. We construct a wide class of models with nondynamical torsion whose gravitational spectra comprise only the massless graviton. Eliminating non-propagating degrees of freedom, we derive an equivalent theory in the metric formulation of gravity. It features contact interactions of a certain form between and among the matter and gauge currents. We also discuss briefly the inclusion of curvature-squared terms.

hep-th↗

arXiv2021

Einstein-Cartan gravity, matter, and scale-invariant generalization

We study gravity coupled to scalar and fermion fields in the Einstein-Cartan framework. We discuss the most general form of the action that contains terms of mass dimension not bigger than four, leaving out only contributions quadratic in curvature. By resolving the theory explicitly for torsion, we arrive at an equivalent metric theory containing additional six-dimensional operators. This lays the groundwork for cosmological studies of the theory. We also perform the same analysis for a no-scale scenario in which the Planck mass is eliminated at the cost of adding an extra scalar degree of freedom. Finally, we outline phenomenological implications of the resulting theories, in particular to inflation and dark matter production.

hep-th↗

arXiv2021

Standard Model Meets Gravity: Electroweak Symmetry Breaking and Inflation

We propose a model for combining the Standard Model (SM) with gravity. It relies on a non-minimal coupling of the Higgs field to the Ricci scalar and on the Palatini formulation of gravity. Without introducing any new degrees of freedom in addition to those of the SM and the graviton, this scenario achieves two goals. First, it generates the electroweak symmetry breaking by a non-perturbative gravitational effect. In this way, it does not only address the hierarchy problem but opens up the possibility to calculate the Higgs mass. Second, the model incorporates inflation at energies below the onset of strong-coupling of the theory. Provided that corrections due to new physics above the scale of inflation are not unnaturally large, we can relate inflationary parameters to data from collider experiments.

hep-th↗

arXiv2020

Quantum Effects in Palatini Higgs Inflation

We study quantum effects in Higgs inflation in the Palatini formulation of gravity, in which the metric and connection are treated as independent variables. We exploit the fact that the cutoff, above which perturbation theory breaks down, is higher than the scale of inflation. Unless new physics above the cutoff leads to unnaturally large corrections, we can directly connect low-energy physics and inflation. On the one hand, the lower bound on the top Yukawa coupling due to collider experiments leads to an upper bound on the non-minimal coupling of the Higgs field to gravity: $ξ\lesssim 10^8$. On the other hand, the Higgs potential can only support successful inflation if $ξ\gtrsim 10^6$. This leads to a fairly strict upper bound on the top Yukawa coupling of $0.925$ (defined in the $\overline{\text{MS}}$-scheme at the energy scale $173.2\,\text{GeV}$) and constrains the inflationary prediction for the tensor-to-scalar ratio. Additionally, we compare our findings to metric Higgs inflation.

hep-ph↗

arXiv2019

Finding Critical States of Enhanced Memory Capacity in Attractive Cold Bosons

We discuss a class of quantum theories which exhibit a sharply increased memory storage capacity due to emergent gapless degrees of freedom. Their realization, both theoretical and experimental, is of great interest. On the one hand, such systems are motivated from a quantum information point of view. On the other hand, they can provide a framework for simulating systems with enhanced capacity of pattern storage, such as black holes and neural networks. In this paper, we develop an analytic method that enables us to find critical states with increased storage capabilities in a generic system of cold bosons with weak attractive interactions. The enhancement of memory capacity arises when the occupation number $N$ of certain modes reaches a critical level. Such modes, via negative energy couplings, assist others in becoming effectively gapless. This leads to degenerate microstates labeled by the occupation numbers of the nearly-gapless modes. In the limit of large $N$, they become exactly gapless and their decoherence time diverges. In this way, a system becomes an ideal storer of quantum information. We demonstrate our method on a prototype model of $N$ attractive cold bosons contained in a one-dimensional box with Dirichlet boundary conditions. Although we limit ourselves to a truncated system, we observe a rich structure of quantum phases with a critical point of enhanced memory capacity.

quant-ph↗

arXiv2019

Quantum Breaking Bound on de Sitter and Swampland

Quantum consistency suggests that any de Sitter patch that lasts a number of Hubble times that exceeds its Gibbons-Hawking entropy divided by the number of light particle species suffers an effect of quantum breaking. Inclusion of other interactions makes the quantum break-time shorter. The requirement that this must not happen puts severe constraints on scalar potentials, essentially suppressing the self-reproduction regimes. In particular, it eliminates both local and global minima with positive energy densities and imposes a general upper bound on the number of e-foldings in any given Hubble patch. Consequently, maxima and other tachyonic directions must be curved stronger than the corresponding Hubble parameter. We show that the key relations of the recently-proposed de Sitter swampland conjecture follow from the de Sitter quantum breaking bound. We give a general derivation and also illustrate this on a concrete example of $D$-brane inflation. We can say that string theory as a consistent theory of quantum gravity nullifies a positive vacuum energy in self-defense against quantum breaking.

hep-th↗