arXiv subjects

Christian F. Steinwachs

Publications and source records attributed to Christian F. Steinwachs.

At least 19 recordsLinked to original sources

arXiv2021

Scalaron-Higgs inflation reloaded: Higgs-dependent scalaron mass and primordial black hole dark matter

We propose an extension of the scalaron-Higgs model by a non-minimal coupling of the Standard Model Higgs boson to the quadratic Ricci scalar resulting in a Higgs-dependent scalaron mass. The model predicts a successful stage of effective single-field Starobinsky inflation. It features a multi-field amplification mechanism leading to a peak in the inflationary power spectrum at small wavelengths which enhances the production of primordial black holes. The extended scalaron-Higgs model unifies inflationary cosmology with elementary particle physics and explains the origin of cold dark matter in terms of primordial black holes without assuming any new particles.

hep-th↗

arXiv2021

Primordial black hole dark matter in dilaton-extended two-field Starobinsky inflation

We investigate the production of primordial black holes and their contribution to the presently observed dark matter in a dilaton two-field extension of Starobinsky's quadratic $f(R)$ model of inflation. The model features a multi-field amplification mechanism which leads to the generation of a sharp peak in the inflationary power spectrum at small wavelengths responsible for the production of primordial black holes. This mechanism is significantly different from single-field models and requires a stochastic treatment during an intermediate phase of the inflationary dynamics. We find that the model leads to a successful phase of effective single-field Starobinsky inflation for wavelengths probed by the cosmic microwave background radiation and explains the observed cold dark matter content in the Universe by the formation of primordial black holes.

hep-th↗

arXiv2021

Non-perturbative quantum Galileon in the exact renormalization group

We investigate the non-perturbative renormalization group flow of the scalar Galileon model in flat space. We discuss different expansion schemes of the Galileon truncation, including a heat-kernel based derivative expansion, a vertex expansion in momentum space and a curvature expansion in terms of a covariant geometric formulation. We find that the Galileon symmetry prevents a quantum induced renormalization group running of the Galileon couplings. Consequently, the Galileon truncation only features a trivial Gaussian fixed point.

hep-th↗

arXiv2020

Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity

For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory, while renormalizability guarantees its completeness. Relativistic invariance, in turn, is a symmetry which derives from the structure of spacetime. So far, the perturbative attempt to formulate a fundamental local quantum field theory of gravity based on the metric field seems to be in conflict with at least one of these properties. In quantum Hořava gravity, a quantum Lifshitz field theory of gravity characterized by an anisotropic scaling between space and time, unitarity and renormalizability can be retained while Lorentz invariance is sacrificed at high energies and must emerge only as approximate symmetry at low energies. I review various approaches to perturbative quantum gravity with a particular focus on recent progress in the quantization of Hořava gravity, supporting its theoretical status as a unitary, renormalizable and ultraviolet-complete quantum theory of gravity.

hep-th↗

arXiv2020

Naked singularities in quadratic f(R) gravity

We find new static, spherically symmetric, and asymptotically flat vacuum solutions without horizon in Starobinsky's quadratic f(R) gravity. We systematically classify these solutions by an asymptotic analysis around the origin and find seven different integer Frobenius families. We numerically solve the exact equations of motion by a double-shooting method and specify boundary conditions by matching the numerical solution to the analytic solution of the linearised field equations in the weak field regime. We find that all integer Frobenius families can be connected to asymptotically flat solutions and trace out lines in the parameter space, allowing to ultimately relate all free parameters to the total mass at infinity.

gr-qc↗

arXiv2020

One-loop renormalization in Galileon effective field theory

We investigate the renormalization structure of scalar Galileons in flat spacetime. We explicitly calculate the ultraviolet divergent one-loop contributions to the 2-point, 3-point, 4-point, and 5-point functions. We discuss the structure of the counterterms and their hierarchy within an effective field theory expansion. We comment on different resummation schemes, including a geometric resummation for which our results could be generalized to arbitrary n-point functions.

hep-th↗

arXiv2020

Geometrized quantum Galileons

We investigate the renormalization structure of the scalar Galileon model in flat spacetime by calculating the one-loop divergences in a closed geometric form. The geometric formulation is based on the definition of an effective Galileon metric and allows to apply known heat-kernel techniques. The result for the one-loop divergences is compactly expressed in terms of curvature invariants of the effective Galileon metric and corresponds to a resummation of the divergent one-loop contributions of all n-point functions. The divergent part of the one-loop effective action therefore serves as generating functional for arbitrary n-point counterterms. We discuss our result within the Galileon effective field theory and give a brief outlook on extensions to more general Galileon models in curved spacetime.

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arXiv2019

Scalaron-Higgs inflation

In scalaron-Higgs inflation the Standard Model Higgs boson is non-minimally coupled to gravity and the Einstein-Hilbert action is supplemented by the quadratic scalar curvature invariant. For the quartic Higgs self-coupling $λ$ fixed at the electroweak scale, we find that the resulting inflationary two-field model effectively reduces to a single field model with the same predictions as in Higgs inflation or Starobinsky inflation, including the limit of a vanishing non-minimal coupling. For the same model, but with the scalar field a priori not identified with the Standard Model Higgs boson, we study the inflationary consequences of an extremely small $λ$. Depending on the initial conditions for the inflationary background trajectories, we find that the two-field dynamics either again reduces to an effective single-field model with a larger tensor-to-scalar ratio than predicted in Higgs inflation and Starobinsky inflation, or involves the full two-field dynamics and leads to oscillatory features in the inflationary power spectrum. Finally, we investigate under which conditions the inflationary scenario with extremely small $λ$ can be realized dynamically by the Standard Model renormalization group flow and discuss how the scalaron-Higgs model can provide a natural way to stabilize the electroweak vacuum.

hep-th↗

arXiv2019

Higgs field in cosmology

The accelerated expansion of the early universe is an integral part of modern cosmology and dynamically realized by the mechanism of inflation. The simplest theoretical description of the inflationary paradigm is based on the assumption of an additional propagating scalar degree of freedom which drives inflation - the inflaton. In most models of inflation the fundamental nature of the inflaton remains unexplained. In the model of Higgs inflation, the inflaton is identified with the Standard Model Higgs boson and connects cosmology with elementary particle physics. A characteristic feature of this model is a non-minimal coupling of the Higgs boson to gravity. I review and discuss several phenomenological and fundamental aspects of this model, including the impact of quantum corrections and the renormalization group, the derivation of initial conditions for Higgs inflation in a quantum cosmological framework and the classical and quantum equivalence of different field parametrizations.

hep-ph↗

arXiv2019

Combinatorial aspects in the one-loop renormalization of higher derivative theories

An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this way, a generic one-loop diagram is reduced to a sum of vacuum diagrams. The logarithmically divergent part can be extracted by power counting arguments. In case of higher derivative theories, the standard implementation of this procedure on a computer algebra system can become quickly inefficient due to a high proliferation of terms coming from the intermediate replacement of high-rank tensor-integrals with symmetrized product of metric tensors. In this note we present a simple combinatorial solution to this problem which makes the implementation much more efficient. This method is especially relevant in the renormalization of higher derivative theories, but might as well be integrated as a standard routine in existing computer algebra programs designed to automatize Feynman diagrammatic calculations.

hep-ph↗

arXiv2019

Quantum gravitational corrections to the inflationary power spectra in scalar-tensor theories

We derive the first quantum gravitational corrections to the inflationary power spectra for a general single-field scalar-tensor theory which includes a non-minimal coupling to gravity, a non-standard scalar kinetic term and an arbitrary potential of the scalar field. We obtain these corrections from a semiclassical expansion of the Wheeler-DeWitt equation, which, in turn, governs the full quantum dynamics in the canonical approach to quantum gravity. We discuss the magnitude and relevance of these corrections, as well as their characteristic signature in the inflationary spectral observables. We compare our results to similar calculations performed for a minimally coupled scalar field with a canonical kinetic term and discuss the impact of the non-minimal coupling on the quantum gravitational corrections.

gr-qc↗

arXiv2018

Quantum effective action for degenerate vector field theories

We calculate the divergent part of the one-loop effective action in curved spacetime for a particular class of second-order vector field operators with a degenerate principal part. The principal symbol of these operators has the structure of a longitudinal projector. In this case, standard heat-kernel techniques are not directly applicable. We present a method which reduces the problem to a nondegenerate scalar operator for which standard heat-kernel techniques are available. Interestingly, this method leads to the identification of an effective metric structure in the longitudinal sector. The one-loop divergences are compactly expressed in terms of invariants constructed from this metric.

hep-th↗

arXiv2018

Quantum gravitational corrections from the Wheeler-DeWitt equation for scalar-tensor theories

We perform the canonical quantization of a general scalar-tensor theory and derive the first quantum gravitational corrections following from a semi-classical expansion of the Wheeler-DeWitt equation. The non-minimal coupling of the scalar field to gravity induces a derivative coupling between the scalar field and the gravitational degrees of freedom, which prevents a direct application of the expansion scheme. We address this technical difficulty by transforming the theory from the Jordan frame to the Einstein frame. We find that a large non-minimal coupling can have strong effects on the quantum gravitational correction terms. We briefly discuss these effects in the context of the specific model of Higgs inflation.

gr-qc↗

arXiv2018

Renormalization of generalized vector field models in curved spacetime

We calculate the one-loop divergences for different vector field models in curved spacetime. We introduce a classification scheme based on their degeneracy structure, which encompasses the well-known models of the non-degenerate vector field, the Abelian gauge field and the Proca field. The renormalization of the generalized Proca model, which has important applications in cosmology, is more complicated. By extending standard heat-kernel techniques, we derive a closed form expression for the one-loop divergences of the generalized Proca model.

hep-th↗

arXiv2018

Hořava gravity is asymptotically free (in 2+1 dimensions)

We compute the $β$-functions of marginal couplings in projectable Hořava gravity in $2+1$ spacetime dimensions. We show that the renormalization group flow has an asymptotically-free fixed point in the ultraviolet (UV), establishing the theory as a UV-complete model with dynamical gravitational degrees of freedom. Therefore, this theory may serve as a toy-model to study fundamental aspects of quantum gravity. Our results represent a step forward towards understanding the UV properties of realistic versions of Hořava gravity.

hep-th↗

arXiv2018

One-loop divergences for $f(R)$ gravity

We calculate the divergent part of the one-loop effective action for $f(R)$ gravity on an arbitrary background manifold. Our result generalizes previous results for quantum corrections in $f(R)$ gravity, which have been limited to spaces of constant curvature. We discuss a new technical aspect connected to operators with degenerate principal symbol. Our result has important applications in cosmology and allows to study the quantum equivalence between $f(R)$ theories and scalar-tensor theories.

gr-qc↗

arXiv2018

Renormalization of gauge theories in the background-field approach

Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.

hep-th↗

arXiv2018

Quantum equivalence of $f(R)$ gravity and scalar-tensor theories

We investigate whether the classical equivalence of $f(R)$ gravity and its formulation as scalar-tensor theory still holds at the quantum level. We explicitly compare the corresponding one-loop divergences and find that the equivalence is broken by off-shell quantum corrections, but recovered on-shell.

gr-qc↗