Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1911.07341

Reformulating Scalar-Tensor Field Theories as Scalar-Scalar Field Theories Using Lorentzian Cofinsler Spaces

Gregory W. Horndeski
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper I shall show how notions of Finsler geometry can be used to construct a new type of geometry using a scalar field, f, on the cotangent bundle of a differentiable manifold, M. This new geometry will be called Lorentzian Cofinsler geometry. This geometry will enable me to use the second vertical derivatives of f, along with the differential of the scalar field, phi on M, to construct a Lorentzian metric tensor on M, that depends upon phi. f will be chosen so that the resultant metric on M has the form of a FLRW metric, with the t equal constant slices being flat. When the Horndeski Lagrangians are evaluated for this choice of geometry the quartic and quintic Lagrangians are of third order, but reduce to non-degenerate second-order Lagrangians plus a divergence. Upon varying phi in these "scalarized" Horndeski Lagrangians, equations will be obtained which admit self-inflating universe solutions, provided that the coefficient functions appearing in the Horndeski Lagrangians are chosen suitably. This approach is also used to study solutions of the most general conformally invariant scalar-tensor field theory which is flat space compatible (i.e., such that the Lagrangians of the field theory are well-defined when either the space is flat or the scalar field is constant). There too the coefficient functions can be chosen to give self-inflating universes. Arguments will be presented to show that it is possible to construct model universes that begin explosively, and then settle down to a period of much quieter acceleration which either continues forever, or stops and collapses to the models original, pre-expansion, state.

Explore related subjects

gr-qc

Keep this discovery

BibTeXRIS

Gregory W. Horndeski. 2019-11-17. Reformulating Scalar-Tensor Field Theories as Scalar-Scalar Field Theories Using Lorentzian Cofinsler Spaces. https://arxiv.org/abs/1911.07341

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

gr-qc↗
arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗