Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2406.09540

Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $Λ$CDM model

Ludovic Ducobu·Nicoleta Voicu
View original source ↗Read source document ↗Export metadata ↓

Abstract

The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing for the construction of modified theories of gravity, since one can take lessons from GR for an "educated guess" of the metric field equations; the field equations for the other fields are then fixed by the obtained Lagrangian (up to terms that are completely independent from the metric tensor). In the present paper, we apply variational bootstrapping to determine metric-affine models which are, in a variational sense, closest to the $Λ$CDM model of cosmology. Starting from an "educated guess" that formally resembles the Einstein field equations with a cosmological "constant" (actually, a scalar function built from the metric and the connection) and a dark matter term, the method then allows to find "corrected" metric equations and to "bootstrap" the connection field equations. Lagrangians obtained via this method, though imposing some restricting criteria, still encompass a wide variety of metric-affine models. In particular, they allow for a subclass of quadratic metric-affine theories restricted to linear terms in the curvature tensor.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ludovic Ducobu, Nicoleta Voicu. 2025-06-14. Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $Λ$CDM model. https://doi.org/10.1140/epjc%2Fs10052-025-13790-1

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

KEEP EXPLORING

Related papers

arXiv2026

An upper bound on the minimum orbital period of black holes

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min} \leqslant 6\sqrt{3}πM$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

gr-qc↗
arXiv2026

Dirac Observables for Gowdy Cosmologies regular at the Big Bang

Gowdy cosmologies are exact, spatially inhomogeneous solutions of the vacuum Einstein equations which describe nonlinear gravitational waves coalescing at the Big Bang singularity. With toroidal spatial sections they provenly have the Asymptotic Velocity Domination property, in that close to the Big Bang dynamical spatial gradients fade out and the dynamics is governed by a Carroll-type gravity theory. Here we construct an infinite set of Dirac observables for Gowdy cosmologies, valid off-shell, strongly, and without gauge fixing. These observables stay regular at the Big Bang and can be matched to much simpler Dirac observables of the Carroll-type gravity theory. Conversely, in an adapted foliation there is a systematic anti-Newtonian expansion (in inverse powers of the reduced Newton constant) of the full Dirac observables whose leading terms are the Carroll ones. In particular, this provides an off-shell generalization of the Asymptotic Velocity Domination property.

gr-qc↗
arXiv2026

Global causality constraints in rotating scalar-tensor spacetimes

Modified gravity is often formulated as an effective field theory (EFT), where higher-order corrections parametrize departures from General Relativity. We argue that such corrections should be constrained by the global causal structure of curved spacetime, in addition to the usual flat-space requirements such as positivity and unitarity. We propose that within the domain of validity of the EFT, the onset of closed timelike curves should not happen in a parametrically more accessible region than in the corresponding GR background. We test this diagnostic in the quadratic k-essence sector of scalar-tensor gravity. For stationary and axisymmetric spacetimes, the invariant test for closed axial orbits is the sign of the azimuthal component of the metric \(g_{φφ}\). We supplement this test by requiring a local time function in the space of Killing vectors. We apply these conditions to quadratic k-essence on Kerr--(A)dS backgrounds, with and without scalar charge. The zero-charge branch is exact Kerr--(A)dS, and we treat the charged branch perturbatively in scalar charge and in Hartle--Thorne slow rotation. Expanding for small spin \(χ=a/(GM)\ll1\), frame dragging begins at \(\mathcal O(χ)\), while the quadrupolar backreaction relevant for circular closed timelike curves enters at second order in both rotation and charge. We find that, in the truncation used here, any occurrence of \(g_{φφ}<0\) also lies outside EFT control. A higher-order calculation or a fully nonlinear treatment is therefore needed. Finally, we discuss how quasinormal modes and black-hole echoes could probe such causal structure.

gr-qc↗