Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1508.06750

Friedmann-Lemaitre Cosmologies via Roulettes and Other Analytic Methods

Shouxin Chen·Gary W. Gibbons·Yisong Yang
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.

Explore related subjects

gr-qcastro-ph.COhep-thmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shouxin Chen, Gary W. Gibbons, Yisong Yang. 2015-09-09. Friedmann-Lemaitre Cosmologies via Roulettes and Other Analytic Methods. https://doi.org/10.1088/1475-7516%2F2015%2F10%2F056

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

KEEP EXPLORING

Related papers

arXiv2026

Naturally Light Distortion

In the most general formulation of gravity, the metric and connection are independent degrees of freedom, and the connection may include torsion and non-metricity (or distortion, collectively) degrees of freedom, resulting in a huge number of possible dynamical fields. However, most fields are either non-dynamical or extremely heavy and the general relativity is recovered at low energy. We find a unique naturally light vector- or scalar-like distortion field, which can be dynamical and have phenomenological implications. In particular, a light scalar particle that mixes with the Higgs boson naturally appears.

gr-qc↗
arXiv2026

Polarization-Dependent Photon Propagation, Quasinormal Modes, and Gravitational Lensing in Higher-Curvature Effective Theories

We investigate the impact of higher-curvature corrections on photon propagation within an effective field theory framework and their observational consequences in strong gravitational fields. We consider polarization-dependent modifications to photon trajectories in static and spherically symmetric spacetimes, focusing on Schwarzschild and Reissner--Nordström black hole backgrounds. Using the geometrical optics approximation, we derive the effective metrics governing photon propagation and study the resulting polarization-dependent shifts of the photon sphere. We compute the corresponding quasinormal modes in the eikonal limit and analyze their polarization dependence. We further investigate gravitational lensing, focusing on polarization-dependent corrections to the deflection angle in both weak- and strong-field regimes. In the strong-deflection regime, we find that even perturbatively small EFT corrections modify the coefficient of the logarithmically divergent part of the deflection angle, resulting in a potentially observable difference from the uncorrected case. This suggests that strong gravitational lensing may provide a sensitive probe of small higher-curvature corrections. While extracting EFT information directly from QNM frequencies is more subtle, QNMs may provide complementary information to gravitational lensing in future studies. Our results establish a framework for probing higher-curvature effects through polarization-dependent strong-field observables.

gr-qc↗
arXiv2026

Dynamics for Spin-$1/2$ Particles in Einstein-Gauss-Bonnet Gravity II: Non-Relativistic Case

In this work, I investigate the non-relativistic quantum dynamics of spin-1/2 particles in Einstein-Gauss-Bonnet (EGB) gravity and establish a direct connection between higher-curvature corrections, fermionic dynamics, and the phenomenology of compact objects. Starting from the Dirac Hamiltonian in a static, spherically symmetric EGB spacetime, we perform a Fold-Wouthuysen transformation and derive the effective Hamiltonian, including relativistic kinetic, gravitational, spin-orbit, and higher-curvature contributions. Heisenberg equations are then used to obtain the dynamics of velocity, force, and spin, revealing explicit EGB corrections for both translational motion and spin transport. In particular, the spin-orbit sector induces a modified precession frequency whose fractional deviation from general relativity scales as $δ_Ω=-4(ξ/M^{2})(M/ρ)^{3}$, providing a clear dimensionless signature of the Gauss-Bonnet coupling. Through Ehrenfest's theorem, we also establish the correspondence between the dynamics of quantum operators and their semiclassical gravitational limit. As an astrophysical application, we consider the stellar-mass black hole A0620-00 and show that prospective relative sensitivities in spin precession on the order of $10^{-3}$ to $10^{-4}$ can probe Gauss-Bonnet couplings in the range of approximately $10^{6}$ to $10^{8}\,{\rm m}^{2}$, depending on the orbital radius. This result identifies fermionic spin precession as a complementary channel for testing gravity with higher-curvature corrections and provides a quantum-mechanical framework connecting modified gravitational dynamics to precision phenomenology in strong-gravity regimes.

gr-qc↗