Gauge-Invariant Perturbations of Varying-Alpha Cosmologies

Abstract

Using a gauge-invariant formalism we derive and solve the perturbed cosmological equations for the BSBM theory of varying fine structure 'constant'. We calculate the time evolution of inhomogeneous perturbations of the fine structure constant, $\frac{\delta \alpha }{\alpha }$ on small and large scales with respect to the Hubble radius. In a radiation-dominated universe small inhomogeneities in $\alpha$ will decrease on large scales but on scales smaller than the Hubble radius they will undergo stable oscillations. In a dust-dominated universe small inhomogeneous perturbations in $\alpha$ will become constant on large scales and on small scales they will increase as $t^{2/3}$, and $\frac{\delta \alpha }{\alpha }$ will track . If the expansion accelerates, as in the case of a $\Lambda$ or quintessence-dominated phase, inhomogeneities in $\alpha$ will decrease on both large and small scales. The amplitude of perturbations in $\alpha$ will be much smaller than that of matter or radiation perturbations. We also present a numerical study of the non-linear evolution of spherical inhomogeneities in radiation and dust universes by means of a comparison between the evolution of flat and closed Friedmann models with time-varying $\alpha .$Various limitations of these simple models are also discussed.

28 pages, 4 figures, 1 table added, some results changed, references added, typos were corrected

References in corpus (1)

• Qualitative Analysis of Universes with Varying Alpha

Cited by in corpus (41)

• Tale of stable interacting dark energy, observational signatures, and the $H_0$ tension
• Varying Alpha in a More Realistic Universe
• Local and Global Variations of The Fine Structure Constant
• Cluster number counts dependence on dark energy inhomogeneities and coupling to dark matter
• Novel approach towards the large-scale stable Interacting Dark-Energy models and their Astronomical Bounds
• Listening to the sound of dark sector interactions with gravitational wave standard sirens
• Models of quintessence coupled to the electromagnetic field and the cosmological evolution of alpha
• Time Variation of the Fine Structure Constant Driven by Quintessence
• K-Chameleon and the Coincidence Problem
• Effects of Anisotropic Stress in Interacting Dark Matter - Dark Energy Scenarios
• Cosmological constraints on parametrized interacting dark energy
• Mapping the Dark Energy with Varying Alpha
• A Generalized Theory of Varying Alpha
• Microscopic and Macroscopic Behaviors of Palatini Modified Gravity Theories
• General Dynamics of Varying-Alpha Universes
• Varying Constants
• Screening mechanisms in hybrid metric-Palatini gravity
• Multidimensional cosmological models: cosmological and astrophysical implications and constraints
• CMB constraints on the fine structure constant
• Linearized Bekenstein Varying Alpha Models
• Varying Couplings in Electroweak Theory
• Varying-Alpha Cosmologies with Potentials
• Domain wall solution in $F(R)$ gravity and variation of the fine structure constant
• Composition-dependent long range forces from varying m_p/m_e
• Measuring the fine structure constant on a white dwarf surface; a detailed analysis of Fe V absorption in G191-B2B
• Spatial variations of the fine-structure constant in symmetron models
• Probing spatial variation of the fine-structure constant using the CMB
• Screenings in Modified Gravity: a perturbative approach
• Varying alpha, thresholds and extra dimensions
• Varying alpha from N-body Simulations
• Cosmological simulations with hydrodynamics of screened scalar-tensor gravity with non-universal coupling
• Evolution of the fine-structure constant in the non-linear regime
• Probing the time variation of fine structure constant using galaxy clusters and quintessence model
• Varying-Alpha and K-Essence
• Corrections to the Fine Structure Constant in D-dimensional Space from the Generalized Uncertainty Principle
• Cosmic strings in Bekenstein-type models
• Redshifting of cosmological black bodies in BSBM varying-alpha theories
• Red Giant evolution in Modified Gravity
• Non-linear Phenomenology of Disformally Coupled Quintessence
• Cosmic acceleration in models with density dependent moduli
• Spacetime variation of $\alpha$ and the CMB power spectra after the recombination