Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/9703052

Time evolution of the perturbations for a complex scalar field in Friedmann-Lemaitre universe

Philippe Jetzer·David Scialom
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the time evolution of small classical perturbations in a gauge invariant way for a complex scalar field in the early zero curvature Friedmann-Lema\^ıtre universe. We, thus, generalize the analysis which has been done so far for a real scalar field. We give also a derivation of the Jeans wavenumber in the Newtonian regime starting from the general relativistic equations, avoiding the so-called Jeans swindle. During the inflationary phase, whose length depends on the value of the bosonic charge, the behavior of the perturbations turns out to be the same as for a real scalar field. In the oscillatory phase the time evolution of the perturbations can be determined analytically as long as the bosonic charge of the corresponding background solution is sufficiently large. This is not possible for the real scalar field, since the corresponding bosonic charge vanishes.

Explore related subjects

gr-qcastro-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Philippe Jetzer, David Scialom. 1997-03-20. Time evolution of the perturbations for a complex scalar field in Friedmann-Lemaitre universe. https://doi.org/10.1103/physrevd.55.7440

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

KEEP EXPLORING

Related papers

arXiv2026

Massive quantum divergence on the Cauchy horizon of a black hole

We investigate a quantum {\it massive} scalar field in the interior of a charged and spherically-symmetric (Reissner-Nordström) black hole. We examine the behaviour for varying values of the black hole charge, field mass and coupling constant when the field is in two quantum states: Hartle-Hawking (representing a black hole in thermal equilibrium) and Unruh (representing a black hole evaporating via the emission of Hawking radiation). We show that the vacuum polarization (in both states) generically {\it diverges} on the Cauchy horizon, in stark contrast to what happens for massless fields; also, the angular components of the quantum stress-energy tensor generically {\it diverge} on the Cauchy horizon and, in at least one of the two states, they do so more strongly than for massless fields. Furthermore, we calculate the energy fluxes in Eddington-Finkelstein coordinates $\{u,v\}$. We show that these fluxes in both states on the Cauchy horizon do not generically vanish. This implies, in particular, that in regular, Kruskal coordinates $\{U,V\}$ the ingoing flux diverges like $V^{-2}$ on the Cauchy horizon (where $V=0$). This divergence suggests that its backreaction via the semiclassical Einstein equations would yield a strong singularity, as opposed to its weaker, classical counterpart. Interestingly, there are exceptions, in which the energy fluxes in Eddington-Finkelstein coordinates vanish: (i) in the extremal limit (where the black hole is maximally charged); (ii) certain fine-tuned regions of parameter space, where the fluxes change sign.

gr-qc↗
arXiv2026

Scattering of massless scalar waves by higher-dimensional regular black holes in general relativity coupled to nonlinear electrodynamics

We study the scattering of planar massless scalar waves by the family of higher-dimensional regular black holes in general relativity coupled to nonlinear electrodynamics, which unifies the Bardeen and Hayward models in any dimension. The scalar field is a neutral test field that propagates in the bulk, and in the geometric-optics limit, its rays are the null geodesics of the spacetime, so that the unstable circular null geodesics of the background geometry control the scattering. We combine the classical scattering of null geodesics, the glory approximation, which we generalize to $D$ dimensions, and the partial-wave analysis in $D=5,6,7$. We show that at a fixed frequency, the wave cross section diverges in the forward direction as $θ^{-4}$ in any dimension, with a coefficient fixed by the mass, while the steeper classical law $θ^{-(D-2)^{2}/(D-3)}$ appears only at larger angles and higher frequencies. The charge parameter decreases the critical and the glory impact parameters and widens the glory fringes, and in higher dimensions, the glory pattern has fewer and wider fringes and a weaker backward intensity. For the matched configurations studied here, backward intensity and low-frequency absorption provide the clearest differences, while the intermediate-to-high-frequency spectra are close.

gr-qc↗
arXiv2026

Self-interacting $p$-forms and the shear-free anisotropic cosmological model

The cosmological principle may require more than observations demand: what is needed is isotropic expansion without vorticity. Extended Friedmann-Lemaitre-Robertson-Walker (eFLRW) cosmologies realise this with a non-vanishing anisotropic spatial curvature that is balanced by an anisotropic stress while the shear vanishes. Thorsrud and others investigated such scenarios for free differential $p$-forms. Here we extend the analysis to non-Abelian $p$-forms ($p=0,\dots,4$) with self interactions. The balance requires the anisotropic stress to decay as $a^{-2}$, $a$ being the cosmological scale factor, which we combine with the gauge-field continuity equation. The general results indicate that, in the presence of a potential, fine-tuning of the same is needed in order to balance the curvature. Notably, this is not the case for a $3$-form field $\underline{H}^a$ with a potential term $V(\underline{H}^2)=A+B\,\underline{H}^2$, where $A$ and $B$ are constants: in Bianchi class A, an uncharged 3-form balances the curvature with this potential without any tuning, and a charged one does so for a suitably chosen connection. This is the only candidate we have found where the potential does not require tuning. It is also an interesting candidate as it can be interpreted as a cosmological constant in combination with a dark-matter sector mimicking curvature.

gr-qc↗