Asymptotically Friedmann self-similar scalar field solutions with potential

Abstract

We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are two distinct one-parameter families of asymptotic solutions,one is asymptotic to the proper Friedmann universe, while the other is asymptotic to the quasi-Friedmann universe, i.e., the Friedmann universe with anomalous solid angle. The asymptotically proper Friedmann solution is possible only if the universe is accelerated or the potential is negative. If the potential is positive, the density perturbation in the asymptotically proper Friedmann solution rapidly falls off at spatial infinity, while the mass perturbation is compensated. In the asymptotically quasi-Friedmann solution, the density perturbation falls off only in proportion to the inverse square of the areal radius and the relative mass perturbation approaches a nonzero constant at spatial infinity. The present result shows that a necessary condition holds in order that a self-gravitating body grows self-similarly due to the constant accretion of quintessence in an accelerating universe.

accepted for publication in Physical Review D, minor correction, typos corrected

References in corpus (16)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Cosmological Imprint of an Energy Component with General Equation of State
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• Gravitational Energy in Spherical Symmetry
• Black hole mass decreasing due to phantom energy accretion
• Could supermassive black holes be quintessential primordial black holes?
• Self-Similarity in General Relativity \endtitle
• The Accretion of Dark Energy onto a Black Hole
• Convergence to a self-similar solution in general relativistic gravitational collapse
• Self-similar cosmological solutions with dark energy. II: black holes, naked singularities and wormholes
• The Similarity Hypothesis in General Relativity
• Non-existence of self-similar solutions containing a black hole in a universe with a stiff fluid or scalar field or quintessence
• Self-similar cosmological solutions with dark energy. I: formulation and asymptotic analysis
• Self-similar spherically symmetric cosmological models with a perfect fluid and a scalar field
• Uniqueness of Self-Similar Asymptotically Friedmann-Robertson-Walker Spacetime in Brans-Dicke theory
• Kink instability and stabilization of the Friedmann universe with scalar fields

Cited by in corpus (2)

• Can a primordial black hole or wormhole grow as fast as the universe?
• Catastrophic fate of Schwarzschild black holes in a thermal bath