Uniqueness of Self-Similar Asymptotically Friedmann-Robertson-Walker Spacetime in Brans-Dicke theory
Hideki Maeda, Jun-ichirou Koga, Kei-ichi Maeda
TL;DR
This paper proves that in Brans-Dicke theory, self-similar solutions asymptotic to flat FRW spacetime do not exist with positive energy density, implying primordial black holes cannot grow at the same rate as the universe.
Contribution
It demonstrates the uniqueness of self-similar solutions in Brans-Dicke theory, showing non-existence of certain asymptotic solutions with positive energy density.
Findings
No non-trivial solutions approach flat FRW spacetime with positive density.
Primordial black holes cannot grow at the same rate as the cosmological horizon in this theory.
Self-similar solutions are unique and limited in this context.
Abstract
We investigate spherically symmetric self-similar solutions in Brans-Dicke theory. Assuming a perfect fluid with the equation of state , we show that there are no non-trivial solutions which approach asymptotically to the flat Friedmann-Robertson-Walker spacetime if the energy density is positive. This result suggests that primordial black holes in Brans-Dicke theory cannot grow at the same rate as the size of the cosmological particle horizon.
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