Abstract
In this work, we study a stochastic version of the Friedmann acceleration equation. This model has been proposed in the cosmology literature as a possible explanation of the uncertainty found in the experimental quantification of the Hubble parameter. Its noise has been tacitly interpreted in the Stratonovich sense. Herein, we prove that this interpretation leads to a positive probability of finite-time blowup of the solution, that is, of the Hubble parameter. In contrast, if we just modify the noise interpretation to that of Itô, then the solution globally exists almost surely. Moreover, the expected asymptotic behavior is found under this interpretation too.
Highlights
The Hubble parameter is a measure of the rate at which the universe expands
We have studied a stochastic version of the Friedmann acceleration equation
This stochastic differential equation (SDE) was introduced in [13] as a possible theoretical explanation of the uncertainty observed in the experimental quantification of the Hubble parameter
Summary
The Hubble parameter is a measure of the rate at which the universe expands. As such, it is a fundamental quantity in cosmology. Perhaps as a consequence of it, there is currently an uncertainty in its experimental quantification. In reference [13], this uncertainty is theoretically approached by means of a stochastic generalization of the Friedmann acceleration equation; that is, the Hubble parameter
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