Statistics of Inflating Regions in Eternal Inflation. (arXiv:1904.04262v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Jain_M/0/1/0/all/0/1">Mudit Jain</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hertzberg_M/0/1/0/all/0/1">Mark P. Hertzberg</a>
We compute the distribution of sizes of inflating regions (surrounded by non
inflating ones) in an eternally inflating Universe. As a first illustrative
problem, we study a simple scenario of an eternally inflating Universe in the
presence of a massless scalar field $varphi$ whose field values lie within
some finite domain $varphiin(-varphi_{cr},varphi_{cr})$, with
$pmvarphi_{cr}$ marking the onset of thermalization/crunching. We compute
many important quantities, including the fractal dimension, distribution of
field values among inflating regions, and the number of inflating and
thermalized Hubble regions. With the aid of simulations in 1 spatial dimension,
we show this eternally inflating Universe reaches a steady state in which
average sizes of inflating regions grows only as a power law in the field’s
crunch value $sim varphi_{cr}^2$ (extension to higher dimensions is
$simvarphi^{2/D}$), contrary to a naive expectation of an exponential
dependence. Furthermore, the distribution in sizes is initally a power law fall
off, followed by an exponential fall off. We leave other interesting cases of
more realistic potentials and time varying Hubble parameter for future work,
with a possible application to the SM Higgs in the early Universe.
We compute the distribution of sizes of inflating regions (surrounded by non
inflating ones) in an eternally inflating Universe. As a first illustrative
problem, we study a simple scenario of an eternally inflating Universe in the
presence of a massless scalar field $varphi$ whose field values lie within
some finite domain $varphiin(-varphi_{cr},varphi_{cr})$, with
$pmvarphi_{cr}$ marking the onset of thermalization/crunching. We compute
many important quantities, including the fractal dimension, distribution of
field values among inflating regions, and the number of inflating and
thermalized Hubble regions. With the aid of simulations in 1 spatial dimension,
we show this eternally inflating Universe reaches a steady state in which
average sizes of inflating regions grows only as a power law in the field’s
crunch value $sim varphi_{cr}^2$ (extension to higher dimensions is
$simvarphi^{2/D}$), contrary to a naive expectation of an exponential
dependence. Furthermore, the distribution in sizes is initally a power law fall
off, followed by an exponential fall off. We leave other interesting cases of
more realistic potentials and time varying Hubble parameter for future work,
with a possible application to the SM Higgs in the early Universe.
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