An Upper Limit on the Initial Temperature of the Radiation-Dominated Universe. (arXiv:2004.02895v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Hu_B/0/1/0/all/0/1">Betty X. Hu</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Loeb_A/0/1/0/all/0/1">Abraham Loeb</a>

Gravitational waves (GWs) are produced by colliding particles through the
gravitational analogue of electromagnetic bremsstrahlung. We calculate the
contribution of free-free emission in the radiation-dominated Universe to the
stochastic GW background. We find that the energy density of the resulting GW
radiation is heavily dependent on the number of elementary particles,
$N_{mathrm{tot}}$, and the maximum initial temperature, $T_{mathrm{max}}$. We
rule out $N_{mathrm{tot}}gtrsim N_{mathrm{SM}}$ for $T_{mathrm{max}}sim
T_{mathrm{Planck}}approx10^{19}$ GeV and
$N_{mathrm{tot}}gtrsim10^{13}times N_{mathrm{SM}}$ for
$T_{mathrm{max}}sim10^{16}$ GeV, where $N_{mathrm{SM}}$ is the number of
particles in the Standard Model. In the case of inflation, existing
cosmological data constrain $T_{mathrm{max}}lesssim10^{16}$ GeV. However,
alternative models to inflation such as bouncing cosmologies allow for
$T_{mathrm{max}}$ near $T_{mathrm{Planck}}$. At the energy scales we are
considering, the extra number of particles arise naturally in models of extra
dimensions.

Gravitational waves (GWs) are produced by colliding particles through the
gravitational analogue of electromagnetic bremsstrahlung. We calculate the
contribution of free-free emission in the radiation-dominated Universe to the
stochastic GW background. We find that the energy density of the resulting GW
radiation is heavily dependent on the number of elementary particles,
$N_{mathrm{tot}}$, and the maximum initial temperature, $T_{mathrm{max}}$. We
rule out $N_{mathrm{tot}}gtrsim N_{mathrm{SM}}$ for $T_{mathrm{max}}sim
T_{mathrm{Planck}}approx10^{19}$ GeV and
$N_{mathrm{tot}}gtrsim10^{13}times N_{mathrm{SM}}$ for
$T_{mathrm{max}}sim10^{16}$ GeV, where $N_{mathrm{SM}}$ is the number of
particles in the Standard Model. In the case of inflation, existing
cosmological data constrain $T_{mathrm{max}}lesssim10^{16}$ GeV. However,
alternative models to inflation such as bouncing cosmologies allow for
$T_{mathrm{max}}$ near $T_{mathrm{Planck}}$. At the energy scales we are
considering, the extra number of particles arise naturally in models of extra
dimensions.

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