Matter Creation via Vacuum Fluctuations in the Early Universe and Observed Ultra-High Energy Cosmic Ray Events

TL;DR

The paper investigates the gravitational production of superheavy X-particles during and after inflation as a mechanism for generating dark matter and potentially explaining Ultra High Energy cosmic rays. It employs Bogolyubov transformations to compute exact particle production in both Friedmann and inflationary backgrounds, across bosons and fermions and for various curvature couplings. The results show that, under plausible reheating conditions, X-particles with $m_X$ around the inflaton scale can naturally yield $\Omega_X h^2 \sim 1$, and that inflationary production can imprint isocurvature fluctuations in the CMB if certain mass relations hold. These X-particles offer a unified link between early-un Universe dynamics, dark matter, and UHECR observations, with concrete observational signatures such as a high-energy spectral cut-off and potential CMB anisotropy imprints.

Abstract

Cosmic rays of the highest energy, above the Greisen-Zatsepin-Kuzmin cut-off of the spectrum, may originate in decays of superheavy long-living X-particles. These particles may be produced in the early Universe from vacuum fluctuations during or after inflation and may constitute a considerable fraction of Cold Dark Matter. We calculate numerically their abundance for a wide range of models. X-particles are considered to be either bosons or fermions. Particles that are several times heavier than inflaton, m_inflaton \approx 10^{13} GeV, and were produced by this mechanism, can account for the critical mass in the Universe naturally. In some cases induced isocurvature density fluctuations can leave an imprint in anisotropy of cosmic microwave background radiation.

Figures (5)

• Figure 1: Coefficient $C_\alpha$, defined in Eq. (9), is shown as a function of $\alpha$ for background cosmology with a power law scale factor $a \propto t^\alpha$.
• Figure 2: Ratio of the energy density in $X$-particles to the total energy density at late times in a model with the massive inflaton, $V(\phi) = m^2\phi^2/2$, as a function of X particle mass, $m_X$. For the inflaton mass we defined $m_{13} \equiv m/10^{13}$ GeV. The dotted line is the low mass asymptotic, Eq. (\ref{['n_fr']}).
• Figure 3: Energy density of created $X$-particles in the massless inflaton model, $V(\phi) = \lambda\phi^4/4$. We defined $\lambda_{13} \equiv \lambda/10^{-13}$.
• Figure 4: Spectrum of created particles, $k^3n(k)$, in a model with massive inflaton is shown for several choices of the mass of scalar X-particle with the minimal coupling (solid lines) and the conformal coupling (dotted line). Masses and momenta, $k$, are given in units of the inflaton mass.
• Figure 5: Ratio of the energy density in $X$-particles to the total energy density at late times in a model with the massive inflaton, $V(\phi) = m^2\phi^2/2$, as a function of $\xi$.