The effects of non Bunch-Davies initial conditions on gravitationally produced relics

Abstract

Typical gravitational production of relics from amplification of inflationary perturbations assumes Bunch-Davies initial conditions, i.e. a vacuum with initially no particles. In this paper we investigate the impact of non Bunch-Davies initial conditions to the final abundance of relics, with particular attention to the parameter space where the total dark matter abundance is reproduced. We present a general framework for any initial condition, through which we show their non-trivial effect on both spectrum and late-time abundance. We argue that for particles whose source of conformal symmetry breaking comes only from a mass term (spin-1/2 fermions and conformally coupled scalars), the choice of initial conditions has little impact on the mass range relevant to dark matter. For other particles, e.g. the longitudinal mode of spin-1, we see a large deviation from the standard computation. We exemplify and quantify our results with an initial thermal state and a two-stage inflation scenario, highlighting that the total dark matter can be obtained for a wide range of masses.

Figures (7)

• Figure 1: Sketch showing the behavior of the transfer function of a vector field, eq. \ref{['eq:transfer_function_vector_text']} for instantaneous reheating. We show the comoving horizon $1/aH$ (black) and the comoving Compton wavelenght $1/am$ (purple). The scale factor $a_e$ denotes the end of inflation and $a_\star$ the moment in which $m=H$ and the evolution becomes adiabatic. We take $H_\text{inf}$ to be the Hubble parameter during inflation.
• Figure 2: Comoving momentum spectrum for a spin-1 relic with a mass $m=10^{-25}$ GeV and reheating temperature $T_\text{RH}=10^{-1}$ GeV. Dashed black denotes results obtained using Bunch--Davies initial conditions, while colors assume different values for the initial temperature $T$ according to the color code.
• Figure 3: Abundance levels for spin-1 DM in the scenario with an initial thermal distribution. We show in the $m-T$ parameter space the curves representing the total DM abundance today. Colors denote different reheating temperatures, namely $T_\text{RH} = 10^{12}$ GeV (solid blue), $T_\text{RH} = 10^{8}$ GeV (dotted orange), $T_\text{RH} = 10^{2}$ GeV (dashed green) and $T_\text{RH} = 10^{-1}$ GeV (dashed-dotted purple). We fix $H_\text{inf}=10^{13}$ GeV. The gray regions are excluded by super-radiance limits, while the yellow bands by eq. \ref{['eq:thermal_bound_density']}, see text for details. The black cross denotes the mass $m\simeq 2\times 10^{-13}$ GeV for which Bunch--Davies initial conditions can produce all the DM.
• Figure 4: Comoving horizon for a two-stage inflation with an intermediate radiation domination phase (solid blue). In orange we show some of the relevant comoving momentum scales and in purple we show an example of comoving Compton wavelength $1/am$. See text for details.
• Figure 5: Comoving momentum spectra for a spin-1 relic with a low mass $m=10^{-20}$ GeV ($m<m_\text{crit}$, left panel) and a high mass $m=10^{3}$ GeV ($m>m_\text{crit}$, right panel). We have fixed for both plots $T_\text{RH}=T_\text{RH}^\text{max}$, i.e. instantaneous reheating. The dashed black lines denotes results obtained with $H_e=H_I$ and $N_\text{dR}=0$. This corresponds to the usual case provided we identify $H_\text{inf} = H_e$. Colors assume an intermediate radiation phase of duration $N_\text{dR}$. The values of $k_\text{dR}$, $k_{\text{d} \Lambda}$ and $k_\star$ are denoted by the circles, diamonds and stars, respectively.