The Gravitational Wave Spectrum from Cosmological B-L Breaking

TL;DR

This work analyzes a GUT-scale cosmological scenario in which spontaneous $B$-$L$ breaking drives hybrid inflation, tachyonic preheating, and cosmic-string formation, producing a rich gravitational-wave spectrum. The authors compute the full spectrum from inflation, tachyonic preheating, and both Abelian-Higgs and Nambu-Goto cosmic strings, incorporating the universe’s changing equation of state via transfer functions and scale-factor evolution. They show that cosmic strings generally dominate the GW signal, with AH strings yielding a plateau several orders of magnitude larger than inflation, while NG strings predict even larger amplitudes and greater uncertainties. A key prediction is a kink in the spectrum at a characteristic wavenumber $k_{ m RH}$ tied to the reheating temperature, potentially allowing future detectors (eLISA, LIGO, ET, BBO/DECIGO) to probe reheating and infer heavy-neutrino and Higgs-sector parameters, despite substantial model uncertainties in the cosmic-string sector.

Abstract

Cosmological B-L breaking is a natural and testable mechanism to generate the initial conditions of the hot early universe. If B-L is broken at the grand unification scale, the false vacuum phase drives hybrid inflation, ending in tachyonic preheating. The decays of heavy B-L Higgs bosons and heavy neutrinos generate entropy, baryon asymmetry and dark matter and also control the reheating temperature. The different phases in the transition from inflation to the radiation dominated phase produce a characteristic spectrum of gravitational waves. We calculate the complete gravitational wave spectrum due to inflation, preheating and cosmic strings, which turns out to have several features. The production of gravitational waves from cosmic strings has large uncertainties, with lower and upper bounds provided by Abelian Higgs strings and Nambu-Goto strings, implying Ω_GW h^2 ~ 10^{-13} - 10^{-8}, much larger than the spectral amplitude predicted by inflation. Forthcoming gravitational wave detectors such as eLISA, advanced LIGO, ET, and BBO/DECIGO will reach the sensitivity needed to test the predictions from cosmological B-L breaking.

Figures (8)

• Figure 1: Upper panel: Comoving number densities of Higgs bosons ($S$), thermally and nonthermally produced heavy (s)neutrinos ($N_1^{\mathrm{th}}$, $N_1^{\mathrm{nt}}$), radiation ($r$), lepton asymmetry ($B$$-$$L$) and gravitinos ($\widetilde{G}$). Lower panel: Emergent plateau of approximately constant temperature. Input parameters: Heavy neutrino mass $M_1 = 10^{11}~\mathrm{GeV}$, effective neutrino mass $\widetilde{m}_1 = 0.04~\mathrm{eV}$. The $B$$-$$L$ scale is fixed by requiring consistency with hybrid inflation, $v_{B-L} = 5\times 10^{15}~\mathrm{GeV}$. As in Ref. Buchmuller:2012wn.
• Figure 2: GW spectrum today due to inflation (gray), preheating (red) and AH cosmic strings (black) for $M_1 = 10^{11}$ GeV, $v_{B-L} = 5 \times 10^{15}$ GeV and $m_S = 3 \times 10^{13}$ GeV. $f_0$, $f_\text{eq}$, $f_\text{RH}$ and $f_\text{PH}$ denote the frequencies associated with a horizon sized wave today, at matter-radiation equality, at reheating and at preheating, respectively. $f_{\text{PH}}^{(s)}$ and $f_{\text{PH}}^{(v)}$ denote the positions of the peaks in the GW spectrum associated with the scalar and the vector boson present at preheating. The dashed segments in the spectrum indicate the uncertainties due to the breakdown of the analytical approximations. The GW spectrum from inflation is based on the analytical approximations as well as the numerical values for the transfer function, cf. Eqs. \ref{['eq:OmegaGWinfresult']}, \ref{['eq:T1T1result']}, and \ref{['transferfktT2']}; the 'steps' in the plateau are determined by the changes in the number of DOFs at the QCD scale and at a SUSY scale of 1 TeV. The GW spectrum from preheating is given by Eqs. \ref{['eq_pred_preheating']} and \ref{['eq_preheating_fit']}, with $c_\text{PH} = 0.05$ and $g^2 = 1/2$. The GW spectrum from AH cosmic strings is determined by Eqs. \ref{['eq_masterformula']} and \ref{['eq_omega_plat']}, with $F^r = F^r_\text{FHU}$.
• Figure 3: Contributions from different epochs to the GW spectrum for NG strings for $\alpha = 10^{-6}$; $G\mu = 2.0\times 10^{-7}$ as obtained e.g. by the parameter choice in Eq. \ref{['eq:exampleparameterpoint']}. $f_c$, $f_\text{eq}^\text{(NG)}$, $f_1$, $f_2$ and $f_\text{RH}^{(\text{NG})}$ mark the bounding values of the intervals calculated in Eq. \ref{['eq:theresult']}. $f_3 \simeq 2.5 \times 10^{39}$ Hz is outside the physically relevant frequency range.
• Figure 4: Comparison of the GW spectra predicted by AH strings and NG strings for two values of $\alpha$. The AH curve is obtained as in Fig. \ref{['fig_infl_vs_cs']}, for the NG curves $G\mu = 2.0\times 10^{-7}$, cf. Fig. \ref{['fig:NGstring10-6']}.
• Figure 5: Evolution of the radiation temperature (upper panel) as well as of the $B$$-$$L$ Higgs $(S)$, nonthermal (s)neutrino $(N_1^\text{nt})$ and radiation $(r)$ energy densities (lower panel) as functions of the scale factor $a$ for three different values of $\widetilde{m}_1$, with all other free parameters kept fixed, $M_1 = m_S/300 = 10^{11}\,\textrm{GeV}$, $v_{B-L} = 5 \times 10^{15}\,\textrm{GeV}$. The ratio $\Gamma_{N_1}^S(a_\text{RH}) / \Gamma_S^0$ consequently takes the values $4.4 \times 10^{-2}$, $2.1 \times 10^0$, $1.5 \times 10^2$ for $\widetilde{m}_1 = 10^{-5},\, 10^{-3},\,10^{-1}\,\textrm{eV}$, respectively. The colored markers indicate the values of the various benchmark temperatures defined in Sec. \ref{['sec:reheatingtemp']} as labeled in the upper panel.