Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity

TL;DR

This work analyzes reheating in a Standard Model scenario where the Higgs field, non-minimally coupled to gravity, acts as the inflaton. It shows that reheating emerges from a complex interplay of perturbative decays and non-perturbative production (via tachyonic/adiabatic violation and parametric resonance), with early decays preventing rapid resonance but later allowing a strong non-linear transfer of energy. The authors quantify energy transfer, backreaction timings, and the evolving energy budget, demonstrating that a full thermalization phase lies in a highly non-linear regime that requires lattice simulations. The results connect Higgs-inflation dynamics to SM couplings at high scales and point toward potential observational implications, such as gravitational waves from preheating.

Abstract

We study the details of preheating in an inflationary scenario in which the Standard Model Higgs, strongly non-minimally coupled to gravity, plays the role of the inflaton. We find that the Universe does not reheat immediately through perturbative decays, but rather initiate a complex process in which perturbative and non-perturbative effects are mixed. The Higgs condesate starts oscillating around the minimum of its potential, producing W and Z gauge bosons non-perturbatively, due to violation of the so-called adiabaticity condition. However, during each semi-oscillation, the created gauge bosons completely decay (perturbatively) into fermions. This way, the decay of the gauge bosons prevents the development of parametric resonance, since bosons cannot accummulate significantly at the beginning. However, the energy transferred to the decay products of the bosons is not enough to reheat the universe, so after about a hundred oscillations, the resonance effect will finally dominate over the perturbative decays. Around the same time (or slightly earlier), backreaction from the gauge bosons onto the Higgs condensate will also start to be significant. Soon afterwards, the Universe is filled with the remnant condensate of the Higgs and a non-thermal distribution of Standard Model particles which redshift as radiation, while the Higgs continues to oscillate as a pressureless fluid. We compute the distribution of energy among all the species present at backreaction. From there on until thermalization, the evolution of the system is highly non-linear and non-perturbative, and will require a careful study via numerical simulations.

Figures (4)

• Figure 1: Comparative plot of the exact solution (red continuous line) obtained parametrically from Eq.(\ref{['sol']}), the analytic formula (\ref{['potentialE2']}) for the potential (blue dashed line), and their parametrization (\ref{['potentialE3']}) (green dotted line).
• Figure 2: Spectral distributions (\ref{['deltaN']}) for the gauge bosons created in a single zero crossing through the first term of Eq. (\ref{['occupnum']}), calculated after $j = 1, 2, 5$ and $10$ oscilations (from left to right). The horizontal axis represents $x \equiv k/Mq^{1/3}$, so $x = 1$ is the typical width of the band of momenta of particles created at the first scattering. For later times, the distributions broaden out to greater momenta, since the argument of Eq. (\ref{['deltaN']}), $x_j$ behaves as $\propto j^{-1/3}$. The typical momenta of the distribution agree with the one calculated in section \ref{['parametricreheating']}.
• Figure 3: Left: The Floquet index for a given polarization of the $W$ and $Z$ bosons as a function of the variable $x_j = k/ k_*{(j)}$. Here we show the maximum (continuous red), the average (short dashed green) and the typical (long dashed blue) indices. Right: The initial spectral distribution $n_k(1^+)$ (lower blue curve) and the Gaussian approximation $n(j^+\geq2)$ (\ref{['occupCombPre']}) for different $j's$ greater than 2 (rest of the curves), describing the resonant behaviour. The approximation is so good that it is hard to distinguish it from the real curve, presenting small deviations just on the tail. The horizontal axis is $x = k/ k_*{(1)}$ and the curves correspond to different $j$'s. It is clearly distinguishable the fact that only the range $x < 1$ ($k < k_*{(1)}$) is filtered and therefore excited through parametric resonance, no matter if $j \gg 2$.
• Figure 4: Left: The ratio $k^2/\langle m^2 \rangle$ between the typical momenta produced around zero and the average mass in every oscillation for the $W$ (dashed blue line) and $Z$ bosons (continuos red line) as a function of the number of oscillations. This ratio is significantly smaller than 1 for all crossings, which allows us to consider the produced gauge bosons as non-relativisitic. Right: Succesive spectral distributions $k^2n_k(1^+)e^{2\pi\sum_{k=2}^{j}\mu_k(j)}$, at different $j$'s, including the volume factor $k^2$. One can see the predicted (\ref{['pico']}) slow displacement of the maxima of the distribution. The x-axis is given in terms of $x = k/( k_*{(1)})$