# Gravitational multifield dynamics on Higgs pre-inflation and preheating

Traditionally the problem of initial conditions for inflation has been treated separately from studies of reheating. To allow for a parametric-type reheating, the inflaton must be allowed to interact with (or decay to) other fields, and, these interactions should be present also during inhomogeneous preinflation. Could they prevent cosmic inflation to start in the first place? In a single-author publication Cristian answers this question for Higgs Inflation: once more, inflation always starts and passes the challenge!

The inflationary paradigm postulates an early phase of accelerated expansion of the Universe. Such a period provides an explanation for the observed large-scale homogeneity and flatness in the cosmos. After the end of inflation, the universe would have gone through a phase where the energy of the inflaton is transferred to Standard Model particles, heating up the universe and leading to a bath of ultra-relativistic particles behaving like radiation. This phase is known as reheating.

Traditionally the problem of initial condition for inflation, i.e., knowing if inflation can start from highly inhomogeneous initial conditions, has been treated separately from studies of reheating. However, they are connected. To allow for the so-called parametric-type reheating, through resonances occurring while the system is oscillating at the bottom of the potential, the inflaton must be microscopically coupled to other fields. So, again, one could raise the question: shouldn’t these interactions be present also during inhomogeneous preinflation? Do they prevent cosmic inflation to start?

In a previous paper, see Ref. [1], we have studied the robustness of single-field Higgs Inflation to inhomogeneous initial conditions of all sizes. We have paid attention to include the gravitational dynamics of the system, showing the possible formation of pre-inflationary black holes, as well as the generation of shear/tensor modes in the metric. In short, we have showed that these gravitational dynamics can only delay the beginning of inflation, but never prevent it.

In Ref. [2], Cristian expands the previous settings by adding an extra field into the Higgs Inflation model. This field is coupled such that it allows for a reheating of the Universe. Reheating is actually successful for a range of the field-field interaction strength, which is numerically explored in full General Relativity simulations. Then the same model is confronted to various preinflationary inhomogeneous settings and the full gravitational and scalar-field dynamics are investigated.

The figure below shows the preheating resonances for the auxiliary field (left panel). Structure formation occurs $$2$$-$$3$$ e-folds after the end of inflation (right panel).

Looking at the exact same model during the inhomogeneous multi-field preinflationary epochs, we confirm that the Higgs non-minimal coupling to gravity acts as a stabilizer as it washes out the energy contribution of the other minimally coupled matter/scalar-field sectors. In Ref [2], it is shown that this occurs naturally when one canonically normalizes the fields in the Einstein frame. This effect generalizes the dynamics of inhomogeneous extra-matter components, making them sub-dominant in comparison to the inflaton.

The above figure illustrates the gravitational and scalar-field dynamics during pre-inflation. Two simulations are shown, one with super-Hubble initial conditions (left) and another with sub-Hubble size inhomogeneities (right).

All in all, these investigations further confirm the robustness of Higgs Inflation to multi-field inhomogeneous initial conditions, while putting in evidence the formation of complex structures during the reheating. The possible production of compact objects during the reheating, such as primordial black holes, will be investigated in future works.

### References

• [1] Joana C and Clesse S 2021 Inhomogeneous initial conditions for inflation: A wibbly-wobbly timey-wimey path to salvation Phys. Rev. D 103 083501
Abstract: arXiv:2011.12190 10.1103/PhysRevD.103.083501

• [2] Joana C 2022 Gravitational dynamics in Higgs inflation: Preinflation and preheating with an auxiliary field Phys. Rev. D 106 023504
Abstract: arXiv:2202.07604 10.1103/PhysRevD.106.023504