Marieke Postma

Quantum corrections in Higgs inflation: the real scalar case

We present a critical discussion of quantum corrections, renormalisation, and the computation of the beta functions and the effective potential in Higgs inflation. In contrast with claims in the literature, we find no evidence for a disagreement between the Jordan and Einstein frames, even at the quantum level. For clarity of discussion we concentrate on the case of a real scalar Higgs. We first review the classical calculation and then discuss the back reaction of gravity. We compute the beta functions for the Higgs quartic coupling and non-minimal coupling constant. Here, the mid-field regime is non-renormalisable, but we are able to give an upper bound on the 1-loop corrections to the effective potential. We show that, in computing the effective potential, the Jordan and Einstein frames are compatible if all mass scales are transformed between the two frames. As such, it is consistent to take a constant cutoff in either the Jordan or Einstein frame, and both prescriptions yield the same result for the effective potential. Our results are extended to the case of a complex scalar Higgs.

Quantum corrections in Higgs inflation: the Standard Model case

We compute the one-loop renormalization group equations for Standard Model Higgs inflation. The calculation is done in the Einstein frame, using a covariant formalism for the multi-field system. All counterterms, and thus the betafunctions, can be extracted from the radiative corrections to the two-point functions; the calculation of higher n-point functions then serves as a consistency check of the approach. We find that the theory is renormalizable in the effective field theory sense in the small, mid and large field regime. In the large field regime our results differ slightly from those found in the literature, due to a different treatment of the Goldstone bosons.

Goldstone bosons and a dynamical Higgs field

Higgs inflation uses the gauge variant Higgs field as the inflaton. During inflation the Higgs field is displaced from its minimum, which results in associated Goldstone bosons that are apparently massive. Working in a minimally coupled U(1) toy model, we use the closed-time-path formalism to show that these Goldstone bosons do contribute to the one-loop effective action. Therefore the computation in unitary gauge gives incorrect results. Our expression for the effective action is gauge invariant upon using the background equations of motion.

Effective action for the Abelian Higgs model in FLRW

We compute the divergent contributions to the one-loop action of the U(1) Abelian Higgs model. The calculation allows for a Friedmann-Lemaˆotre-Robertson-Walker space-time and a time-dependent expectation value for the scalar field. Treating the time-dependent masses as two-point interactions, we use the in-in formalism to compute the first, second and third order graphs that contribute quadratic and logarithmic divergences to the effective scalar action. Working in Rξ gauge we show that the result is gauge invariant upon using the equations of motion.

Electroweak stability and non-minimal coupling

The measured values of the Higgs and top quark mass indicate that the electroweak vacuum is metastable if there is no new physics below the Planck scale. This is at odds with a period of high scale inflation. A non-minimal coupling between the Higgs field and the Ricci scalar can stabilize the vacuum as it generates a large effective Higgs mass during inflation. We consider the effect of this coupling during preheating, when Higgs modes can be produced very efficiently due to the oscillating Ricci scalar. We compute their effect on the effective potential and the energy density. The Higgs excitations are defined with respect to the adiabatic vacuum. We study the adiabaticity conditions and find that the dependence of our results on the choice of the order of the adiabatic vacuum increases with time. For large enough coupling particle production is so efficient that the Higgs decays to the true vacuum before this is an issue. However, for smaller values of the Higgs-curvature coupling no definite statements can be made as the vacuum dependence is large.

Hybrid inflation with moduli stabilization and low scale supersymmetry breaking

We study the supergravity hybrid inflation model of Antusch in the presence of a modulus field. The η-problem is solved by a shift symmetry for the inflaton, which protects the inflaton mass even in the presence of the modulus field. Inflation is (nearly) unaffected by moduli stabilization, provided the scale of supersymmetry breaking in the post-inflation vacuum is small. Therefore the model has the nice phenomenology that it combines low scale supersymmetry breaking with high scale (grand unification scale) inflation.

Neutrino production in matter with time-dependent density or velocity

We show that neutrinos can be produced through standard electroweak interactions in matter with time-dependent density.

Electroweak Baryogenesis and the Standard Model Effective Field Theory

A bstractWe investigate electroweak baryogenesis within the framework of the Standard Model Effective Field Theory. The Standard Model Lagrangian is supplemented by dimension-six operators that facilitate a strong first-order electroweak phase transition and provide sufficient CP violation. Two explicit scenarios are studied that are related via the classical equations of motion and are therefore identical at leading order in the effective field theory expansion. We demonstrate that formally higher-order dimension-eight corrections lead to large modifications of the matter-antimatter asymmetry. The effective field theory expansion breaks down in the modified Higgs sector due to the requirement of a first-order phase transition. We investigate the source of the breakdown in detail and show how it is transferred to the CP-violating sector. We briefly discuss possible modifications of the effective field theory framework.

A no-go for no-go theorems prohibiting cosmic acceleration in extra dimensional models

A four-dimensional effective theory that arises as the low-energy limit of some extra-dimensional model is constrained by the higher dimensional Einstein equations. Steinhardt & Wesley use this to show that accelerated expansion in our four large dimensions can only be transient in a large class of Kaluza-Klein models that satisfy the (higher dimensional) null energy condition [1]. We point out that these no-go theorems are based on a rather ad-hoc assumption on the metric, without which no strong statements can be made.

Unitarity and predictiveness in new Higgs inflation

A bstractIn new Higgs inflation the Higgs kinetic terms are non-minimally coupled to the Einstein tensor, allowing the Higgs field to play the role of the inflaton. The new interaction is non-renormalizable, and the model only describes physics below some cutoff scale. Even if the unknown UV physics does not affect the tree level inflaton potential significantly, it may still enter at loop level and modify the running of the Standard Model (SM) parameters. This is analogous to what happens in the original model for Higgs inflation. A key difference, though, is that in new Higgs inflation the inflationary predictions are sensitive to this running. Thus the boundary conditions at the EW scale as well as the unknown UV completion may leave a signature on the inflationary parameters. However, this dependence can be evaded if the kinetic terms of the SM fermions and gauge fields are non-minimally coupled to gravity as well. Our approach to determine the model’s UV dependence and the connection between low and high scale physics can be used in any particle physics model of inflation.