The effective Higgs potential and vacuum decay in Starobinsky inflation

Abstract

Based on the current experimental data, the Standard Model predicts that the current vacuum state of the Universe is metastable, leading to a non-zero rate of vacuum decay through nucleation of bubbles of true vacuum. Our existence implies that there cannot have been any such bubble nucleation events anywhere in our whole past lightcone. We consider a minimal scenario of the Standard Model together with Starobinsky inflation, using three-loop renormalization group improved Higgs effective potential with one-loop curvature corrections. We show that the survival of the vacuum state through inflation places a lower bound ξ ≳ 0.1 on the non-minimal Higgs curvature coupling, the last unknown parameter of the Standard Model. This bound is significantly stronger than in single field inflation models with no Higgs-inflaton coupling. It is also sensitive to the details of the dynamics at the end of inflation, and therefore it can be improved with a more detailed study of that period.

Ending inflation with a bang: Higgs vacuum decay in $R^2$ gravity

“…The horizontal black line lies at the conformal point ξ = 1/6 and the vertical dashed black line depicts the minimum m t , below which the EW vacuum is stable. [3] Therefore, in Starobinsky inflation ξ EW ≳ 0.13, as opposed to the field theory result ξ EW ≳ 0.06, for m t = 172.76 GeV and where the end of inflation is set at a = 0. However, because bubbles are predominantly produced very close to the inflationary finale, due to the negative terms in m 2 eff , we have to be more conservative with our definition of inflation's endpoint, for the ξ-bounds to be valid.…”

“…In this work, we presented an overview of our latest study [3], where we have assumed a minimal model to describe the early Universe, consisting of the SM and Starobinsky inflation. The latter is supported by observations and arises from the simple modification of gravity R + R 2 , where a higher-order geometric term is included in the action.…”

“…The survival of the Higgs vacuum during our cosmological evolution can be utilised to impose significant constraints on fundamental physics in a manner that would enable this long-lasting metastability [7]. In our studies [1,2], we adopted a minimal model of the early universe consisting of the SM and cosmological inflation in order to obtain vacuum decay bounds on the Higgs curvature coupling ξ. This coupling is the last missing renormalizable parameter of the SM, since it is impossible to probe it with accelerators in the flat spacetime of our late Universe, and thus can only be constrained by cosmological studies.…”

“…Figure 1: Left: The evolution of the Higgs self interaction λ with the renormalisation scale µ for the current experimental measurements of the Higgs m h and top quark m t masses, and the strong coupling a S to 3σ variance [3]. Right: A metastable double-well potential for a scalar field φ that can decay to its true vacuum via fluctuations, quantum tunnelling, or a combination of both [4].…”

“…Consequently, decaying from the electroweak to the true vacuum nucleates bubbles that expand rapidly and can have dire consequences for our Universe. This overview of our last study [1] regarding the cosmological implications of vacuum metastability during Starobinsky inflation was presented at the HEP2023 conference. Following the framework established in [2], we showcased our state-of-the-art lower bounds on the non-minimal coupling ξ, which resulted from a dedicated treatment of the effective Higgs potential in R + R 2 gravity.…”