On the effective field theory for quasi-single field inflation

Abstract

We study the effective field theory (EFT) description of the virtual particle effects in quasi-single field inflation, which unifies the previous results on large mass and large mixing cases. By using a horizon crossing approximation and matching with known limits, approximate expressions for the power spectrum and the spectral index are obtained. The error of the approximate solution is within 10% in dominate parts of the parameter space, which corresponds to less-than-0.1% error in the ns-r diagram. The quasi-single field corrections on the ns-r diagram are plotted for a few inflation models. Especially, the quasi-single field correction drives m 2 φ 2 inflation to the best fit region on the ns-r diagram, with an amount of equilateral non-Gaussianity which can be tested in future experiments.

Gravitational production of superheavy dark matter and associated cosmological signatures

“…Here let us assume that m X H. The dominant contribution to the non-Gaussianity is from integrating out the dark matter field [69][70][71][72][73]. The resulting non-Gaussianity is of the shape of general single field inflation [74] and of equilateral shape.…”

Higgs as heavy-lifted physics during inflation

“…Given that Higgs behaves as a heavy degree of freedom in the strong-mixing limit (µ > H), one may consider to integrate out the heavy Higgs to obtain an effective single-field theory. We denote the integrate-out process of the heavy Higgs as the effective field theory (EFT) approach [9,38,39,47,49,52,53], which is to be distinguished from the effective theory discussed in Section II.…”

“…The EFT approach for the two-field system (27) has been studied in the large mass regime (m h µ with m h H) [38,39] and in the large mixing regime (m h µ with µ H) [35,47]. In our case, both m h and µ are controlled by the parameterθ 0 so that the generalized method [49,52,53] applied for (m 2 h + µ 2 ) 1/2 > H is required. Note that the effective mass for the heavy mode ω + is nothing but (m 2 h + µ 2 ) 1/2 when taking k → 0 into (34).…”

“…Note that the effective mass for the heavy mode ω + is nothing but (m 2 h + µ 2 ) 1/2 when taking k → 0 into (34). To derive the effective action with a modified speed of sound, one solves the heavy Higgs field in the conformally flat space with a = −1/(Hη) [52]. The solution is…”

“…where η * = −β/(kc θ ) is taken to be the value at the sound horizon crossing. The value of β can be determined by matching the analytical solutions obtained in the m h → 0 limit, which gives β 1/2 = Γ(−1/4) 2 /(16π) [47,49,52]. In the strong-mixing limit withθ 0 /H 1, where ⌘ ⇤ = /(kc ✓ ) is taken to be the value at the sound horizon crossing.…”