2023/08/22 by Sourav Bhattacharya, Bhattacharya, Sourav, Moutushi Dutta Choudhury +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2308.11384
openalex publication_date 2023/08/22 · openalex created_date 2023/08/24 · openalex updated_date 2026/07/28
We consider a massless minimally coupled self interacting quantum scalar field coupled to fermion via the Yukawa interaction, in the inflationary de Sitter background. The fermion is also taken to be massless and the scalar potential is taken to be a hybrid, V(ϕ)= λϕ4/4!+ βϕ3/3! (λ>0). The chief physical motivation behind this choice of V(ϕ) corresponds to, apart from its boundedness from below property, the fact that shape wise V(ϕ) has qualitative similarity with standard inflationary classical slow roll potentials. Also, its vacuum expectation value can be negative, suggesting some screening of the inflationary cosmological constant. We choose that ⟨ ϕ⟩∼ 0 at early times with respect to the Bunch-Davies vacuum, so that perturbation theory is valid initially. We consider the equations satisfied by ⟨ ϕ(t) ⟩ and ⟨ ϕ2(t) ⟩, constructed from the coarse grained equation of motion for the slowly rolling ϕ. We then compute the vacuum diagrammes of various relevant operators using the in-in formalism up to three loop, in terms of the leading powers of the secular logarithms. For a closed fermion loop, we have restricted ourselves here to only the local contribution. These large temporal logarithms are then resummed by constructing suitable non-perturbative equations to compute ⟨ ϕ⟩ and ⟨ ϕ2 ⟩. ⟨ ϕ⟩ turns out to be at least approximately an order of magnitude less compared to the minimum of the classical potential, -3β/λ, owing to the strong quantum fluctuations. For ⟨ ϕ2 ⟩, we have computed the dynamically generated scalar mass at late times, by taking the appropriate purely local contributions. Variations of these quantities with respect to different couplings have also been presented.