Abstract
We use conformal symmetry to constrain the shape of inflationary correlators in the presence of long-lived vector field perturbations. Applying conformal Ward identities, we derive general expressions, up to amplitudes and normalization factors, for the two and three-point correlators in the presence of vector fields mediated by the interaction fleft(phi right)kern0.1em left({F}_{mu v}{F}^{mu v}+kern0.5em alpha {tilde{F}}_{mu v}{F}^{mu v}right) , where f(ϕ) is a suitable coupling function between the scalar and the vector field. This interaction allows for isotropy and parity symmetry breaking and is consistent with super horizon conformal symmetry. As an application of the conformal field theory techniques followed here, we evaluate the mixed tensor-scalar 〈γζ〉 and tensor-scalar-scalar 〈γζζ〉 correlators which are interesting to look for parity violating effects related with chiral gravitational waves. Finally, we derive consistency relations for the three-point correlators obtained.
Highlights
Idea of this method comes from the fact that, during the inflationary expansion, deep in the super horizon regime, the fields behave like conformal fields
As an application of the conformal field theory techniques followed here, we evaluate the mixed tensor-scalar γζ and tensorscalar-scalar γζζ correlators which are interesting to look for parity violating effects related with chiral gravitational waves
Our main purpose in this paper is to extend the application of conformal field theory (CFT) to derive general expressions for the inflationary correlators in Fourier space involving tensor perturbations/gravitational waves γij sourced by the vector fields
Summary
We study a cosmological scenario, in which a single U(1) invariant vector field Aμ is coupled to a single scalar field φ, not necessarily the inflaton, during the inflationary period. Our main interest for such particular case resides on the fact that, when the coupling function f (φ) is a homogeneous function of time, deep in the super horizon regime k/(aH) → 0, the generated vector perturbations preserve conformal invariance [75, 76]. This fact becomes very useful because the inflationary coupled scalar-vector system can be analyzed by using the vast quantity of tools, techniques and results of CFT. Further details of the mode solutions can be found in [50, 68, 69, 73, 75, 76]
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