Inflation with vector fields revisited: non-Gaussianities

The gist Inflationary models with vector fields provide a controlled setting in which additional degrees of freedom can modify primordial perturbations, and this paper revisits the resulting bispectrum by organizing dynamics in terms of h, which measures the vector kinetic contribution relative to that of the scalar field The bispectrum therefore distinguishes vector-supported inflationary dynamics even for an exactly isotropic background

How it works

The paper investigates how the relative importance of vector and scalar kinetic sectors, parametrized by h, governs the non-Gaussianities generated during inflation When h is small (h ≪ 1), vector perturbations act as weakly coupled additional modes whose transfer to the curvature perturbation continues on superhorizon scales, generating a local-type bispectrum with an amplitude enhanced by the duration of inflation after horizon exit This cumulative behavior places a stringent constraint on the weak-vector regime, implying a tiny but non-zero parameter that may give rise to fine-tuning challenges.

When h is large (h ≳ 1), the vector fields cannot be treated as weakly coupled modes, and in this regime, the entropic fluctuation becomes heavy and can be integrated out at low energies, leaving an effective single-mode description for the curvature perturbation with an imaginary sound speed. This EFT applies after a mode is redshifted to p ∼ ms ∼ hH, during which the curvature mode undergoes transient exponential growth before horizon crossing.

The regimes of h

The parameter h is defined by the ratio of kinetic contributions as h ≡ rϵA/2ϵϕ. The dynamics are qualitatively different depending on whether h is small or large. For intermediate h, the competition between signals yields a local-dominated signal, while for larger h, a flattened-dominated signal is present.

Non-Gaussianities in the small h regime

For small h (h ≪ 1), the cubic Lagrangian can be expanded in powers of h up to L(3)2 as L(3)0 + hL(3) 1 + h2L(3) 2 + O(h3). The leading non-Gaussian contribution is provided by the diagram in FIG. 1(right), and the shape function becomes Sh≪1(k, k, q) = 128h2N3K r + O(r2). This result shows that vector fields source the curvature perturbation cumulatively on superhorizon scales: R continues to evolve after horizon crossing. Observational constraints in this regime force h to be very small, with CMB bounds imposing the stringent constraint h ≲ O(10−4).

Non-Gaussianities in the large h regime

In the large-h regime (h ≫ 1), the dominant contribution comes from a one-vertex diagram, and the leading three-point correlation function of R is therefore given by. The low-energy EFT for this model has a sound speed cs ≃ i p1/3 which is imaginary, and the EFT applies after a mode is redshifted to p ∼ hH, during which the curvature mode undergoes transient exponential growth. The leading non-vanishing term is therefore of order e4x and contains one decaying-mode insertion.

Competition of shapes

The total projected amplitude results from competition among the interactions, and the behavior is naturally divided into three regions depending on x. For moderate x, the negative RR˙ 2 term controls the signal. In the intermediate range 8 ≲ x ≲ 11, cancellations suppress the principal nonlocal projections and leave a local-dominated total amplitude. At larger x, the x3 growth of the derivative interactions makes the flattened component dominant.

Conclusion

The large-h regime is not characterized by a single universal template; its observational signature varies from local-dominated to flattened-dominated as the EFT matching scale changes. The paper shows that the non-Gaussianities with vector fields indicate correlation between long wavelength and short wavelength modes, which is possible for primordial black holes and induced gravitational waves on small scales. This non-Gaussianities indicates correlation between long wavelength and short wavelength modes. The information of small-scale anisotropy of IGWs can be encoded into the large-scale anisotropy due to the non-trivial local shape non-Gaussianities generated by coupling with vector fields.

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The gist Inflationary models with vector fields provide a controlled setting in which additional degrees of freedom can modify primordial perturbations, and this paper revisits the resulting bispectrum by organizing dynamics in terms of h, which measures the vector kinetic contribution relative to that of the scalar field

Non-Gaussianities in the large h regime

In the large-h regime (h ≫ 1), the dominant contribution comes from a one-vertex diagram, and the leading three-point correlation function of R is therefore given by. The low-energy EFT for this model has a sound speed cs ≃ i p1/3 which is imaginary, and the EFT applies after a mode is redshifted to p ∼ hH, during which the curvature mode undergoes transient exponential growth before horizon crossing.

1. The improved AI system can perform template analysis of large-h non-Gaussianities by distinguishing between flattened-enhanced signals scaling as h 3 and a flattened-enhanced signal scaling as h squared and a pronounced local projection scaling as h.

2. The system can accurately predict the dominance of the bispectrum shape based on the EFT matching scale, stating that Their competition yields a local-dominated signal for intermediate h and a flattened-dominated signal at larger h.

3. The AI can calculate non-Gaussianity shapes for different regimes, noting that For moderate x, the negative RR˙ 2 term controls the signal, and that in the intermediate range 8 ≲ x ≲ 11, cancellations suppress the principal nonlocal projections and leave a local-dominated total amplitude.

4. The system can analyze the dependence of projected amplitudes on h by stating that For large h, the interaction coefficients in the EFT depend only weakly on h; the significant h dependence instead enters through the mode evolution during the EFT regime.

5. The system can identify that for large x, the flattened shape therefore dominates the total bispectrum, and for moderate x, it can distinguish between shapes by noting that "fNL,flat < 0, fNL,eq < 0, and fNL,local < 0" in the range 5 ≲ x ≲ 8.