Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

Abstract

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f (φ). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass M CS . In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra γγζ for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f (φ) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.

Parity-violating gravity and GW170817 in non-Riemannian cosmology

“…The form of L QGR was given in (2. 15) and the function f (which could be just a constant) depends on the theory. We found that the magnitude of f , which controls the proportion of the parity-violating corrections, is not efficiently constrained by the present GW data.…”

Probing P and CP violations on the cosmological collider

“…Existing studies of P-violating bispectra and trispectra [62][63][64][65][66][67][68][69][70][71][72][73][74][75] require the presence of either tensor modes or broken rotational symmetry. These studies are thus aimed to probe the P or CP of the inflaton background or the gravitational interactions.…”

Measuring chiral gravitational waves in Chern-Simons gravity with CMB bispectra

“…In ref. [1] we showed that the assumption of an approximately constant M CS during inflation constrains the value of Π to be not greater than the ratio Θ/ , being the well-known slow roll parameter. In such a case it is not possible to detect Π, since in order to increase the value of Π we should reduce the value of (or better to say r), causing at the same time the reduction of the S/N ratio on Π, as we can see in figure 1 (for instance, if we take r = 10 −2 and we assume Θ = 10 −1 , then we would get Π < 10 2 and ∆Π = 10 6 , making the detection of Π impossible).…”

“…In ref. [1] we analyzed the theoretical bispectra of primordial perturbations arising from a Chern-Simons modified gravity term coupled to the inflaton field through a generic coupling function f (φ). In particular, the action of the model reads…”

“…The quantity Θ must be very small during inflation (Θ 1) to avoid any instability (for more details on this parameter see ref. [1]).…”