Higher-curvature corrections and tensor modes

Higher-curvature corrections to the effective gravitational action may leave signatures in the spectrum of primordial tensor perturbations if the inflationary energy scale is sufficiently high. In this paper, we further investigate the effects of a coupling of the Inflaton field to higher-curvature tensors in models with a minimal breaking of conformal symmetry. We show that an observable violation of the tensor consistency relation from higher-curvature tensors implies also a relatively large running of the tensor tilt, enhanced even by some order of magnitude with respect to the standard slow-roll case. This may leave signatures in the tensor two-point function that we could test to recognize higher-curvature effects, above all if they are translated into a blue tilted spectrum visible by future gravitational wave experiments. Exploiting current cosmic microwave background and gravitational wave data, we also derive constraints on the inflationary parameters, inferring that large higher-curvature corrections seem to be disfavored.

Figure 1

Tensor spectrum expected by higher-curvature corrections. For each point in the plane $(r,n_{\mathrm{T}})$, the tensor running ${\alpha }_{\mathrm{T}}$ is fixed by Eqs. (7) and (10). The dashed region is excluded by the LIGO/VIRGO limit on the stochastic background (14); the black solid (dashed) line represents the sensitivity expected by LISA (Einstein Telescope). The blue contours are the 68% and 95% C.L. bounds for a combination of Planck 2018 [91, 92], BICEP2/Keck 2015 [31], and the LIGO/VIRGO [93, 94] ($\mathrm{P}18+\mathrm{BK}15+\mathrm{LV}$) data.

Figure 2

Marginalized two- and one-dimensional posteriors for the combination of Planck 2018 [91, 92], BICEP2/Keck 2015 [31], and the LIGO/VIRGO upper limit on amplitude of the stochastic background [93, 94] ($\mathrm{P}18+\mathrm{BK}15+\mathrm{LV}$).

Figure 3

Tensor running for a generic coupling $f(\varphi )$. The dashed line represents the model adopted in the paper.