Probing the inflationary background of gravitational waves from large to small scales

Abstract

The detection of Primordial Gravitational Waves (PGWs) is one of the most important goals of modern cosmology since PGWs can both provide substantial evidence for primordial inflation and shed light on its physical nature. Small scale experiments on gravitational waves such as Ligo-Virgo and, in future, LISA and Einstein Telescope (ET), are sensitive to the stochastic background, ΩGW. So they can be used to constrain the inflationary parameters. In performing this kind of analysis, as recently done also by the Planck collaboration, the primordial spectrum of gravitational waves is usually parametrized with a power law that includes only the amplitude and the spectral tilt. In this paper, we investigate the robustness of such constraints showing that the higher-order terms in the power law approximation (i.e. the runnings of the tensor tilt), even small on the CMB scales, can lead to non-negligible corrections on small scales. We start investigating these corrections in the simplest scenario of slow-roll inflation that predicts an almost scale-invariant, slightly red tilted primordial spectrum of gravitational waves. Nevertheless also in this case, fixing the tensor to scalar ratio to r = 0.064, we estimate a correction on ΩGW of about 39% on the Ligo-Virgo scales. Then we focus on blue models of inflation analyzing the robustness of the constraints that can be obtained using small scale measurements of the stochastic background. We prove that it is effectively possible to constrain the inflationary parameters on the CMB scales with the small scale data, but also that the higher-order corrections are nonnegligible on small scales. We provide an example of this, constraining with the Ligo Virgo data a physical model of blue inflation that employs a pseudo scalar axion naturally coupled to gauge fields, both including and neglecting the spectral runnings. For the same model, we also study the future constraints from the next generation of gravitational waves experiments such as Lisa and ET. We prove that, once the higher-order corrections are considered in the analysis, future experiments can tightly constraints the spectral tilt nt improving at least of an order of magnitude the constraints.

Constraints on primordial gravitational waves from the cosmic microwave background

“…At higher frequencies, the expected signal can be extrapolated, assuming the power-law is valid across many decades in scale. However, the assumption of a power-law across a large frequency range was shown to introduce sizeable errors on the scales probed by interferometers [8]. In this work we did not assume a powerlaw, instead directly reconstructing the tensor power spectrum in logarithmic frequency bins using the latest data from Planck and BICEP2/Keck.…”

Higher-Curvature Corrections and Tensor Modes

“…In this work we further investigate higher-curvature corrections at leading order in the breaking of de Sitter isometries. We show that, along with the above mentioned violation of the consistency relation, other non trivial signatures can be left in the tensor two-point function and in particular the running of the tensor tilt can be some order of magnitude larger than expected in the standard slow roll hierarchy [21,66,67], possibly affecting the small scale behavior of tensor perturbations [68][69][70][71][72]. If a violation of the slow roll consistency relation will be observed, a combined analysis of the tilt and the running could in principle shed light on its higher-curvature nature.…”

Let Effective Field Theory of inflation flow: stochastic generation of models with red/blue tensor tilt

“…Indeed, even a small positive spectral index could produce an enhanced signal on small scales, given that the predicted power-spectra span ∼ 25 orders of magnitude in the frequency domain [7,62]. In recent works [63,64] it has been shown that in order to be detectable with the Laser Interferometer Space Antenna (LISA) and the Einstein Telescope the spectrum for inflationary gravitational waves must be considerably enhanced at scales smaller than the CMB ones. In particular, this requires a blue spectrum with n t 0.1 − 0.2, which is almost one order of magnitude greater than the typical values that we are finding.…”