Sensitivity of wide band detectors to quintessential gravitons

TL;DR

This paper investigates how the spectral shape of relic gravitons, especially in quintessential inflation models with blue or violet spectra, affects the sensitivity of interferometric detectors to these signals.

Contribution

It provides general formulas for the signal-to-noise ratio for blue spectra and applies them to quintessential gravitons, comparing detector sensitivities with theoretical predictions.

Findings

Derived expressions for SNR depending on spectral shape.

Calculated minimum sensitivities for detector pairs.

Compared sensitivities with theoretical graviton spectra expectations.

Abstract

There are no reasons why the energy spectra of the relic gravitons, amplified by the pumping action of the background geometry, should not increase at high frequencies. A typical example of this behavior are quintessential inflationary models where the slopes of the energy spectra can be either blue or mildly violet. In comparing the predictions of scenarios leading to blue and violet graviton spectra we face the problem of correctly deriving the sensitivities of the interferometric detectors. Indeed, the expression of the signal-to-noise ratio not only depends upon the noise power spectra of the detectors but also upon the spectral form of the signal and, therefore, one can reasonably expect that models with different spectral behaviors will produce different signal-to-noise ratios. By assuming monotonic (blue) spectra of relic gravitons we will give general expressions for the signal-to-noise ratio in this class of models. As an example we studied the case of quintessential gravitons. The minimum achievable sensitivity to $h^2_{0} \Omega_{GW}$ of different pairs of detectors is computed, and compared with the theoretical expectations.