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Gravitational waves, inflation and the cosmic microwave background: towards testing the slow-roll paradigm

Carlo Ungarelli, Pier Stefano Corasaniti, R. A. Mercer, Alberto Vecchio

TL;DR

This work investigates whether a space-based gravitational-wave detector operating around the 0.1–1 Hz band, embodied by the Big-Bang-Observer (BBO), can directly detect the stochastic gravitational-wave background predicted by single-field slow-roll inflation, and how such direct observations complement indirect constraints from future CMB missions. It derives the CGWB spectrum in terms of the primordial parameters $n_s$ and $r$, with a late-time normalization $A$ set to 0.7, and formulates the detectability of the signal via cross-correlation of multiple interferometers using a standard S/N expression. The analysis shows that a more ambitious BBO configuration (BBO-standard or BBO-grand) could probe inflationary parameter space down to $r \sim 5 \times 10^{-3}$ to $5 \times 10^{-4}$, while a conservative BBO-lite would be unlikely to improve upon current CMB limits; however, astrophysical foregrounds and CMB lensing impose fundamental sensitivity floors that must be accounted for. The study highlights the complementary value of direct GW measurements and CMB polarization data in constraining inflationary physics and provides guidance for the design of future space-based GW observatories.

Abstract

One of the fundamental and yet untested predictions of inflationary models is the generation of a very weak cosmic background of gravitational radiation. We investigate the sensitivity required for a space-based gravitational wave laser interferometer with peak sensitivity at $\sim 1$ Hz to observe such signal as a function of the model parameters and compare it with indirect limits that can be set with data from present and future cosmic microwave background missions. We concentrate on signals predicted by slow-roll single field inflationary models and instrumental configurations such as those proposed for the LISA follow-on mission: Big Bang Observer.

Gravitational waves, inflation and the cosmic microwave background: towards testing the slow-roll paradigm

TL;DR

This work investigates whether a space-based gravitational-wave detector operating around the 0.1–1 Hz band, embodied by the Big-Bang-Observer (BBO), can directly detect the stochastic gravitational-wave background predicted by single-field slow-roll inflation, and how such direct observations complement indirect constraints from future CMB missions. It derives the CGWB spectrum in terms of the primordial parameters and , with a late-time normalization set to 0.7, and formulates the detectability of the signal via cross-correlation of multiple interferometers using a standard S/N expression. The analysis shows that a more ambitious BBO configuration (BBO-standard or BBO-grand) could probe inflationary parameter space down to to , while a conservative BBO-lite would be unlikely to improve upon current CMB limits; however, astrophysical foregrounds and CMB lensing impose fundamental sensitivity floors that must be accounted for. The study highlights the complementary value of direct GW measurements and CMB polarization data in constraining inflationary physics and provides guidance for the design of future space-based GW observatories.

Abstract

One of the fundamental and yet untested predictions of inflationary models is the generation of a very weak cosmic background of gravitational radiation. We investigate the sensitivity required for a space-based gravitational wave laser interferometer with peak sensitivity at Hz to observe such signal as a function of the model parameters and compare it with indirect limits that can be set with data from present and future cosmic microwave background missions. We concentrate on signals predicted by slow-roll single field inflationary models and instrumental configurations such as those proposed for the LISA follow-on mission: Big Bang Observer.

Paper Structure

This paper contains 4 sections, 15 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Single-field slow roll inflation
  3. Testing inflationary models with the Big-Bang-Observer
  4. Conclusions

Figures (2)

  • Figure 1: The sensitivity of the Big-Bang-Observer mission to a cosmic gravitational wave background generated by a single field slow-roll inflationary model. The plot shows the region in the parameter space $r$ and $n_s$ (see Section 2) that can be detected (corresponding to a false alarm alarm probability of $1\%$ and false dismissal rate of $10\%$). The magenta, yellow and red regions correspond to the limits obtained in a 3 yr long observation with BBO-lite, BBO-standard, and BBO-grand, respectively. The solid line correspond to the present best upperlimit set by WMAP observations Kinneyetal04
  • Figure 2: The sensitivity of Planck and CMBPol to indirect observations of a cosmic gravitational wave background produced during inflation. The plots show the region of the the parameter space $r$ and $n_s$ corresponding to the 68% and 95% confidence level upper-limit to a CGWB (red and yellow areas, respectively). The left plot corresponds to Planck observations and the line refers to the detection limit obtained with the BBO-standard configuration, cf Figure \ref{['fig:snr']}. The plot on the right corresponds to CMBPol observations and the line refers to the detection limit obtained with the BBO-grand configuration, cf Figure \ref{['fig:snr']}.