Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Prospects for direct detection of primordial gravitational waves

Sirichai Chongchitnan, George Efstathiou

TL;DR

This work assesses the prospects for directly detecting the primordial gravitational-wave background from single-field inflation in the $1\,\mathrm{mHz}$–$1\,\mathrm{Hz}$ range using the inflationary flow formalism to sample a broad class of potentials. It derives a model-independent upper bound $\omega_{\mathrm{gw}}\lesssim1.6\times10^{-15}$ for tensor-to-scalar ratios $r<0.36$ and shows that incorporating current constraints on the scalar spectral index $n_s$ and its running typically reduces $\omega_{\mathrm{gw}}$ far below this bound unless the inflaton potential contains a sharp feature near the end of inflation. The paper contrasts flow-based results with simple power-law extrapolations, illustrating that extrapolation can be misleading when no prior knowledge of the potential is assumed. In addition to inflation, it surveys other cosmological sources of primordial gravitational waves (e.g., bubbles, turbulence, cosmic strings, pre-Big Bang/cyclic models, braneworlds) and discusses how direct-detection experiments (LISA, BBO, DECIGO) might distinguish or be dominated by these signals. Overall, the findings suggest that detecting the inflationary background directly is challenging unless nontrivial features are present, while recognizing that other early-Universe processes could yield detectable backgrounds in this frequency band.

Abstract

We study the primordial gravitational wave background produced in models of single field inflation. Using the inflationary flow approach, we investigate the amplitude of gravitational wave spectrum in the frequency range 1 mHz - 1 Hz pertinent to future space-based laser interferometers. For models that satisfy the current observational constraint on the tensor-to-scalar ratio, r<0.36, we derive a strict upper bound of omega_{gw}<1.6 x 10^{-15}, independent of the form of the inflationary potential. Applying, in addition, the observational constraints on the spectral index and its running, omega_{gw} is expected to be considerably lower than this bound unless the shape of the potential is finely tuned. We contrast our numerical results with those based on simple power-law extrapolation of the tensor power spectrum from CMB scales. In addition to single field inflation, we summarise a number of other possible cosmological sources of primordial gravitational waves and assess what might be learnt from direct detection experiments such as LISA, Big Bang Observer and beyond.

Prospects for direct detection of primordial gravitational waves

TL;DR

This work assesses the prospects for directly detecting the primordial gravitational-wave background from single-field inflation in the – range using the inflationary flow formalism to sample a broad class of potentials. It derives a model-independent upper bound for tensor-to-scalar ratios and shows that incorporating current constraints on the scalar spectral index and its running typically reduces far below this bound unless the inflaton potential contains a sharp feature near the end of inflation. The paper contrasts flow-based results with simple power-law extrapolations, illustrating that extrapolation can be misleading when no prior knowledge of the potential is assumed. In addition to inflation, it surveys other cosmological sources of primordial gravitational waves (e.g., bubbles, turbulence, cosmic strings, pre-Big Bang/cyclic models, braneworlds) and discusses how direct-detection experiments (LISA, BBO, DECIGO) might distinguish or be dominated by these signals. Overall, the findings suggest that detecting the inflationary background directly is challenging unless nontrivial features are present, while recognizing that other early-Universe processes could yield detectable backgrounds in this frequency band.

Abstract

We study the primordial gravitational wave background produced in models of single field inflation. Using the inflationary flow approach, we investigate the amplitude of gravitational wave spectrum in the frequency range 1 mHz - 1 Hz pertinent to future space-based laser interferometers. For models that satisfy the current observational constraint on the tensor-to-scalar ratio, r<0.36, we derive a strict upper bound of omega_{gw}<1.6 x 10^{-15}, independent of the form of the inflationary potential. Applying, in addition, the observational constraints on the spectral index and its running, omega_{gw} is expected to be considerably lower than this bound unless the shape of the potential is finely tuned. We contrast our numerical results with those based on simple power-law extrapolation of the tensor power spectrum from CMB scales. In addition to single field inflation, we summarise a number of other possible cosmological sources of primordial gravitational waves and assess what might be learnt from direct detection experiments such as LISA, Big Bang Observer and beyond.

Paper Structure

This paper contains 8 sections, 39 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Inflationary Perturbations
  3. Gravitational Wave Spectrum
  4. Numerical method
  5. Dependence of $\omega_{\hbox{\scriptsize{gw}}}$ on $r$
  6. Dependence of $\omega_{\hbox{\scriptsize{gw}}}$ on scalar tilt $n_s$
  7. Prospects for direct detection
  8. Conclusions

Figures (3)

  • Figure 1: (Colour online) Plots of gravitational wave spectrum $\omega_{\hbox{\scriptsize{gw}}}$ against tensor-to-scalar ratio $r$ for a large number of models evolved with the inflationary flow equations. Square (red) points indicate models satisfying the observational constraints on $n_s$ and $dn_s/d\ln k$ given by (\ref{['niceobs']}). In panel (a), $\omega_{\hbox{\scriptsize{gw}}}$ is calculated using the extrapolation formula (\ref{['large']}). The solid line is the first order approximation given by Equation (\ref{['largeeps']}). In panel (b), $\omega_{\hbox{\scriptsize{gw}}}$ is calculated using the formula (\ref{['largest']}). The solid (green) curve in panel (b) shows the bound given by Equation (\ref{['upper']}), with the parameter $A=7$ .
  • Figure 2: (Colour online) Some trajectories $H(N)$, from CMB scales ($N\simeq60$) to the end of inflation $(N=0)$, for models evolved using the inflationary flow equations. The models plotted in panel (a) have high gravitational wave amplitudes at direct detection scales ($\omega_{\hbox{\scriptsize{gw}}} > 2.5 \times 10^{-16}$), whilst those shown in panel (b) have low amplitudes ($\omega_{\hbox{\scriptsize{gw}}} < 5 \times 10^{-17}$). All of these models satisfy the observational constraints on $n_s$ and $dn_s/d\ln k$ given by Equation (\ref{['niceobs']}), and have high tensor amplitudes in the range $0.15 \le r \le 0.25$.
  • Figure 3: (Colour online) The gravitational wave spectrum $\omega_{\hbox{\scriptsize{gw}}}$ plotted against scalar spectral index $n_s$ for a large number of models evolved using the inflationary flow equations. Square (red) points indicate models satisfying the observational constraints on $n_s$ and $dn_s/d\ln k$ (Equation (\ref{['niceobs']})) and satisfying $r<0.36$. In panel (a), $\omega_{\hbox{\scriptsize{gw}}}$ is calculated using the extrapolation formula (\ref{['large']}). The (green) solid curve shows the bound given by Eq. (\ref{['env']}). In panel (b), $\omega_{\hbox{\scriptsize{gw}}}$ is calculated using formula (\ref{['largest']}) and the flow equation integration.