Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Gravitational-wave cosmology across 29 decades in frequency

Paul D. Lasky, Chiara M. F. Mingarelli, Tristan L. Smith, John T. Giblin, Eric Thrane, Daniel J. Reardon, Robert Caldwell, Matthew Bailes, N. D. Ramesh Bhat, Sarah Burke-Spolaor, Shi Dai, James Dempsey, George Hobbs, Matthew Kerr, Yuri Levin, Richard N. Manchester, Stefan Osłowski, Vikram Ravi, Pablo A. Rosado, Ryan M. Shannon, Renée Spiewak, Willem van Straten, Lawrence Toomey, Jingbo Wang, Linqing Wen, Xiaopeng You, Xingjiang Zhu

TL;DR

The paper tackles constraining the primordial stochastic gravitational-wave background across 29 frequency decades by marrying data from the CMB, pulsar timing arrays, ground-based interferometers, and indirect bounds (BAO, BBN, lensing). It models the spectrum with a power-law form $\Omega_{gw}(f) = \Omega_{gw}^{CMB}(f/f_{CMB})^{n_t}[\tfrac{1}{2}(f_{eq}/f)^2 + \tfrac{16}{9}]$ linked to the tensor-to-scalar ratio $r$, enabling a joint inference on $n_t$ and $r$ and comparisons to inflationary theories. The analysis yields a current combined constraint of $n_t<0.36$ at 95% CL for $r=0.11$, with future aLIGO and PPTA data expected to tighten this to $n_t<0.34$, thereby probing non-standard early-Universe scenarios such as ekpyrosis and string-gas cosmologies. This cross-frequency synthesis demonstrates the power of integrating diverse observational windows to test fundamental cosmology and informs strategies for distinguishing primordial signals from astrophysical backgrounds.

Abstract

Quantum fluctuations of the gravitational field in the early Universe, amplified by inflation, produce a primordial gravitational-wave background across a broad frequency band. We derive constraints on the spectrum of this gravitational radiation, and hence on theories of the early Universe, by combining experiments that cover 29 orders of magnitude in frequency. These include Planck observations of cosmic microwave background temperature and polarization power spectra and lensing, together with baryon acoustic oscillations and big bang nucleosynthesis measurements, as well as new pulsar timing array and ground-based interferometer limits. While individual experiments constrain the gravitational-wave energy density in specific frequency bands, the combination of experiments allows us to constrain cosmological parameters, including the inflationary spectral index, $n_t$, and the tensor-to-scalar ratio, $r$. Results from individual experiments include the most stringent nanohertz limit of the primordial background to date from the Parkes Pulsar Timing Array, $Ω_{\rm gw}(f)<2.3\times10^{-10}$. Observations of the cosmic microwave background alone limit the gravitational-wave spectral index at 95\% confidence to $n_t\lesssim5$ for a tensor-to-scalar ratio of $r = 0.11$. However, the combination of all the above experiments limits $n_t<0.36$. Future Advanced LIGO observations are expected to further constrain $n_t<0.34$ by 2020. When cosmic microwave background experiments detect a non-zero $r$, our results will imply even more stringent constraints on $n_t$ and hence theories of the early Universe.

Gravitational-wave cosmology across 29 decades in frequency

TL;DR

The paper tackles constraining the primordial stochastic gravitational-wave background across 29 frequency decades by marrying data from the CMB, pulsar timing arrays, ground-based interferometers, and indirect bounds (BAO, BBN, lensing). It models the spectrum with a power-law form linked to the tensor-to-scalar ratio , enabling a joint inference on and and comparisons to inflationary theories. The analysis yields a current combined constraint of at 95% CL for , with future aLIGO and PPTA data expected to tighten this to , thereby probing non-standard early-Universe scenarios such as ekpyrosis and string-gas cosmologies. This cross-frequency synthesis demonstrates the power of integrating diverse observational windows to test fundamental cosmology and informs strategies for distinguishing primordial signals from astrophysical backgrounds.

Abstract

Quantum fluctuations of the gravitational field in the early Universe, amplified by inflation, produce a primordial gravitational-wave background across a broad frequency band. We derive constraints on the spectrum of this gravitational radiation, and hence on theories of the early Universe, by combining experiments that cover 29 orders of magnitude in frequency. These include Planck observations of cosmic microwave background temperature and polarization power spectra and lensing, together with baryon acoustic oscillations and big bang nucleosynthesis measurements, as well as new pulsar timing array and ground-based interferometer limits. While individual experiments constrain the gravitational-wave energy density in specific frequency bands, the combination of experiments allows us to constrain cosmological parameters, including the inflationary spectral index, , and the tensor-to-scalar ratio, . Results from individual experiments include the most stringent nanohertz limit of the primordial background to date from the Parkes Pulsar Timing Array, . Observations of the cosmic microwave background alone limit the gravitational-wave spectral index at 95\% confidence to for a tensor-to-scalar ratio of . However, the combination of all the above experiments limits . Future Advanced LIGO observations are expected to further constrain by 2020. When cosmic microwave background experiments detect a non-zero , our results will imply even more stringent constraints on and hence theories of the early Universe.

Paper Structure

This paper contains 9 sections, 7 equations, 2 figures, 1 table.

Table of Contents

  1. Gravitational wave experiments
  2. CMB Intensity and Polarization
  3. Pulsar Timing Arrays
  4. Ground-based interferometers
  5. Indirect constraints
  6. Combined constraints on the primordial tilt
  7. Combined experimental constraints
  8. Comparison with theory
  9. Conclusion

Figures (2)

  • Figure 1: Experimental constraints on $\Omega_{\rm gw}(f)$; the black star is the current PPTA upper limit and all black curves and data points are current 95% confidence upper limits. The grey curve and triangle are respectively the predicted aLIGO sensitivity and PPTA sensitivity with five more years of data. The indirect GW limits are from CMB temperature and polarization power spectra, lensing, BAOs, and BBN. Models predicting a power-law spectrum that intersect with an observational constraint are ruled out at $>95\%$ confidence. We show five predictions for the GW background, each with $r=0.11$, and with $n_t=0.68$ (orange curve), $n_t=0.54$ (blue), $n_t=0.36$ (red), $n_t=0.34$ (magenta), and the consistency relation, $n_t=-r/8$ (green), corresponding to minimal inflation.
  • Figure 2: Combined, two-dimensional posterior distribution for the tensor-to-scalar ratio, $r$, and the blue tilt of the GW spectrum, $n_t$, using CMB, PPTA, indirect, and LIGO observations. The contours are the $95$ and $99\%$ limits. The green, dashed curve shows the consistency relation, $n_t=-r/8$, while the red and blue triangles correspond respectively to the red and blue curves in Fig \ref{['Omega_freq']}. For clarity, the right panel is a zoomed-in version of the left panel, with additional posterior distributions shown. See Section \ref{['results']} for a description of each posterior distribution.