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, $\Omega_{\rm gw}(f)<2.3\times10^{-10}$. 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.
Highlights
From the cosmic microwave background (CMB) to ground-based gravitational waves (GWs) interferometers, these experiments cover more than 21 orders of magnitude in frequency—29 with complementary but indirect bounds from big bang nucleosynthesis (BBN), CMB temperature and polarization power spectra and lensing, and baryon acoustic oscillation (BAO) measurements
Constraints on the total energy density of GWs from BBN, gravitational lensing, CMB power spectra, and BAO are sensitive to GWs as high as 109 Hz
The new Parkes Pulsar Timing Array (PPTA) limit reported here is the first time a GW limit in either the pulsar timing arrays (PTAs) or Laser Interferometer Gravitational-wave Observatory (LIGO) band has gone under this optimistic threshold, marking the first time the detection of cosmological GWs could have been possible according to arguments in Ref. [63]
Summary
A red spectrum, combined with observational constraints on the amplitude of GWs from the CMB, imply that GW detectors such as pulsar timing arrays (PTAs) and groundbased interferometers such as the Laser Interferometer Gravitational-wave Observatory (LIGO) [7] and Virgo [8] are not sufficiently sensitive to detect primordial GWs predicted by the simplest model of inflation Blue spectra can be generated if the propagation speed of primordial GWs varies during inflation [20], or by introducing new interactions between the scalar field and gravity, where these interactions are low-energy remnants of some (unknown) modification of general relativity at much higher energy scales, such as the Planck scale Couplings of this form do not change any of the standard predictions of general relativity, but the theories that predict them allow us to treat the (unknown) high-energy theory of gravity in an effective low-energy limit for some energy scales. We show how the combination of constraints on the primordial GW background from CMB, PTA, BBN, BAO, and groundbased interferometer GW experiments can place stringent constraints on nt, yielding insights into the physics of the early Universe not accessible by any other means
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