Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: implications for the early universe

By Latham Boyle, A. Buonanno. 2007

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gw 0 (f1) and gw 0 (f2). Here r is the so-called “tensor-to-scalar ratio,” which is constrained by cosmic-microwave-background (CMB) experiments; and gw (f) is the energy spectrum of primordial gravitational-waves, which is constrained e.g. by pulsar-timing (PT) measurements, laser-interferometer (LI) experiments, and the standard Big Bang Nucleosynthesis (BBN) bound. Differentiating the master equation yields a new expression for the tilt dln gw (f)/dlnf of the present-day gravitational-wave spectrum. The relationship between r and gw (f) depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities: ˆ w(f) and ˆ nt(f), where ˆ nt(f) is a certain logarithmic average over nt(k) (the primordial tensor spectral index); and ˆ w(f) is a certain logarithmic average over ˜ w(a) (the effective equation-of-state parameter in the early universe, after horizon re-entry). Here the effective equation-of-state parameter ˜ w(a) is a combination of the ordinary equation-of-state parameter w(a) and the bulk viscosity �(a). Thus, by comparing observational constraints on r and gw (f), one obtains (remarkably tight) constraints in the { ˆ w(f), ˆ nt(f)} plane. In particular, this is the best way to constrain (or detect) the presence of a “stiff” energy component (with w > 1/3) in the early universe, prior to BBN. (The discovery of such a component would be no more surprising than the discovery of a tiny cosmological constant at late times!) Finally, although most of our analysis does not assume inflation, we point out that if CMB experiments detect a non-zero value for r, then we will immediately obtain (as a free by-product) a new upper bound ˆ w < 0.55 on the logarithmically averaged effective equation-of-state parameter during

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/db2285722274af2f9865312173ef6edc24a5e963

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Citations in the corpus

Observable Spectra of Induced Gravitational Waves from Inflation (2012, background): “It may be necessary to asses the impact a matter dominated reheating phase 6 could have on the eventual induced spectrum of gravitational waves [72, 73, 75, 76].”
Timing stability of millisecond pulsars and prospects for gravitational-wave detection (2009, background): “…/ 3 was a reasonable approximation for practical purposes. a For background of GWs that were formed in the early Universe, α ≈ − 1 and the amplitude range predicted by Grishchuk (2005) is A = 10 − 17 − 10 − 15 , but standard models (e.g. predict Boyle & Buonanno 2008) predict much lower amplitudes.”
Particle production during inflation and gravitational waves detectable by ground-based interferometers (2011, background): “The direct detectability of tensor modes produced during inﬂation was also considered by [15], where it was shown that, if the post-inﬂationary Universe is dominated by a ﬂuid stiﬀer than radiation, the primordial tensors amplitude can be signiﬁcantly enhanced.”
CMB-S4 Science Case, Reference Design, and Project Plan (2019, background): “Even without new light particles, Neff is a probe of new physics that changes our thermal history, including processes that result in a stochastic background of gravitational waves [203, 204, 205].”
The International Pulsar Timing Array: First Data Release (2016, background): “First, it could be the gravitational equivalent to the cosmic microwave background: a GWB arising from the era of graviton decoupling in the early Universe [Grishchuk 2005; Boyle & Buonanno 2008 or from phase transitions in the early Universe (Schwaller 2015)].”