TASI Lectures on Gravitational Waves from the Early Universe

TL;DR

This work surveys how relic gravitational waves can illuminate the very early Universe, connecting theoretical mechanisms—standard inflation, string-inspired pre-big-bang and bouncing models, non-standard post-inflationary equations of state, cosmic strings, and other high-energy processes—to observables. It derives the GW spectrum and its relation to detector sensitivities, discusses amplification of vacuum fluctuations via Bogoliubov transformations, and outlines phenomenological bounds from BBN, COBE, and pulsar timing. The authors assess detectability with current and planned detectors (LIGO, LISA), highlight the role of cosmic-string bursts and phase-transitions, and discuss prospects for brane-world scenarios and parameter extraction from GW signals. The paper emphasizes that, despite challenges, GWs offer a promising, multi-frequency probe of physics at the highest energies.

Abstract

These lectures discuss how the direct detection of gravitational waves can be used to probe the very early Universe. We review the main cosmological mechanisms which could have produced relic gravitational waves, and compare theoretical predictions with capabilities and time scales of current and upcoming experiments.

Figures (6)

• Figure 1: Sensitivities, expressed in terms of $\Omega_{\rm GW}$, versus frequency of LISA and ground-based detectors of first, second and third generation. On the top axis, the estimated temperature of the Universe when GWs are produced by causal mechanisms during RD era [see Eq. (\ref{['fRD']})].
• Figure 2: Summary of phenomenological bounds on energy density of relic GWs.
• Figure 3: In the left panel we sketch the evolution of the expansion rate of the Universe $H$ and of some physical wavelengths during a period of standard inflation, followed by RD and MD eras. In the right panel we plot the stochastic GW background for slow-roll inflation obtained in Ref. [ ?] for $T/S =0.18$ and $dn_T/d \log k = 0$ (continuous line), $T/S =0.18$ and $dn_T/d \log k = -10^{-3}$ (dot line), $T/S =0.0018$ and $dn_T/d \log k = 0$ (dash line) and $T/S =0.0018$ and $dn_T/d \log k = -10^{-3}$ (dot-dash line) The sensitivity of space-, (correlated) ground-based detectors and the stochastic background from WD binaries is also shown for comparison.
• Figure 4: In the left panel we sketch the evolution of $H$ and of some physical wavelengths during the superinflationary PBB phase, RD and MD eras. The shaded box refers to the spacetime region around the would-be big-bang singularity for which we do not have a complete description, yet. In the right panel we show two examples of the stochastic GW spectrum.
• Figure 5: We show an example of the stochastic GW spectrum originated in quintessential inflation and contrast it with the sensitivity of space- and (correlated) ground-based GW detectors. For a detail discussion of the GW spectra as function of the free parameters see Ref. [ ?].