Deciphering Inflation with Gravitational Waves: Cosmic Microwave Background Polarization vs. Direct Detection with Laser Interferometers

TL;DR

This work investigates how combining cosmic microwave background (CMB) polarization data with direct gravitational-wave detection from space-based laser interferometers can sharpen constraints on the inflationary potential. Using a Monte Carlo implementation of the Hubble Slow-Roll flow equations, it samples slow-roll, single-field potentials without assuming a fixed form, predicting observables such as $n_s$, $r$, $n_t$, and their running under Planck and future facilities. It then assesses how these constraints map across scales, and examines the potential to test the single-field consistency relation $\\mathcal{R} \equiv -r/(8 n_t)$ by adding direct-detection information, particularly with DECIGO. The results indicate that while direct detection can improve potential constraints relative to Planck, it is generally outperformed by CMBPol in the joint analysis, and that DECIGO offers the best prospects for testing the consistency relation, unless the tensor amplitude is relatively large.

Abstract

A detection of the primordial gravitational wave background is considered to be the ``smoking-gun '' evidence for inflation. While super-horizon waves are probed with cosmic microwave background (CMB) polarization, the relic background will be studied with laser interferometers. The long lever arm spanned by the two techniques improves constraints on the inflationary potential and validation of consistency relations expected under inflation. If gravitational waves with a tensor-to-scalar amplitude ratio greater than 0.01 are detected by the CMB, then a direct detection experiment with a sensitivity consistent with current concept studies should be pursued vigorously. If no primordial tensors are detected by the CMB, a direct detection experiment to understand the simplest form of inflation must have a sensitivity improved by two to three orders of magnitude over current plans.

Figures (2)

• Figure 1: The set of potentials satisfying $0.9<n_s<1.0$ from the Monte Carlo flow simulations: Left: constraints from Planck with $r=0.02 \pm 0.01$, $d n_s/d\ln k = 0.0\pm 0.01$, BBO-standard, BBO-grand (factor 10 more sensitive than BBO-standard) Center: constraints from CMBPol with optimistic foregrounds verde/etal:2005: $r=0.001 \pm 0.0003$, $d n_s/d\ln k = 0.0\pm 0.005$, BBO-standard, BBO-grand, and Right: the sensitivity limit due to foregrounds for CMBPol with $r<10^{-4}$ and DECIGO (factor 400 more sensitive than BBO-standard). Color coding: red and blue denote the CMB experiment without and with the $d n_s/d\ln k$ constraint, respectively. Green: BBO-standard. Black: BBO-grand ( Left, Center) and DECIGO ( Right). The direct detection constraints are applied to the tensor amplitude and tilt at 1 Hz, following the procedure described in the text. If a particular color does not appear in a plot, it has been overwritten by the next tightest constraint, and the latter is therefore not helpful in constraining the potential. The meaning of the color coding is further clarified in the text. Here $\phi=0$ corresponds to CMB scales while curves end at $\phi <0$ corresponding to a frequency of 1 Hz probed by direct detection methods.
• Figure 2: Left: The mapping between tensor-to-scalar ratio $r$ at CMB scales and $\Omega_{\rm GW}h^2$ at 1 Hz for a direct detection. The gray shaded region shows the uncertainty implied with $n_s=0.95 \pm 0.1$Seljak by keeping terms up to second order (running of the tensor spectral index) in the slow-roll power-law expansion. We include the line 'Unphysical for inflation' to indicate the region above which $n_t > 0$. The three horizontal curves are the 2$\sigma$ detection amplitudes for BBO-standard, BBO-grand, and DECIGO in solid, dashed, and dotted lines respectively. In these three experiments, at 1 Hz, the signal-to-noise ratio for detecting the gravitational wave background is ${\rm SNR} = X (\Omega_{\rm GW}/10^{-18})$, with values for $X$ shown in the panel. Right: The $1 \sigma$ uncertainty in the single-field consistency relation $\mathcal{R}\equiv-r/8n_t$. The thin lines follow laser interferometers in the right panel, showing the error expected by combining direct detection measurements of $n_t$ with CMBPol measurements of the tensor-to-scalar ratio, $r$. The two thick lines indicate errors in $\mathcal{R}$ when $n_t$ is determined from CMB alone. The thick solid curve corresponds to the expected accuracy of ESA's Planck satellite, the thick dashed curve corresponds to CMBPol. The shaded region indicates a 50% determination of the consistency relation ($\mathcal{R} = 1.0 \pm 0.5$). For direct-detection observations, sensitivity is degraded at large $r$ because of an increase in the uncertainty of the importance of the running of the tensor spectral index from direct detection scales to CMB scales; at small $r$, the accuracy with which $\mathcal{R}$ can be determined is dominated by the error in measuring $n_t$ with CMB Song and laser interferometers Seto:06, where the latter is $\sigma_{\small n_t} \propto 1/r$.