[Paper Review] Probing inflation models with gravitational waves

Valerie Domcke|arXiv (Cornell University)|May 20, 2016

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper proposes that a pseudoscalar inflaton coupling to abelian gauge fields induces a tachyonic instability, leading to enhanced gravitational wave (GW) production during inflation. The resulting non-perturbative gauge field production significantly boosts the high-frequency GW spectrum, making Starobinsky-like models (p=2) the most promising candidates for detection by advanced LIGO and eLISA, enabling direct probing of inflation's microphysics through GW interferometers.

ABSTRACT

A direct detection of primordial gravitational waves is the ultimate probe for any inflation model. While current CMB bounds predict the generic scale-invariant gravitational wave spectrum from slow-roll inflation to be below the reach of upcoming gravitational wave interferometers, this prospect may dramatically change if the inflaton is a pseudoscalar. In this case, a coupling to any abelian gauge field leads to a tachyonic instability for the latter and hence to a new source of gravitational waves, directly related to the dynamics of inflation. In this contribution we discuss how this setup enables the upcoming gravitational wave interferometers advanced LIGO/VIRGO and eLISA to probe the microphysics of inflation, distinguishing between different universality classes of single-field slow-roll inflation models. We find that the prime candidate for an early detection is a Starobinsky-like model.

Motivation & Objective

• To investigate how pseudoscalar inflaton couplings to abelian gauge fields can generate observable primordial gravitational waves (GWs) beyond standard slow-roll predictions.
• To determine whether upcoming GW interferometers (advanced LIGO/VIRGO and eLISA) can detect these enhanced GW signals and distinguish between different universality classes of single-field slow-roll inflation models.
• To identify which inflation models—particularly those with varying scalar potential power-law behavior—maximize GW signal strength while remaining consistent with CMB constraints.
• To explore the complementarity between CMB measurements and future GW observations in constraining inflationary parameters such as the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$.

Proposed method

• Model the inflationary dynamics using a pseudoscalar inflaton $\phi$ coupled to $\mathcal{N}$ abelian gauge fields via the interaction Lagrangian $\mathcal{L}_{\text{int}} \sim \phi F_{\mu\nu} \tilde{F}^{\mu\nu}/\Lambda$.
• Derive the equations of motion for the inflaton and gauge field fluctuations, showing that one helicity mode of the gauge field experiences a tachyonic instability when $\xi = \alpha |\dot{\phi}| / (2\Lambda H)$ becomes large.
• Compute the induced energy density $\langle \vec{E} \cdot \vec{B} \rangle \propto H^4 / \xi^4 e^{2\pi\xi}$, which acts as an effective friction term in the inflaton equation, modifying the slow-roll dynamics.
• Calculate the enhanced tensor power spectrum $\Omega_{\text{GW}} \propto (H/M_P)^2 \left(1 + 10^{-7} \mathcal{N} H^2 / (M_P^2 \xi^6) e^{4\pi\xi} \right)$, showing strong high-frequency enhancement.
• Parametrize single-field slow-roll models by $\epsilon_V \sim \beta / N^p$, allowing classification into universality classes by the exponent $p$, and map the resulting GW spectra across these classes.
• Use numerical and analytical tools to map the parameter space of the Starobinsky model ($p=2$) in terms of $\alpha/\Lambda$ and $\gamma$, assessing detectability by LIGO and eLISA under CMB constraints.

Experimental results

Research questions

• RQ1 Can the coupling of a pseudoscalar inflaton to abelian gauge fields produce a detectable enhancement of primordial gravitational waves beyond the standard slow-roll spectrum?
• RQ2 Which universality class of single-field inflation models—characterized by the exponent $p$ in $\epsilon_V \sim \beta / N^p$—maximizes the high-frequency gravitational wave signal while satisfying CMB constraints?
• RQ3 How do the projected sensitivities of advanced LIGO and eLISA compare in probing the parameter space of pseudoscalar inflation models, particularly for $p=2$?
• RQ4 To what extent can future gravitational wave observations distinguish between different inflation models based on the frequency-dependent shape of the enhanced GW spectrum?
• RQ5 What are the implications of this mechanism for other early-universe observables, such as primordial black hole formation or CMB $\mu$-distortions?

Key findings

• The tachyonic instability of gauge fields in pseudoscalar inflation leads to a non-perturbative production of gauge field modes, significantly enhancing the primordial gravitational wave spectrum at high frequencies.
• The enhanced GW spectrum scales as $\Omega_{\text{GW}} \propto (H/M_P)^2 \left(1 + 10^{-7} \mathcal{N} H^2 / (M_P^2 \xi^6) e^{4\pi\xi} \right)$, with the second term dominating at large $\xi$, leading to a strongly frequency-dependent, chiral signal.
• Among all single-field slow-roll models, the Starobinsky-like model with $p=2$ yields the strongest GW signal at high frequencies, making it the prime candidate for detection by advanced LIGO and eLISA.
• The parameter space of the Starobinsky model is mapped in terms of $\alpha/\Lambda$ and $\gamma$, showing that the projected sensitivity of LIGO O2 and O5 runs, as well as eLISA, can probe a significant portion of the viable parameter space.
• CMB constraints on the scalar spectral index $n_s$ and non-Gaussianity limit the parameter space, especially for high-$p$ models like hilltop inflation, which require small $\alpha/\Lambda$ to remain consistent with observations.
• The model predicts additional observable signatures, including primordial black hole formation, excess radiation contributing to $N_{\text{eff}}$, and potentially detectable $\mu$-distortions in the CMB spectrum.