[Paper Review] High-frequency Graviton from Inflaton Oscillation

Yohei Ema, Ryusuke Jinno+1 more|arXiv (Cornell University)|Jan 1, 2020

Cosmology and Gravitation Theories42 references1 citations

TL;DR

This paper identifies a high-frequency tail in the stochastic gravitational wave background generated by coherent oscillations of the inflaton field during reheating, which scales as f^{-1/2} in frequency. The signal arises from vacuum graviton fluctuations amplified by the oscillating inflaton, encoding information on the inflaton mass, decay rate, and early-universe thermal history, offering a quantum probe of inflationary dynamics beyond standard horizon-exit mechanisms.

ABSTRACT

We point out that there is a high-frequency tail of the stochastic inflationary gravitational wave background that scales as $f^{-1/2}$ with frequency $f$. This contribution comes from the graviton vacuum fluctuation amplified by the inflaton coherent oscillation during the reheating stage. It contains information on inflaton properties such as the inflaton mass as well as the thermal history of the early Universe.

Motivation & Objective

• To identify a previously overlooked source of high-frequency stochastic gravitational wave (GW) background from inflaton coherent oscillations during reheating.
• To analyze how vacuum graviton fluctuations are amplified by the time-varying inflaton background, leading to a distinct high-frequency spectral component.
• To quantify the GW spectrum's dependence on inflaton mass, reheating temperature, and potential shape, particularly in the subhorizon regime.
• To assess the detectability of this signal in the context of competing high-frequency GW sources such as SM thermal plasma and bremsstrahlung.
• To highlight the quantum nature of this GW signal, as it originates from subhorizon vacuum fluctuations never exiting the horizon.

Proposed method

• Solving the graviton equation of motion in the transverse-traceless gauge during the reheating epoch, with time-dependent background from inflaton oscillations.
• Using the Bunch-Davies vacuum state and canonical quantization to compute the graviton wave function evolution under the oscillating inflaton potential.
• Applying the WKB approximation and adiabatic expansion to analytically estimate the power spectrum of graviton production during inflaton oscillation.
• Numerically solving the mode equation for the graviton to validate analytical results and compute the full GW energy density spectrum.
• Deriving the stochastic GW background energy density spectrum, ΩGW(f), and identifying the f^{-1/2} scaling in the high-frequency tail.
• Comparing the inflaton-oscillation-induced GWs with competing contributions from SM thermal plasma and inflaton decay bremsstrahlung.

Experimental results

Research questions

• RQ1 Does coherent inflaton oscillation during reheating produce a detectable high-frequency tail in the stochastic gravitational wave background?
• RQ2 What is the frequency dependence of the GW spectrum generated by inflaton oscillations, and does it follow a universal scaling like f^{-1/2}?
• RQ3 How do the inflaton mass and reheating temperature influence the amplitude and shape of the high-frequency GW signal?
• RQ4 Can this GW signal be distinguished from other high-frequency contributions such as those from SM thermal plasma or inflaton decay bremsstrahlung?
• RQ5 What quantum information about the inflaton sector and early-universe conditions is encoded in this subhorizon, vacuum-amplified GW signal?

Key findings

• A high-frequency tail in the stochastic gravitational wave background emerges from vacuum graviton fluctuations amplified by inflaton coherent oscillations during reheating, scaling as f^{-1/2} with frequency f.
• The GW spectrum extends beyond the standard inflationary GWs that exit the horizon during inflation, with the high-frequency component originating from subhorizon modes never exiting the horizon.
• The amplitude of the high-frequency tail depends on the inflaton mass and reheating temperature, with the spectrum suppressed at frequencies above fend ≃1.1 × 10^6 Hz for Hend = 10^13 GeV.
• The signal is quantum in origin, as the graviton occupation number remains much less than unity, making its detection a direct probe of quantum gravitational effects.
• The contribution from SM thermal plasma dominates over the inflaton-oscillation signal in most parameter regions, but the latter may still be extractable after foreground subtraction.
• The f^{-1/2} scaling is robust for quadratic inflaton potentials and may exhibit richer structure for more general potentials, suggesting a unique probe of inflaton dynamics.