Gravitational Waves Induced by non-Gaussian Scalar Perturbations (1810.11000v3)

Abstract: We study gravitational waves (GWs) induced by non-Gaussian curvature perturbations. We calculate the density parameter per logarithmic frequency interval, $\Omega_\text{GW}(k)$, given that the power spectrum of the curvature perturbation $\mathcal{P}\mathcal{R}(k)$ has a narrow peak at some small scale $k$, with a local-type non-Gaussianity, and constrain the nonlinear parameter $f_\text{NL}$ with the future LISA sensitivity curve as well as with constraints from the abundance of the primordial black holes (PBHs). We find that the non-Gaussian contribution to $\Omega_\text{GW}$ increases as $k^3$, peaks at $k/k_=4/\sqrt{3}$, and has a sharp cutoff at $k=4k_*$. The non-Gaussian part can exceed the Gaussian part if $\mathcal{P}\mathcal{R}(k)f\text{NL}^2\gtrsim1$. If both a slope $\Omega_\text{GW}(k)\propto k^\beta$ with $\beta\sim3$ and the multiple-peak structure around a cutoff are observed, it can be recognized as a smoking gun of the primordial non-Gaussianity. We also find that if PBHs with masses of $10^{20}\text{g}$ to $10^{22}\text{g}$ are identified as cold dark matter of the Universe, the corresponding GWs must be detectable by LISA-like detectors, irrespective of the value of $\mathcal{P}\mathcal{R}$ or $f\text{NL}$.

• The paper shows that non-Gaussian contributions to gravitational wave energy grow as k^3, peaking near a characteristic scale.
• It links the generated gravitational waves to primordial black holes (10^20–10^22 g), suggesting new detection prospects with LISA.
• The study refines early universe models by incorporating local-type non-Gaussianity, providing a framework for probing dark matter candidates.

Gravitational Waves Induced by Non-Gaussian Scalar Perturbations

The investigation into gravitational waves (GWs) arising from non-Gaussian scalar perturbations offers valuable insights into early universe cosmology and potential dark matter candidates. In this context, the detailed paper by Cai, Pi, and Sasaki focuses on the cosmological consequences of non-Gaussian curvature perturbations on the generation of GWs, particularly assessing the implications for the primordial black holes (PBHs).

Summary of Key Findings

The paper addresses how GWs are produced due to nonlinear interactions between scalar perturbations, particularly beyond the Gaussian approximation. The primary aim is to evaluate the energy density spectrum of these GWs, denoted by $\Omega_\text{GW}(k)$, for scenarios where the power spectrum of the scalar perturbation $\mathcal{P}_\mathcal{R}(k)$ is sharply peaked at some scale $k_*$. A notable feature of the paper is the inclusion of local-type non-Gaussianity characterized by the nonlinear parameter $f_\text{NL}$.

Key findings are as follows:

• Growth of Non-Gaussian Contribution: The paper demonstrates that the contribution to $\Omega_\text{GW}$ from non-Gaussianity increases as $k^3$, peaking at $k/k_*=4/\sqrt{3}$, with a sharp decline beyond $k=4k_*$. This non-Gaussian part can surpass the Gaussian contribution when $\mathcal{P}_\mathcal{R}(k)f_\text{NL}^2\gtrsim1$. Such a scenario is characterized by a specific spectral slope, $\beta \sim 3$, which, in the presence of multiple peaks, acts as a good indicator of primordial non-Gaussianity.
• PBH and GW Connection: For PBH masses in the range of $10^{20}$ to $10^{22}$ grams, identified as possible constituents of cold dark matter, the associated GWs should be detectable by observatories like LISA. This finding is robust across a wide parameter space, irrespective of $\mathcal{P}_\mathcal{R}$ or $f_\text{NL}$, underscoring the utility of GWs as probes for PBH abundances.

Implications and Future Directions

The implications of this research are profound both in practical observational astronomy and theoretical cosmology. From a detection standpoint, the results suggest that future gravitational wave observatories, particularly LISA, could effectively constrain PBH dark matter models if these objects are prominent.

Theoretically, the exploration of non-Gaussianities in the early universe presents avenues not only to refine inflationary models but also to better understand the initial conditions of the universe. Establishing a non-Gaussian signature in the GW spectrum can shed light on the physical processes occurring at scales largely inaccessible to electromagnetic observations.

Speculation on Future Developments

Advancements in gravitational wave detection capabilities and data analysis techniques will likely enhance our understanding of the processes described in the paper. The ability to isolate and identify multiple peaks in the GW spectrum associated with $k^3$ scaling would facilitate unprecedented tests of the inflationary paradigm and non-Gaussian perturbations.

Multi-messenger astronomy, combining gravitational wave data with electromagnetic and cosmic microwave background observations, may offer a more holistic view of the early universe's structural evolution, potentially corroborating the findings from theoretical studies like this one.

In conclusion, the work by Cai, Pi, and Sasaki continues to propel the frontier of cosmological research, providing a framework to explore the primordial universe with an augmented set of observational tools. The pursuit of understanding non-Gaussian scalar perturbations and their gravitational wave signatures holds the promise of deepening our grasp of cosmic history and the constituents of dark matter.