Induced gravitational waves: the effect of first order tensor perturbations

Abstract

Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to constrain models of inflation. These waves are sourced by terms quadratic in perturbations and hence appear at second order in cosmological perturbation theory. While the focus of research so far was on purely scalar source terms we also study the effect of including first order tensor perturbations as an additional source. This gives rise to two additional source terms: a term quadratic in the tensor perturbations and a cross term involving mixed scalar and tensor perturbations. We present full analytical expressions for the spectral density of these new source terms and discuss their general behaviour. To illustrate the generation mechanism we study two toy models containing a peak on small scales. For these models we show that the scalar-tensor contribution becomes non-negligible compared to the scalar-scalar contribution on smaller scales. We also consider implications for future gravitational wave surveys.

31 pages, 7 figures. v2 typos corrected and citations added. v3 switched to circular polarizations. v3 matches published version

References in corpus (40)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Planck 2018 results. X. Constraints on inflation
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• Sensitivity Studies for Third-Generation Gravitational Wave Observatories
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• Cosmological Backgrounds of Gravitational Waves
• Physics, Astrophysics and Cosmology with Gravitational Waves
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• Gravitational-wave sensitivity curves
• The cosmological gravitational wave background from primordial density perturbations
• Cosmological perturbations
• Semianalytic Calculation of Gravitational Wave Spectrum Nonlinearly Induced from Primordial Curvature Perturbations
• Primordial black holes from single field models of inflation
• Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
• Relativistic second-order perturbations of the Einstein-de Sitter Universe
• A Cosmological Signature of the SM Higgs Instability: Gravitational Waves
• Cosmology with the Laser Interferometer Space Antenna
• Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers
• The second data release from the European Pulsar Timing Array I. The dataset and timing analysis
• Primordial Black Holes and Slow-Roll Violation
• General Relativistic Dynamics of Irrotational Dust: Cosmological Implications
• The Parkes Pulsar Timing Array Third Data Release
• Generating PBHs and small-scale GWs in two-field models of inflation
• Seeding primordial black holes in multifield inflation
• Primordial Gravitational Waves from Axion-Gauge Fields Dynamics
• Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak
• A Hamilton-Jacobi approach to non-slow-roll inflation
• Finding the chiral gravitational wave background of an axion-SU(2) inflationary model using CMB observations and laser interferometers
• Log-dependent slope of scalar induced gravitational waves in the infrared regions
• Turning in the landscape: a new mechanism for generating Primordial Black Holes
• xPand: An algorithm for perturbing homogeneous cosmologies
• Revisiting small-scale fluctuations in $\alpha$-attractor models of inflation
• A not so short note on the Klein-Gordon equation at second order
• Gravitational waves induced by scalar-tensor mixing
• Missing one-loop contributions in secondary gravitational waves
• Gravitational waves from primordial scalar and tensor perturbations
• Primordial Gravitational Waves Assisted by Cosmological Scalar Perturbations

Cited by in corpus (5)

• Primordial black holes: constraints, potential evidence and prospects
• Fundamental Physics and Cosmology with TianQin
• Multiple peaks in gravitational waves induced from primordial curvature perturbations with non-Gaussianity
• Scalar-Induced Gravitational Waves in Modified Gravity
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity