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Constraints on primordial gravitational waves from the Cosmic Microwave Background

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arxiv 2004.11396 v2 pith:YCUCBE4S submitted 2020-04-23 astro-ph.CO

classification astro-ph.CO
keywords gravitationalomegatextrmwavesconstraintsscalestimes10finding
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Searches for primordial gravitational waves have resulted in constraints in a large frequency range from a variety of sources. The standard Cosmic Microwave Background (CMB) technique is to parameterise the tensor power spectrum in terms of the tensor-to-scalar ratio, $r$, and spectral index, $n_{\rm t}$, and constrain these using measurements of the temperature and polarization power spectra. Another method, applicable to modes well inside the cosmological horizon at recombination, uses the shortwave approximation, under which gravitational waves behave as an effective neutrino species. In this paper we give model-independent CMB constraints on the energy density of gravitational waves, $\Omega_\textrm{gw} h^2$, for the entire range of observable frequencies. On large scales, $f \lesssim 10^{-16}\, \text{Hz}$, we reconstruct the initial tensor power spectrum in logarithmic frequency bins, finding maximal sensitivity for scales close to the horizon size at recombination. On small scales, $f \gtrsim10^{-15}\,\mbox{Hz}$, we use the shortwave approximation, finding $\Omega_\textrm{gw} h^2 < 1.7 \times10^{-6}$ for adiabatic initial conditions and $\Omega_\textrm{gw} h^2 < 2.9 \times10^{-7}$ for homogeneous initial conditions (both $2\sigma$ upper limits). For scales close to the horizon size at recombination, we use second-order perturbation theory to calculate the back-reaction from gravitational waves, finding $\Omega_\textrm{gw} h^2 < 8.4 \times10^{-7}$, in the absence of neutrino anisotropic stress and $\Omega_\textrm{gw} h^2 < 8.6 \times10^{-7}$ when including neutrino anisotropic stress. These constraints are valid for $ 10^{-15}\, \text{Hz} \gtrsim f \gtrsim 3 \times 10^{-16}\, \text{Hz}$.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Gravitational Waves as a Source of Large-Scale White Noise: New Constraints

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    A gravitational-wave background produced before z≈10^8 at pulsar-timing-array amplitudes would create observable white noise in the CMB, so such early backgrounds are ruled out.

  2. Searching Stochastic Gravitational Wave Background Landscape Across Frequency Bands

    gr-qc 2025-11 conditional novelty 5.0 of 10

    A hybrid cosmic string–domain wall model can fit the NANOGrav 15-year signal, and its high-frequency tail lies within LISA's projected reach, making the interpretation testable.

  3. Gravitational Waves from Primordial Black Holes formed by Null Energy Condition Violation during Inflation

    gr-qc 2026-02 conditional novelty 4.0 of 10

    A transient null-energy-condition violation during inflation is shown to produce a four-component gravitational-wave background — primordial, scalar-induced, PBH ringdown, and binary-merger — with only the solar-mass ...

  4. Tensor induced gravitational waves

    astro-ph.CO 2025-07 conditional novelty 4.0 of 10

    Second-order tensor-induced gravitational waves can shift the inferred parameters of small-scale primordial gravitational wave models fitted to NANOGrav 15-year data, with one model favored by Bayes factors.

  5. Effective Equation of State Oscillations at Matter-Radiation Equality and Primordial Gravitational Waves

    gr-qc 2025-07 reject novelty 4.0 of 10

    An exponentially deformed R^2 gravity model is claimed to produce total equation-of-state oscillations near z~3400 that enhance the primordial gravitational wave spectrum at LiteBIRD frequencies.

  6. Cosmological constraints on small-scale primordial non-Gaussianity

    astro-ph.CO 2025-05 conditional novelty 4.0 of 10

    Current pulsar-timing, CMB, BAO and PBH data constrain the small-scale local f_NL to -10.0 < f_NL < 1.2 for a monochromatic primordial power spectrum, with that constraint conditional on the spectral amplitude A_zeta = 10^-2.

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