Constraints on Scalar and Tensor spectra from $N_{eff}$

Abstract

At the linear level, the gravitational wave (GW) spectrum predicted by inflation, and many of its alternatives, can have arbitrarily small amplitude and consequently an unconstrained tilt. However, at second order, tensor fluctuations are sourced by scalar fluctuations that have been measured in the cosmic microwave background (CMB). These second order fluctuations generically produce a minimum amount of tensor perturbations corresponding to a tensor-to-scalar ratio of $r\sim 10^{-6}$. Inverting this relationship yields a bound on the tensor tilt sourced by scalar fluctuations. Since this induced GW spectrum depends on the scalar spectrum, we derive a new indirect bound that involves \textit{all scales} of the scalar spectrum based on CMB observations. This bound comes from the constraint on the number of effective relativistic degrees of freedom, $N_{eff}$. We estimate the bound using current data, and the improvements expected by future CMB experiment. The bound forces the running and running of running to conform to standard slow-roll predictions of $\alpha ,\beta \lesssim (n_s-1{)}^2$, improving on current CMB measurements by an order of magnitude. This bound has further implications for the possibility of primordial black holes as dark matter candidates. Performing a likelihood analysis including this new constraint, we find that positive $\alpha$ and/or $\beta$ are disfavored at least at $1\sigma$. Finally, using bounds on the fractional energy density of gravitational waves today obtained by LIGO and the Pulsar Timing Array, we obtain a bound on the primordial scalar spectrum on these scales and give forecast for future measurements.

arXiv comment28 pages, 19 figures; Updated to conform to published version

References in corpus (31)

• Planck 2015 results. XIII. Cosmological parameters
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• The Simons Observatory: Science goals and forecasts
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• BICEP2 / Keck Array VI: Improved Constraints On Cosmology and Foregrounds When Adding 95 GHz Data From Keck Array
• Semianalytic Calculation of Gravitational Wave Spectrum Nonlinearly Induced from Primordial Curvature Perturbations
• BICEP2 / Keck Array x: Constraints on Primordial Gravitational Waves using Planck, WMAP, and New BICEP2/Keck Observations through the 2015 Season
• Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
• CMB-S4 Science Book, First Edition
• Steepest growth of the power spectrum and primordial black holes
• Upper Limits on the Stochastic Gravitational-Wave Background from Advanced LIGO's First Observing Run
• CMB polarization from secondary vector and tensor modes
• Probing the inflaton: Small-scale power spectrum constraints from measurements of the CMB energy spectrum
• Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum
• Improved constraints on the primordial power spectrum at small scales from ultracompact minihalos
• Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: implications for the early universe
• Observable Spectra of Induced Gravitational Waves from Inflation
• Cosmic Microwave Background Observables of Small Field Models of Inflation
• Towards a measurement of the spectral runnings
• Multi-wavelength constraints on the inflationary consistency relation
• Spectral distortions from the dissipation of tensor perturbations
• POLARBEAR-2: an instrument for CMB polarization measurements
• Gravitational Waves in Bouncing Cosmologies from Gauge Field Production
• Constraining the primordial power spectrum from SNIa lensing dispersion
• Constraints on small-scale cosmological fluctuations from SNe lensing dispersion
• Small field models with gravitational wave signature supported by CMB data
• Can power spectrum observations rule out slow-roll inflation?
• Likelihood analysis of small field polynomial models of inflation yielding a high Tensor-to-Scalar ratio
• Lensing dispersion of SNIa and small scales of the primordial power spectrum
• LOFAR, LEAP and beyond: Using next generation telescopes for pulsar astrophysics

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• Broken blue-tilted inflationary gravitational waves: a joint analysis of NANOGrav 15-year and BICEP/Keck 2018 data
• Inflation, the Hubble Tension and Early Dark Energy: an alternative overview
• Implications of the NANOGrav result on primordial gravitational waves in nonstandard cosmologies
• Probing The Early Universe Cosmology With NANOGrav: Possibilities and Limitations
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• Inflationary Potential as seen from Different Angles: Model Compatibility from Multiple CMB Missions
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