The probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum

Considerable recent attention has focussed on the prospects to use the cosmic microwave background (CMB) trispectrum to probe the physics of the early universe. Here we evaluate the probability distribution function (PDF) for the standard estimator tau_nle for the amplitude tau_nl of the CMB trispectrum both for the null-hypothesis (i.e., for Gaussian maps with tau_nl = 0) and for maps with a non-vanishing trispectrum (|tau_nl|>0). We find these PDFs to be highly non-Gaussian in both cases. We also evaluate the variance with which the trispectrum amplitude can be measured, , as a function of its underlying value, tau_nl. We find a strong dependence of this variance on tau_nl. We also find that the variance does not, given the highly non-Gaussian nature of the PDF, effectively characterize the distribution. Detailed knowledge of these PDFs will therefore be imperative in order to properly interpret the implications of any given trispectrum measurement. For example, if a CMB experiment with a maximum multipole of lmax = 1500 (such as the Planck satellite) measures tau_nle = 0 then at the 95% confidence our calculations show that we can conclude tau_nl < 1005; assuming a Gaussian PDF but with the correct tau_nl-dependent variance we would incorrectly conclude tau_nl < 4225; further neglecting the tau_nl-dependence in the variance we would incorrectly conclude tau_nl < 361.Comment: 9 pages, 5 figure

LISA For Cosmologists: Calculating The Signal-To-Noise Ratio For Stochastic And Deterministic Sources

We present the steps to forecast the sensitivity of the Laser Interferometer Space Antenna (LISA) to both a stochastic gravitational wave background and deterministic wave sources. We show how to use these expressions to estimate the precision with which LISA can determine parameters associated with these sources. Tools are included to enable easy calculation of the signal-to-noise ratio and draw sensitivity curves. Benchmark values are given for easy comparison and checking of methods in the case of three worked examples. The first benchmark is the threshold stochastic gravitational wave background ΩGWh2 that LISA can observe. The second is the signal-to-noise ratio that LISA would observe for a binary black hole system identical to GW150914, radiating four years before merger. The third is the case of a monotone source, such as a binary that is far from merger

LISA For Cosmologists: Calculating The Signal-To-Noise Ratio For Stochastic And Deterministic Sources

We present the steps to forecast the sensitivity of the Laser Interferometer Space Antenna (LISA) to both a stochastic gravitational wave background and deterministic wave sources. We show how to use these expressions to estimate the precision with which LISA can determine parameters associated with these sources. Tools are included to enable easy calculation of the signal-to-noise ratio and draw sensitivity curves. Benchmark values are given for easy comparison and checking of methods in the case of three worked examples. The first benchmark is the threshold stochastic gravitational wave background ΩGWh2 that LISA can observe. The second is the signal-to-noise ratio that LISA would observe for a binary black hole system identical to GW150914, radiating four years before merger. The third is the case of a monotone source, such as a binary that is far from merger

Constraints on neutrino and dark radiation interactions using cosmological observations

Observations of the cosmic microwave background (CMB) and large-scale structure (LSS) provide a unique opportunity to explore the fundamental properties of the constituents that compose the cosmic dark radiation background (CDRB), of which the three standard neutrinos are thought to be the dominant component. We report on the first constraint to the CDRB rest-frame sound speed, ceff^2, using the most recent CMB and LSS data. Additionally, we report improved constraints to the CDRB viscosity parameter, cvis^2. For a non-interacting species, these parameters both equal 1/3. Using current data we find that a standard CDRB, composed entirely of three non-interacting neutrino species, is ruled out at the 99% confidence level (C.L.) with ceff^2 = 0.30 +0.027 -0.026 and cvis^2 = 0.44 +0.27 -0.21 (95% C.L.). We also discuss how constraints to these parameters from current and future observations (such as the Planck satellite) allow us to explore the fundamental properties of any anomalous radiative energy density beyond the standard three neutrinos.Comment: 6 pages, 3 figures, comments welcome; v2: updated with SPT data, corrected minor typos; v3: version accepted for publication in PR

Inflationary gravitational-wave background and measurements of the scalar spectral index

Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO), currently under study. In a previous paper [Phys. Rev. D 73, 023504 (2006)] we connected CMB constraints to the amplitude and tensor spectral tilt of the inflationary gravitational-wave background (IGWB) at BBO frequencies for four classes of models of inflation by directly solving the inflationary equations of motion. Here we extend that analysis by including results obtained in the Wilkinson Microwave Anisotropy Probe third-year data release as well as by considering two additional classes of inflationary models. As often noted in the literature, the recent indication that the primordial density power spectrum has a red spectral index implies (with some caveats) that the amplitude of the IGWB may be large enough to be observable in the CMB polarization. Here we also explore the implications for the direct detection of the IGWB

How Sound Are Our Ultralight Axion Approximations?

Ultralight axions (ULAs) are a promising dark-matter candidate. ULAs may have implications for small-scale challenges to the ΛCDM model and arise in string scenarios. ULAs are already constrained by cosmic microwave background (CMB) experiments and large-scale structure surveys, and will be probed with much greater sensitivity by future efforts. It is challenging to compute observables in ULA scenarios with sufficient speed and accuracy for cosmological data analysis because the ULA field oscillates rapidly. In past work, an effective fluid approximation has been used to make these computations feasible. Here this approximation is tested against an exact solution of the ULA equations, comparing the induced error of CMB observables with the sensitivity of current and future experiments. In the most constrained mass range for a ULA dark-matter component (10−27  eV≤max≤10−25  eV), the induced bias on the allowed ULA fraction of dark matter from Planck data is less than 1σ. In the cosmic-variance limit (including temperature and polarization data), the bias is ≲2σ for primary CMB anisotropies, with more severe biases (as high as ∼4σ) resulting for less reliable versions of the effective fluid approximation. If all of the standard cosmological parameters are fixed by other measurements, the expected bias rises to 4−20σ (well beyond the validity of the Fisher approximation), though the required level of degeneracy breaking will not be achieved by any planned surveys

Direct detection of the inflationary gravitational-wave background

Inflation generically predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO) or Japan's Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO), both currently under study. Here we investigate the detectability of the inflationary gravitational-wave background at BBO/DECIGO frequencies. To do so, we survey a range of slow-roll inflationary models consistent with constraints from the CMB and large-scale structure (LSS). We go beyond the usual assumption of power-law power spectra, which may break down given the 16 orders of magnitude in frequency between the CMB and direct detection, and solve instead the inflationary dynamics for four classes of inflaton potentials. Direct detection is possible in a variety of inflationary models, although probably not in any in which the gravitational-wave signal does not appear in the CMB polarization. However, direct detection by BBO/DECIGO can help discriminate between inflationary models that have the same slow-roll parameters at CMB/LSS scales

An improved estimator for non-Gaussianity in cosmic microwave background observations

An improved estimator for the amplitude fnl of local-type non-Gaussianity from the cosmic microwave background (CMB) bispectrum is discussed. The standard estimator is constructed to be optimal in the zero-signal (i.e., Gaussian) limit. When applied to CMB maps which have a detectable level of non-Gaussianity the standard estimator is no longer optimal, possibly limiting the sensitivity of future observations to a non-Gaussian signal. Previous studies have proposed an improved estimator by using a realization-dependent normalization. Under the approximations of a flat sky and a vanishingly thin last-scattering surface, these studies showed that the variance of this improved estimator can be significantly smaller than the variance of the standard estimator when applied to non-Gaussian CMB maps. Here this technique is generalized to the full sky and to include the full radiation transfer function, yielding expressions for the improved estimator that can be directly applied to CMB maps. The ability of this estimator to reduce the variance as compared to the standard estimator in the face of a significant non-Gaussian signal is re-assessed using the full CMB transfer function. As a result of the late time integrated Sachs-Wolfe effect, the performance of the improved estimator is degraded. If CMB maps are first cleaned of the late-time ISW effect using a tracer of foreground structure, such as a galaxy survey or a measurement of CMB weak lensing, the new estimator does remove a majority of the excess variance, allowing a higher significance detection of fnl.Comment: 21 pages, 7 figure