Gravitational Wave Constraints Research Articles

Gravitational-Wave Constraints on the Abundance of Primordial Black Holes

We thank T. Suyama for helpful comments. Top: The energy density of the induced GWs for the power spectrum for a peak width, Δ = 0.0, 1.0 × 10−3, 1.0 × 10−1, 1.0. Bottom: Energy density of scalar-induced GWs associated with PBH formation together with current pulsar constraint (thick solid line segment) and sensitivity of various GW detectors (convex curves). Solid wedged lines indicate the energy density with the parameters (ΩPBHh2, MPBH) = (10−5, 102M⊙) (left), (10−1, 1020g) (right) for sufficiently small Δ (thick lines) and Δ = 1.0 (thin lines).

Multi-field DBI inflation: introducing bulk forms and revisiting the gravitational wave constraints

We study multi-field Dirac-Born-Infeld (DBI) inflation models, taking into account the NS-NS and R-R bulk fields present in generic flux compactifications. We compute the second-order action, which governs the behaviour of linear cosmological perturbations, as well as the third-order action, which can be used to calculate non-Gaussianities in these models. Remarkably, for scalar-type perturbations, we show that the contributions due to the various form fields exactly cancel in both the second- and third-order actions. Primordial perturbations and their non-Gaussianities are therefore unaffected by the presence of form fields and our previous results are unmodified. We also study vector-type perturbations associated with the U(1) gauge field confined on the D3-brane, and discuss whether their quantum fluctuations can be amplified. Finally, we revisit the gravitational wave constraints on DBI inflation and show that an ultra-violet DBI multi-field scenario is still compatible with data, in contrast with the single field case, provided there is a transfer from entropy into adiabatic perturbations.

Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: Implications for the early universe

We derive a general equation relating the gravitational-wave observables $r$ and ${\ensuremath{\Omega}}_{0}^{\mathrm{gw}}(f)$; or the observables ${\ensuremath{\Omega}}_{0}^{\mathrm{gw}}({f}_{1})$ and ${\ensuremath{\Omega}}_{0}^{\mathrm{gw}}({f}_{2})$. Here, $r$ is the so-called ``tensor-to-scalar ratio,'' which is constrained by cosmic-microwave-background experiments; and ${\ensuremath{\Omega}}_{0}^{\mathrm{gw}}(f)$ is the energy spectrum of primordial gravitational waves, which is constrained, e.g., by pulsar-timing measurements, laser-interferometer experiments, and the standard big bang nucleosynthesis bound. Differentiating this equation yields a new expression for the tilt $d\mathrm{ln}{\ensuremath{\Omega}}_{0}^{\mathrm{gw}}(f)/d\mathrm{ln}f$ of the present-day gravitational-wave spectrum. The relationship between $r$ and ${\ensuremath{\Omega}}_{0}^{\mathrm{gw}}(f)$ depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities: $\stackrel{^}{w}(f)$ and ${\stackrel{^}{n}}_{t}(f)$, where ${\stackrel{^}{n}}_{t}(f)$ is a certain logarithmic average over ${n}_{t}(k)$ (the primordial tensor spectral index); and $\stackrel{^}{w}(f)$ is a certain logarithmic average over $\stackrel{\texttildelow{}}{w}(a)$ (the effective equation-of-state parameter in the early universe, after horizon re-entry). Here, the effective equation-of-state parameter $\stackrel{\texttildelow{}}{w}(a)$ is a combination of the ordinary equation-of-state parameter $w(a)$ and the bulk viscosity $\ensuremath{\zeta}(a)$. Thus, by comparing observational constraints on $r$ and ${\ensuremath{\Omega}}_{0}^{\mathrm{gw}}(f)$, one obtains (remarkably tight) constraints in the ${\stackrel{^}{w}(f),{\stackrel{^}{n}}_{t}(f)}$ plane. In particular, this is the best way to constrain (or detect) the presence of a stiff energy component (with $w>1/3$) in the early universe, prior to big bang nucleosynthesis. (The discovery of such a component would be no more surprising than the discovery of a tiny cosmological constant at late times!) Finally, although most of our analysis does not assume inflation, we point out that if cosmic-microwave-background experiments detect a nonzero value for $r$, then we will immediately obtain (as a free by-product) a new upper bound $\stackrel{^}{w}\ensuremath{\lesssim}0.55$ on the logarithmically averaged effective equation-of-state parameter during the ``primordial dark age'' between the end of inflation and the start of big bang nucleosynthesis.

Gravitational wave constraints on multi-brane inflation

A class of non-canonical inflationary models is identified, where the leading-ordercontribution to the non-Gaussianity of the curvature perturbation is determined bythe sound speed of the fluctuations in the inflaton field. Included in this classof models is the effective action for multiple coincident branes in the finiten limit. The action for this configuration is determined using a powerfuliterative technique, based upon the fundamental representation ofSU(2). In principle the upper bounds on the tensor–scalar ratio that arise in the standard,single-brane DBI inflationary scenario can be relaxed in such multi-brane configurations if alarge and detectable non-Gaussianity is generated. Moreover models with a small numberof coincident branes could generate a gravitational wave background that will be observablein future experiments.

Gravitational wave constraints on Dirac–Born–Infeld inflation

An upper bound on the amplitude of the primordial gravitational wave spectrumgenerated during ultra-violet Dirac–Born–Infeld (DBI) inflation is derived. The boundis insensitive to the form of the inflaton potential and the warp factor of thecompactified dimensions and can be expressed entirely in terms of observationalparameters once the volume of the five-dimensional sub-manifold of the throathas been specified. For standard type-IIB compactification schemes, the boundpredicts undetectably small tensor perturbations with a tensor–scalar ratior<10−7. This is incompatible with a corresponding lower limit ofr>0.1(1−ns), which applies to any model that generates a red spectral indexns<1 and a potentially detectable non-Gaussianity in the curvature perturbation. Possible waysof evading these bounds in more general DBI-type scenarios are discussed and amultiple-brane model is investigated as a specific example.

Dark synergy: Gravitational lensing and the CMB

Power spectra and cross-correlation measurements from the weak gravitational lensing of the cosmic microwave background (CMB) and the cosmic shearing of faint galaxies images will help shed light on quantities hidden from the CMB temperature anisotropies: the dark energy, the end of the dark ages, and the inflationary gravitational wave amplitude. Even with modest surveys, both types of lensing power spectra break CMB degeneracies and they can ultimately improve constraints on the dark energy equation of state w by over an order of magnitude. In its cross correlation with the integrated Sachs-Wolfe effect, CMB lensing offers a unique opportunity for a more direct detection of the dark energy and enables study of its clustering properties. By obtaining source redshifts and cross-correlations with CMB lensing, cosmic shear surveys provide tomographic handles on the evolution of clustering and correspondingly better precision on the dark energy equation of state and density. Both can indirectly provide detections of the reionization optical depth and modest improvements in gravitational wave constraints which we compare to more direct constraints. Conversely, polarization B-mode contamination from CMB lensing, like any other residual foreground, darkens the prospects for ultrahigh precision on gravitational waves through CMB polarization requiring large areas of sky for statistical subtraction. To evaluate these effects we provide a fitting formula for the evolution and transfer function of the Newtonian gravitational potential.

Gravitational wave constraints on post-inflationary phases stiffer than radiation

We point out that the existence of post-inflationary phases stiffer than radiation leads to the production of stochastic gravitational wave (GW) backgrounds whose logarithmic energy spectra (in critical units) are typically ``blue'' at high frequencies. The maximal spectral slope (for present frequencies larger than ${10}^{\ensuremath{-}16}$ Hz) is of order 1 and is related to the maximal sound velocity of the stiff plasma governing the evolution of the geometry. The duration of the stiff phase is crucially determined by the back reaction of the GW leaving the horizon during the de Sitter phase and reentering during the stiff phase. Therefore, the maximal (inflationary) curvature scale has to be fine-tuned to a value smaller than the limits set by the large scale measurements ${(H}_{\mathrm{dS}}\ensuremath{\lesssim}{10}^{\ensuremath{-}6} {M}_{P})$ in order to have a sufficiently long stiff phase reaching an energy scale of the order of $1 \mathrm{TeV}$ and even lower if we want the stiff phase to touch the hadronic era (corresponding to ${T}_{\mathrm{had}}\ensuremath{\sim}140 \mathrm{MeV}).$ By looking more positively at our exercise we see that, if an inflationary phase is followed by a stiff phase, there exists the appealing possibility of ``graviton reheating'' whose effective temperature can be generally quite low.

LARGE SCALE STRUCTURE BY GLOBAL MONOPOLES AND COLD DARK MATTER

A cosmological model in which the primordial perturbations are provided by global monopoles and in which the dark matter is cold has several interesting features. The model is normalized by choosing its single parameter within the bounds obtained from gravitational wave constraints and by demanding coherent velocity flows of about 600 km/sec on scales of 50h-1 Mpc . Using this normalization, the model predicts the existence of dominant structures with mass 2×1016M⊙ on a scale 35h-1 Mpc , i.e., larger than the horizon at t ep . The magnitude of the predicted mass function in the galactic mass range is in good agreement with the observed Schechter function.