We calculate the frequency dependence of gravitational wave background arising at second order of cosmological perturbation theory due to mixing of tensor and scalar modes. The calculation of the induced gravitational background is performed for two special cases: for the power spectrum of scalar perturbations which has a peak at some scale and for the scalar spectrum predicted by the inflationary model with the running mass potential. We show that the amplitudes of the induced gravitational background, in the frequency region $\sim 10^{-3} - 10^3 $Hz, are effectively constrained by results of studies of primordial black hole production in early universe. We argue that though today's LIGO bound on ${\cal P}_{\cal R}(k)$ is weaker than the PBH one, Advanced LIGO will be able to set a stronger bound, and in future the ground-based interferometers of LIGO type will be suitable for obtaining constraints on PBH number density in the mass range $\sim 10^{11} - 10^{15}$ g.
We constrain the primordial gravitational waves from cosmic microwave background (CMB) and stochastic gravitational wave background (SGWB) observations. SGWB provides the latest way to explore the early universe and the cosmological evolution which can be reflected by primordial gravitational waves. We not only combine LIGO observations with CMB to measure primordial gravitational waves, but also forecast the potential abilities of the LISA detector and PTA projects. In the $Λ$CDM+$r$+$n_t$ model, the standard six parameters change slightly from SGWB observations. While the constraints on tens…
The rate of gravitational wave bursts from the mergers of massive primordial black holes in clusters is calculated. Such clusters of black holes can be formed through phase transitions in the early Universe. The central black holes in clusters can serve as the seeds of supermassive black holes in galactic nuclei. The expected burst detection rate by the LISA gravitational wave detector is estimated.
We explore the effect of relic gravitational waves on the primordial phase change from the quark-gluon plasma into the low density hadron gas that occurred approximately $10^{-5}$s after the beginning. We show that the gravitational wave, through doing work on the fluid, modulates the local volumes, causing a pressure modulation which either suppresses or boosts the bubble cavitation rate. The boosted rate is significant, implying that the phase transition could have occurred earlier than if this interaction is not considered.
We study the generation and evolution of second-order energy-density perturbations arising from primordial gravitational waves. Such "tensor-induced scalar modes" approximately evolve as standard linear matter perturbations and may leave observable signatures in the Large-Scale Structure of the Universe. We study the imprint on the matter power-spectrum of some primordial models which predict a large gravitational-wave signal at high frequencies. This novel mechanism in principle allows us to constrain or detect primordial gravitational waves by looking at specific features in the matter or ga…
One of the most promising ways of detecting primordial gravitational waves generated during inflation is to observe B-modes of polarization, generated by Thomson scattering after reionization, in the cosmic microwave background (CMB). Large scale foregrounds though are expected to be a major systematic issue, so -- in the event of a tentative detection -- an independent confirmation of large scale gravitational waves would be most welcome. Previous authors have suggested searching for the analogous mode of cosmic shear in weak lensing surveys but have shown that the signal to noise of this mod…
The orbital evolution of a binary system consisting of two primordial black hole clusters is investigated. Such clusters are predicted in some theoretical models with broken symmetry in the inflation Lagrangian. A cluster consists of the most massive central black hole surrounded by many smaller black holes. Similar to single primordial black holes, clusters can form gravitationally bounded pairs and merge during their orbital evolution. The replacement of single black holes by such clusters significantly changes the entire merger process and the final rate of gravitational wave bursts in some…
Unbiased Primordial Gravitational Wave Inference from the CMB with SMICA
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；CNRS-UCB International Research Laboratory, Centre Pierre Binétruy（法国国家科学研究中心-巴黎第十一大学国际联合实验室，皮埃尔·比内屈中心）
The today's energy density of the induced (second order) gravitational wave background in the frequency region $\sim 10^{-3} - 10^3$ Hz is constrained using the existing limits on primordial black hole production in the early Universe. It is shown, in particular, that at frequencies near $\sim 40$ Hz (which is the region explored by LIGO detector), the value of the induced part of $Ω_{GW}$ cannot exceed $(1-3)\times 10^{-7}$. The spread of values of the bound is caused by the uncertainty in parameters of the gravitational collapse of black holes.
We perform a consistent calculation of primordial black hole (PBH) mass spectrum and second-order induced gravitational wave (GW) background produced from primordial scalar perturbations in radiation era of the early Universe. It is shown that the maximal amplitudes of the second order GW spectrum that can be approached without conflicting with the PBH data do not depend significantly on the shape of primordial perturbation spectrum. The constraints on the GW background obtained in previous works are extended to a wider GW frequency range. We discuss the applicability of the currently availabl…
It is shown that small-scale magnetic fields present before recombination induce baryonic density inhomogeneities of appreciable magnitude. The presence of such inhomogeneities changes the ionization history of the Universe, which in turn decreases the angular scale of the Doppler peaks and increases Silk damping by photon diffusion. This unique signature could be used to (dis)prove the existence of primordial magnetic fields of strength as small as B~10^(-11) Gauss by upcoming cosmic microwave background observations.
Primordial black holes and secondary gravitational waves can be used to probe the small scale physics at very early time. For secondary gravitational waves produced after the horizon reentry, we derive an analytical formula for the time integral of the source and analytical behavior of the time dependence of the energy density of induced gravitational waves is obtained. By proposing a piecewise power law parametrization for the power spectrum of primordial curvature perturbations, we use the observational constraints on primordial black hole dark matter to obtain an upper bound on the power sp…
We propose a novel method to probe primordial gravitational waves by means of primordial black holes (PBHs). When the amplitude of primordial tensor perturbations on comoving scales much smaller than those relevant to Cosmic Microwave Background is very large, it induces scalar perturbations due to second-order effects substantially. If the amplitude of resultant scalar perturbations becomes too large, then PBHs are overproduced to a level that is inconsistent with a variety of existing observations constraining their abundance. This leads to upper bounds on the amplitude of initial tensor per…
Polarizations of primordial gravitational waves can be relevant when considering inflationary universe in modified gravity or when matter fields survive during inflation. Such polarizations have been discussed in the Bunch-Davies vacuum. Instead of taking into account dynamical generation of polarizations of gravitational waves, in this paper, we consider polarized initial states constructed from $SU(2)$ coherent states. We then evaluate the power spectrums of the primordial gravitational waves in the states.
The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it is consistent with many inflation models that can produce primordial black holes, such as nonminimal derivative coupling inflation, scalar-tensor inflation, Gauss-Bonnet inflation, and K/G inflation. The constraints from primordial black holes on the primordial curvature power spectrum with the broken power law form are obtained, where the fra…
We consider the stochastic background of gravitational waves produced during the radiation-dominated hot big bang as a constraint on the primordial density perturbation on comoving length scales much smaller than those directly probed by the cosmic microwave background or large-scale structure. We place weak upper bounds on the primordial density perturbation from current data. Future detectors such as BBO and DECIGO will place much stronger constraints on the primordial density perturbation on small scales.
Primordial gravitational waves with extremely low frequency are expected to origin from inflation in the early Universe. The detection of such kind of gravitational waves is of great significance to verify the inflationary theory and determine the energy scale of inflation. B-mode of polarization of cosmic microwave background shows to be a promising probe of extremely low frequency primordial gravitational wave. In order to find a complementary observational feature induced by primordial gravitational wave with extremely low frequency, we propose an alternative way of detection by investigati…
Composite Hybrid Inflation : Primordial Black Holes and Stochastic Gravitational Waves
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Yonsei University（延世大学）；Université Claude Bernard Lyon 1（里昂第一大学）；IP2I（伊恩·皮埃尔·加朗物理研究所）；University of Johannesburg（约翰内斯堡大学）；Korea Institute for Advanced Study（韩国高等研究院）；Kavli Institute for the Physics and Mathematics of the Universe（卡弗里宇宙物理学和数学研究所）；The University of Tokyo（东京大学）；Tongji University（同济大学）
There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $α$-attractors and nonminimal derivative coupling i…
There exist two kinds of stochastic gravitational-wave backgrounds associated with the primordial curvature perturbations. One is called induced gravitational wave due to the nonlinear coupling of curvature perturbations to tensor perturbations, while the other is produced by coalescences of binary primordial black holes formed when the large amplitude curvature perturbations reenter the horizon in the radiation dominant era. In this paper we find a quite useful relation for the peak frequencies of these two stochastic gravitational-wave backgrounds. This relation can not only offer a smoking-…
The gravitational waves measured at LIGO are presumed here to come from merging primordial black holes. We ask how these primordial black holes could arise through inflationary models while not conflicting with current experiments. Among the approaches that work, we investigate the opportunity for corroboration through experimental probes of gravitational waves at pulsar timing arrays. We provide examples of theories that are already ruled out, theories that will soon be probed, and theories that will not be tested in the foreseeable future. The models that are most strongly constrained are th…
We consider the primordial gravity wave background produced by inflation. We compute the small anisotropy produced by the primordial scalar fluctuations.
With the enhancement mechanism provided by a noncanonical kinetic term with a peak, the amplitude of primordial curvature perturbations can be enhanced by seven orders of magnitude at small scales while keeping to be consistent with observations at large scales. The peak function and inflationary potential are not restricted in this mechanism. We use the Higgs model and T-model as examples to show how abundant primordial black hole dark matter with different mass and scalar induced secondary gravitational waves with different peak frequency are generated. We also show that the enhanced power s…
A cosmological gauge field with isotropic stress-energy introduces parity violation into the behavior of gravitational waves. We show that a primordial spectrum of inflationary gravitational waves develops a preferred handedness, left- or right-circularly polarized, depending on the abundance and coupling of the gauge field during the radiation era. A modest abundance of the gauge field would induce parity-violating correlations of the cosmic microwave background temperature and polarization patterns that could be detected by current and future experiments.
Primordial Gravitational Waves are the next target of modern cosmology. They represent a window on the early Universe and the only probe of the physics and microphysics of the inflationary period. When the production of GWs happens in scenarios richer than the standard single-field slow-roll, the GW signal becomes potentially detectable also on scales smaller than the Cosmic Microwave Background. LISA will be extremely complementary to CMB experiments to extract information about primordial inflationary models and in particular to probe phases of the inflationary period for which we have very …
We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho${\rm\check{r}}$ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.
We investigate the stochastic gravitational wave background produced by primordial black hole binaries during their early inspiral stage while accreting high-density radiation surrounding them in the early universe. We first show that the gravitational wave amplitude produced from a primordial black hole binary has correction terms because of the rapid rate of increase in masses of the primordial black holes. These correction terms arise due to non-vanishing first and second time derivatives of the masses and their contribution to the overall second time derivative of quadrupole moment tensor.…
Phase transitions in the early universe can readily create an observable stochastic gravitational wave background. We show that such a background necessarily contains anisotropies analogous to those of the cosmic microwave background (CMB) of photons, and that these too may be within reach of proposed gravitational wave detectors. Correlations within the gravitational wave anisotropies and their cross-correlations with the CMB can provide new insights into the mechanism underlying primordial fluctuations, such as multi-field inflation, as well as reveal the existence of non-standard ``hidden s…
Proposed space-based gravitational-wave (GW) detectors such as DECIGO and BBO will detect ~10^6 neutron-star (NS) binaries and determine the luminosity distances to the binaries with high precision. Combining the luminosity distances with cosmologically-induced phase corrections on the GWs, cosmological expansion out to high redshift can be measured without the redshift determinations of host galaxies by electromagnetic observation and be a unique probe for dark energy. On the other hand, such a NS-binary foreground should be subtracted to detect primordial GWs produced during inflation. Thus,…
Assuming that primordial black holes compose a fraction of dark matter, some of them may accumulate at the center of galaxy and perform a prograde or retrograde orbit against the gravity pointing towards the center exerted by the central massive black hole. If the mass of primordial black holes is of the order of stellar mass or smaller, such extreme mass ratio inspirals can emit gravitational waves and form a background due to incoherent superposition of all the contributions of the Universe. We investigate the stochastic gravitational-wave background energy density spectra from the direction…
Stochastic background of gravitational waves (GW) generated by the interactions between primordial black holes (PBH) in the early universe and by PBH evaporation is considered. If PBHs dominated in the cosmological energy density prior to their evaporation, GWs from the earlier stages (e.g. inflation) would be noticeably diluted. On the other hand, at the PBH dominance period they could form dense clusters where PBH binary formation might be significant. These binaries would be efficient sources of the gravitational waves.
Recent Advanced LIGO detections of binary black hole mergers have prompted multiple studies investigating the possibility that the heavy GW150914 binary system was of primordial origin, and hence could be evidence for dark matter in the form of black holes. We compute the stochastic background arising from the incoherent superposition of such primordial binary black hole systems in the universe and compare it to the similar background spectrum due to binary black hole systems of stellar origin. We investigate the possibility of detecting this background with future gravitational wave detectors…
Recently we have proposed a novel method to probe primordial gravitational waves from upper bounds on the abundance of primordial black holes (PBHs). When the amplitude of primordial tensor perturbations generated in the early Universe is fairly large, they induce substantial scalar perturbations due to their second-order effects. If these induced scalar perturbations are too large when they reenter the horizon, then PBHs are overproduced, their abundance exceeding observational upper limits. That is, primordial tensor perturbations on superhorizon scales can be constrained from the absence of…
We study the formation of primordial black holes and the generation of gravitational waves in a class of cosmological models that are direct supersymmetric analogs of the observationally favored nonminimally coupled Higgs inflation model. It is known that this type of model naturally includes multiple scalar fields which may be regarded as the inflaton. For the sake of simplicity we focus on the case where the inflaton field space is two dimensional. We analyze the multifield dynamics and find the region of parameters that gives copious production of primordial black holes that may comprise a …
We investigate a new mechanism to create large curvature perturbations on small scales due to parameter resonance in a single-field inflationary model with a small periodic structure upon the potential. After reentering the horizon, the amplified curvature perturbations can lead to observable primordial black holes as well as stochastic gravitational waves. The mass of primordial black holes and frequency of the induced gravitational waves depend on the model parameters. The resulted primordial black hole could constitute all dark matter or a fraction of dark matter in the universe, and corres…
The General Relativity affirms that any field is a source of gravitational field, thus one should affirm that the energy of Cosmic Microwave Background (CMB) generated primordial gravitational waves. The present article shows that a gravitational wave with dimensionless amplitude $\sim 10^{-5}$ and large wave length $\sim 10$ megaparsecs shifts temperature of CMB radiation about of a part in $10^{5}$.
The spectrum of primordial gravitational waves (GWs), especially its tilt $n_T$, carries significant information about the primordial universe. Combining recent aLIGO and Planck2015+BK14 data, we find that the current limit is $n_T=0.016^{+0.614}_{-0.989}$ at 95% C.L. We also estimate the impacts of Einstein Telescope and LISA on constraining $n_T$. Moreover, based on the effective field theory of cosmological perturbations, we make an attempt to confront some models of early universe scenarios, which produce blue-tilted GWs spectrum ($n_T>0$), with the corresponding datasets.
We simulate the evolution of a dust universe from $z=1089$ to $z=0$ by numerically integrating the Einstein's equation for a spatially flat Friedmann-Lemaire-Robertson-Walker (FLRW) background spacetime with scalar perturbations which are derived from the matter power spectrum produced with the Code for Anisotropies in the Microwave Background (CAMB). To investigate the effects of primordial gravitational waves (GWs) on the inhomogeneity of the universe, we add an additional decaying, divergenceless and traceless primordial tensor perturbation with its initial amplitude being $3\times 10^{-4}$…
Primordial black hole (PBH) mergers have been proposed as an explanation for the gravitational wave events detected by the LIGO collaboration. Such PBHs may be formed in the early Universe as a result of the collapse of extremely rare high-sigma peaks of primordial fluctuations on small scales, as long as the amplitude of primordial perturbations on small scales is enhanced significantly relative to the amplitude of perturbations observed on large scales. One consequence of these small-scale perturbations is generation of stochastic gravitational waves that arise at second order in scalar pert…
We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for full frequency range with assumption that the phase transition between two consecutive regimes to be abrupt during evolution of the Universe. The suppression of energy spectrum is found in our model for the decreasing frequency of gravitational waves depending on the model parameter. To realize the suppression of energy spectrum of the primordial gravitational wav…
The next generation of gravitational-wave experiments, such as Einstein Telescope, Cosmic Explorer and LISA, will test the primordial black hole scenario. We provide a forecast for the minimum testable value of the abundance of primordial black holes as a function of their masses for both the unclustered and clustered spatial distributions at formation. In particular, we show that these instruments may test abundances, relative to the dark matter, as low as $10^{-10}$.
Compared to primordial perturbations on large scales, roughly larger than $1$ megaparsec, those on smaller scales are not severely constrained. We revisit the issue of probing small-scale primordial perturbations using gravitational waves (GWs), based on the fact that, when large-amplitude primordial perturbations on small scales exist, GWs with relatively large amplitudes are induced at second order in scalar perturbations, and these induced GWs can be probed by both existing and planned gravitational-wave projects. We use accurate methods to calculate these induced GWs and take into account …
We devise a novel mechanism and for the first time demonstrate that the Higgs model in particle physics can drive the inflation to satisfy the cosmic microwave background observations and simultaneously enhance the curvature perturbations at small scales to explain the abundance of dark matter in our universe in the form of primordial black holes. The production of primordial black holes is accompanied by the secondary gravitational waves induced by the first order Higgs fluctuations which is expected observable by space-based gravitational wave detectors. We propose possible cosmological prob…
Advanced LIGO's discovery of gravitational-wave events is stimulating extensive studies on the origin of binary black holes. Assuming that the gravitational-wave events can be explained by binary primordial black hole mergers, we utilize the upper limits on the stochastic gravitational-wave background given by Advanced LIGO as a new observational window to independently constrain the abundance of primordial black holes in dark matter. We show that Advanced LIGO's first observation run gives the best constraint on the primordial black hole abundance in the mass range $1 M_\odot \lesssim M_\text…
