Measuring the spectrum of primordial gravitational waves with CMB, PTA and Laser Interferometers
Paolo Campeti, Eiichiro Komatsu, Davide Poletti, Carlo Baccigalupi
备注：
Accepted in JCAP. Improved treatment of foregrounds for interferometers and more realistic analytical formula for $Ω_{GW}$. Python code to reproduce figures is available at the link https://github.com/pcampeti/SGWBProbe
We investigate the possibility of measuring the primordial gravitational wave (GW) signal across 21 decades in frequencies, using the cosmic microwave background (CMB), pulsar timing arrays (PTA), and laser and atomic interferometers. For the CMB and PTA experiments we consider the LiteBIRD mission and the Square Kilometer Array (SKA), respectively. For the interferometers we consider space mission proposals including the Laser Interferometer Space Antenna (LISA), the Big Bang Observer (BBO), the Deci-hertz Interferometer Gravitational wave Observatory (DECIGO), the $μ$Ares experiment, the Decihertz Observatory (DO), and the Atomic Experiment for Dark Matter and Gravity Exploration in Space (AEDGE), as well as the ground-based Einstein Telescope (ET) proposal. We implement the mathematics needed to compute sensitivities for both CMB and interferometers, and derive the response functions for the latter from the first principles. We also evaluate the effect of the astrophysical foreground contamination in each experiment. We present binned sensitivity curves and error bars on the energy density parameter, $Ω_{GW}h^2$, as a function of frequency for two representative classes of models for the stochastic background of primordial GW: the quantum vacuum fluctuation in the metric from single-field slow-roll inflation, and the source-induced tensor perturbation from the spectator axion-SU(2) inflation models. We find excellent prospects for joint measurements of the GW spectrum by CMB and space-borne interferometers mission proposals.
Many recent works have shown that the angular resolution of ground-based detectors is too poor to characterize the anisotropies of the stochastic gravitational-wave background (SGWB). For this reason, we asked ourselves if a constellation of space-based instruments could be more suitable. We consider the Laser Interferometer Space Antenna (LISA), a constellation of multiple LISA-like clusters, and the Deci-hertz Interferometer Gravitational-wave Observatory (DECIGO). Specifically, we test whether these detector constellations can probe the anisotropies of the SGWB. For this scope, we considere…
Measuring the B modes of the CMB polarization fluctuations would provide very strong constraints on inflation. The main challenge in this measurement is the treatment of systematic effects. CMB observations with imagers and interferometers, subject to very different systematics, are complementary in this respect. Interferometry provides direct access to the Fourier transform of the sky signal. In bolometric interferometry, the interference pattern produced by the sky through a few hundred horns is imaged on a bolometer array. Several such modules are needed to achieve the required sensitivity.…
We investigate whether an Early-Universe stochastic gravitational-wave background (SGWB) can account for the common spectrum process reported by NANOGrav, while also being consistent with current and projected CMB measurements of extra radiation. We compute the contribution of effective number of relativistic species, $ΔN_{eff}$, for a number of Early-Universe models proposed to explain the pulsar timing array (PTA) spectrum. We demonstrate that models predicting $ΔN_{eff}$ above the CMB limit would be firmly excluded, implying that the NANOGrav signal in tension with these bounds must instead…
The black hole merging rates inferred after the gravitational-wave detection by Advanced LIGO/VIRGO and the relatively high mass of the progenitors are consistent with models of dark matter made of massive primordial black holes (PBH). PBH binaries emit gravitational waves in a broad range of frequencies that will be probed by future space interferometers (LISA) and pulsar timing arrays (PTA). The amplitude of the stochastic gravitational-wave background expected for PBH dark matter is calculated taking into account various effects such as initial eccentricity of binaries, PBH velocities, mass…
A detection of B-mode polarization of the Cosmic Microwave Background (CMB) anisotropies would confirm the presence of a primordial gravitational wave background (GWB). In the inflation paradigm this would be an unprecedented probe of the energy scale of inflation as it is directly proportional to the power spectrum of the GWB. However, similar tensor perturbations can be produced by the matter fields present during inflation, breaking this simple relationship. It is therefore important to be able to distinguish between different generation mechanisms of the GWB. In this paper, we analyse the …
In the non-standard model of relic gravitational waves (RGWs) generated in the early universe, the theoretical spectrum of is mainly described by an amplitude $r$ and a spectral index $β$, the latter usually being determined by the slope of the inflation potential. Pulsar timing arrays (PTAs) data have imposed constraints on the amplitude of strain spectrum for a power-law form as a phenomenological model. Applying these constraints to a generic, theoretical spectrum with $r$ and $β$ as independent parameters, we convert the PTAs constraint into an upper bound on the index $β$, which turns out…
Probing small-scale anisotropic inflation with stochastic gravitational-wave background
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院量子联合研究中心及物理系）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础科学与数学学院）
The NANOGrav collaboration for the pulsar timing array (PTA) observation recently announced evidence of an isotropic stochastic process, which may be the first detection of the stochastic gravitational-wave (GW) background. We discuss the possibility that the signal is caused by the second-order GWs associated with the formation of solar-mass primordial black holes (PBHs). This possibility can be tested by future interferometer-type GW observations targeting the stochastic GWs from merger events of solar-mass PBHs as well as by updates of PTA observations.
Measurements of the 2.7 K cosmic microwave background (CMB) radiation now provide the most stringent constraints on cosmological models. The power spectra of the temperature anisotropies and the $E$-mode polarization of the CMB are explained well by the inflationary paradigm. The next generation of CMB experiments aim at providing the most direct evidence for inflation through the detection of $B$-modes in the CMB polarization, presumed to have been caused by gravitational waves generated during the inflationary epoch around $10^{-34}$s. The $B$-mode polarization signals are very small ($\leq$…
PTA-Compatible Domain Walls at LISA and Taiji: Bayesian Reconstruction and Multiband Inference
Nanjing Normal University（南京师范大学）；Scuola Superiore Meridionale, Università degli studi di Napoli “Federico II”（那不勒斯费德里科二世大学南方高等学院）；INFN - Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
We describe a method for forecasting errors in interferometric measurements of polarization of the cosmic microwave background (CMB) radiation, based on the use of the Fisher matrix calculated from the visibility covariance and relation matrices. In addition to noise and sample variance, the method can account for many kinds of systematic error by calculating an augmented Fisher matrix, including parameters that characterize the instrument along with the cosmological parameters to be estimated. The method is illustrated with examples of gain errors and errors in polarizer orientation. The augm…
Models of inflation based on axions, which owe their popularity to the robustness against UV corrections, have also a very distinct class of signatures. The relevant interactions of the axion are a non-perturbative oscillating contribution to the potential and a shift-symmetric coupling to gauge fields. We review how these couplings affect the cosmological perturbations via a unified study based on the in-in formalism. We then note that, when the inflaton coupling to gauge fields is high enough to lead to interesting observational results, the backreaction of the produced gauge quanta on the i…
Interferometry has been a very successful tool for measuring anisotropies in the cosmic microwave background. Interferometers provided the first constraints on CMB anisotropies on small angular scales (l~10000) in the 1980s and then in the late 1990s and early 2000s made ground-breaking measurements of the CMB power spectrum at intermediate and small angular scales covering the l-range ~100-4000. In 2002 the DASI made the first detection of CMB polarization which remains a major goal for current and future CMB experiments. Interferometers have also made major contributions to the detection and…
We study future observational constraints on cosmic string parameters from various types of next-generation experiments: direct detection of gravitational waves (GWs), pulsar timing array, and the cosmic microwave background (CMB). We consider both GW burst and stochastic GW background searches by ground- and space-based interferometers as well as GW background detection in pulsar timing experiments. We also consider cosmic string contributions to the CMB temperature and polarization anisotropies. These different types of observations offer independent probes of cosmic strings and may enable u…
General relativity (GR) predicts concordant trajectories for photons and gravitational waves (GW). We propose a new multi-messenger avenue (GW-CMB-CMB) to prove this aspect of fundamental physics by cross-correlating the GW signal of astrophysical origin with the lensing field derived from the cosmic microwave background (CMB). This new window will allow robust measurement of the prediction from GR with high signal-to-noise and will be able to unveil the true nature of gravity using the GW sources detected by missions such as the Laser Interferometer Space Antenna (LISA), Einstein Telescope an…
A stochastic background of primordial gravitational waves could be detected soon in the polarization of the CMB and/or with laser interferometers. There are at least three GWB coming from inflation: those produced during inflation and associated with the stretching of space-time modes; those produced at the violent stage of preheating after inflation; and those associated with the self-ordering of Goldstone modes if inflation ends via a global symmetry breaking scenario, like in hybrid inflation. Each GW background has its own characteristic spectrum with specific features. We discuss the pros…
Chromo-natural inflation (CNI) is an inflationary model where an axion coupled with SU$(2)$ gauge fields acts as the inflaton. In CNI, the gauge fields have nonzero vacuum expectation values (VEVs), which results in the enhancement of gravitational waves (GWs). The original CNI is ruled out by the Planck observations due to the overproduction of GWs. In this work, we consider an inflationary model where the gauge fields acquire nonzero VEVs after the CMB modes exit the horizon. Moreover, we add to the model another field that dominates the universe and drives inflation after the axion starts t…
Massive black-hole binaries, formed when galaxies merge, are among the primary sources of gravitational waves targeted by ongoing Pulsar Timing Array (PTA) experiments and the upcoming space-based LISA interferometer. However, their formation and merger rates are still highly uncertain. Recent upper limits on the stochastic gravitational-wave background obtained by PTAs are starting being in marginal tension with theoretical models for the pairing and orbital evolution of these systems. This tension can be resolved by assuming that these binaries are more eccentric or interact more strongly wi…
Gravitational waves coming from Super Massive Black Hole Binaries (SMBHBs) are targeted by both Pulsar Timing Array (PTA) and Space Laser Interferometry (SLI). The possibility of a single SMBHB being tracked first by PTA, through inspiral, and later by SLI, up to merger and ring down, has been previously suggested. Although the bounding parameters are drawn by the current PTA or the upcoming Square Kilometer Array (SKA), and by the New Gravitational Observatory (NGO), derived from the Laser Interferometer Space Antenna (LISA), this paper also addresses sequential detection beyond specific proj…
With an energy scale that can be as high as $10^{14}\,{\rm GeV}$, inflation may provide a unique probe of high-energy physics. Both scalar and tensor fluctuations generated during this early accelerated expansion contain crucial information about the particle content of the primordial universe. The advent of ground- and space-based interferometers enables us to probe primordial physics at length-scales much smaller than those corresponding to current CMB constraints. One key prediction of single-field slow-roll inflation is a red-tilted gravitational wave spectrum, currently inaccessible at in…
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…
A Unified Origin of Primordial Black Hole Dark Matter and Nanohertz Gravitational Waves
Leibniz University Hannover（汉诺威莱布尼茨大学）；Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut（马克斯·普朗克引力物理学研究所，阿尔伯特·爱因斯坦研究所）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙物质与宇宙学 Kavli 前沿研究所（WPI））；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Physics, Kyoto University（京都大学物理系）
Current bounds from the polarization of the CMB predict the scale-invariant gravitational wave (GW) background of inflation to be out of reach for upcoming GW interferometers. This prospect dramatically changes if the inflaton is a pseudoscalar, in which case its generic coupling to any abelian gauge field provides a new source of GWs, directly related to the dynamics of inflation. This opens up new ways of probing the scalar potential responsible for cosmic inflation. Dividing inflation models into universality classes, we analyze the possible observational signatures. One of the most promisi…
We study the effects of pre-recombination physics on the Stochastic Gravitational Wave Background (SGWB) anisotropies induced by the propagation of gravitons through the large-scale density perturbations and their cross-correlation with Cosmic Microwave Background (CMB) temperature and E-mode polarization ones. As examples of Early Universe extensions to the $Λ$CDM model, we consider popular models featuring extra relativistic degrees of freedom, a massless non-minimally coupled scalar field, and an Early Dark Energy component. Assuming the detection of a SGWB, we perform a Fisher analysis to …
QUBIC (Q \& U Bolometric Interferometer for Cosmology) is an international ground-based experiment dedicated in the measurement of the polarized fluctuations of the Cosmic Microwave Background (CMB). It is based on bolometric interferometry, an original detection technique which combine the immunity to systematic effects of an interferometer with the sensitivity of low temperature incoherent detectors. QUBIC will be deployed in Argentina, at the Alto Chorrillos mountain site near San Antonio de los Cobres, in the Salta province. The QUBIC detection chain consists in 2048 NbSi Transition Edge S…
We revisit the possibility that the stochastic common-spectrum process recently detected by the NANOGrav pulsar timing array experiment could be due to primordial gravitational waves (GWs). A naïve extrapolation down to interferometer scales of the blue GW spectrum required to explain NANOGrav consistently with Cosmic Microwave Background (CMB) observations would strongly violate upper limits on the stochastic GW background (SGWB) amplitude from LIGO/Virgo. In combination with the fact that there are over 19 decades in frequency between CMB and interferometer scales, this motivates us to move …
We construct evolutionary tracks for massive black hole binaries (MBHBs) embedded in a surrounding distribution of stars. The dynamics of the binary is evolved by taking into account the erosion of the central stellar cusp bound to the massive black holes, the scattering of unbound stars feeding the binary loss cone, and the emission of gravitational waves (GWs). Stellar dynamics is treated in a hybrid fashion by coupling the results of numerical 3-body scattering experiments of bound and unbound stars to an analytical framework for the evolution of the stellar density distribution and for the…
Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data
a Service de Physique Th\'eorique, Brussels Laboratory of the Universe BLU-ULB, Universit\'e Libre de Bruxelles, Boulevard du Triomphe, CP225, 1050 Brussels, Belgium
We extend the reach of the ``cosmological collider'' for massive gauge boson production during inflation from the CMB scales to the interferometer scales. Considering a Chern-Simons coupling between the gauge bosons and the pseudoscalar inflaton, one of the transverse gauge modes is efficiently produced and its inverse decay leaves an imprint in the primordial scalar and tensor perturbations. We study the correlation functions of these perturbations and derive the updated constraints on the parameter space from CMB observables. We then extrapolate the tensor power spectrum to smaller scales co…
The BISOU (Balloon Interferometer for Spectral Observations of the Universe) project aims to study the viability and prospects of a balloon-borne spectrometer, pathfinder of a future space mission dedicated to the measurements of the CMB spectral distortions. We present here a preliminary concept based on previous space mission proposals, together with some sensitivity calculation results for the observation goals, showing that a 5-sigma measurement of the y-distortions is achievable.
Cosmic string networks offer one of the best prospects for detection of cosmological gravitational waves (GWs). The combined incoherent GW emission of a large number of string loops leads to a stochastic GW background (SGWB), which encodes the properties of the string network. In this paper we analyze the ability of the Laser Interferometer Space Antenna (LISA) to measure this background, considering leading models of the string networks. We find that LISA will be able to probe cosmic strings with tensions $Gμ\gtrsim \mathcal{O}(10^{-17})$, improving by about $6$ orders of magnitude current pu…
We consider inflation driven by an axion-like particle coupled to an SU(2) gauge sector via a Chern-Simons term. Known as chromo-natural inflation, this scenario is in tension with CMB observations. In order to remedy this fact and preserve both the symmetries and the intriguing gravitational wave phenomenology exhibited by the model, we explore the non-minimal coupling of the axion-inflaton to the Einstein tensor. We identify regions of parameter space corresponding to a viable cosmology at CMB scales. We also highlight the possibility of a large and chiral gravitational wave signal at small …
In many particle physics models, domain wall can form during the phase transition process after discrete symmetry breaking. We study the scenario within a complex singlet extended Standard Model framework, where a strongly first order phase transition can occur depending on the hidden scalar mass and the mixing between the extra heavy Higgs and the SM Higgs mass. The gravitational wave spectrum is of a typical two-peak shape, the amplitude and the peak from the strongly first order phase transition is able to be probed by the future space-based interferometers, and the one locates around the p…
Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early Universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs which are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs and thus we have several other probes to test this scenario. We point out that the cur…
We study the production of gravitational waves from primordial scalar perturbations in double-inflection-point inflation, in which one of the inflection points predicts the power spectra consistent with CMB observations at large scales and the other generates a large peak in the power spectrum of scalar perturbations at small scales. We find that the reduced gravitational waves at low frequencies can be detected by future space-based laser interferometers.
