Gravitational waves from warped spacetime

We calculate the gravitational wave spectrum generated by sound waves during a cosmological phase transition, incorporating several advancements beyond the current state-of-the-art. Rather than relying on the bag model or similar approximations, we derive the equation of state directly from the effective potential. This approach enables us to accurately determine the hydrodynamic quantities, which serve as initial conditions in a generalised hybrid simulation. This simulation tracks the fluid evolution after bubble collisions, leading to the generation of gravitational waves. Our work thus provides a self-consistent numerical calculation of gravitational waves for the real singlet extension of the standard model. Our computational method is adaptable to any particle physics model, offering a fast and reliable way to calculate gravitational waves generated by sound waves. With fewer approximations, our approach provides a robust foundation for precise gravitational wave calculations and allows for the exploration of model-independent features of gravitational waves from phase transitions.

In the singlet Majoron model, we study cosmological phase transitions (PTs) and their resulting gravitational waves (GWs), in the two-field phase space, without freezing any of the field directions. We first calculate the effective potential, at one loop and at finite temperature, of the Standard Model Higgs doublet together with one extra Higgs singlet. We make use of the public available Python package ‘CosmoTransitions’ to simulate the two-dimensional (2D) cosmological PTs and evaluate the gravitational waves generated by first-order PTs. With the full 2D simulation, we are able not only to confirm the PTs’ properties previously discussed in the literature, but also we find new patterns, such as strong first-order PTs tunneling from a vacuum located on one axis to another vacuum located on the second axis. The two-field phase space analysis presents a richer panel of cosmological PT patterns compared to analysis with a single-field approximation. The PTGW amplitudes turn out to be out of the reach for the space-borne gravitational wave interferometers such as LISA, DECIGO, BBO, TAIJI and TianQin when constraints from colliders physics are taken into account.

In recent years, the prospect of detecting gravitational waves sourced from a strongly first-order cosmological phase transition has emerged as one of the most exciting frontiers of gravitational wave astronomy. Cosmological phase transitions are an essential ingredient in the Standard Model of particle cosmology, and help explain the mechanism for creation of matter in the early Universe, provide insights into fundamental theories of physics, and shed light on the nature of dark matter. This underscores the significance of developing robust end-to-end tools for determining the resulting gravitational waves from these phase transitions. In this article we present PhaseTracer2, an improved version of the C++ software package PhaseTracer, designed for mapping cosmological phases and transitions in Standard Model extensions of multiple scalar fields. Building on the robust framework of its predecessor, PhaseTracer2 extends its capabilities by including new features crucial for a more comprehensive analysis of cosmological phase transitions. It can calculate more complex properties, such as the bounce action through the path deformation method or an interface with BubbleProfiler, thermodynamic parameters, and gravitational wave spectra. Its applicability has also been broadened via incorporating the dimensionally reduced effective potential for models obtained from DRalgo, as well as calculations in the MS¯ and OS-like renormalisation schemes. This modular, flexible, and practical upgrade retains the speed and stability of the original PhaseTracer, while significantly expanding its utility.

With the recent claim that gravitational waves were finally detected and with other efforts around the world for GWs detection, its is reasonable to imagine that the relic gravitational wave background could be detected in some time in the future and with such information gather some hints about the origin of the universe. But, it’s also be considered that gravity has self-interaction, with such assumption it’s reasonable to expect that these gravitational wave will interact with the relic or nonrelic GW background by scattering, for example. Such interaction should decrease the distance which such propagating waves could be detected The propagation of gravitational waves (GWs) is analyzed in an asymptotically de Sitter space by the perturbation expansion around Minkowski space using a scalar component. Using the case of de Sitter inflationary phase scenario, the perturbation propagates through a FRW background. The GW, using the actual value for the Hubble scale (Ho), has a damping factor with a very small valor for the size of the observational universe; the stochastic relic GW background is given by a dimensionless function of the frequency. In this work we analyze this same damping including the gravitational wave background due to astrophysical sources such background is 3 orders of magnitude bigger in some frequencies and produces a higher damping factor.

Monday, 5th of September 2016Chair: M. ColpiS. VitaleThe LTP experiment on LISA Pathfinder and its first resultsK. DooleyAdvanced LIGO: news from the dark universeB. SchutzLIGOs Black Holes and Science in the LISA EraP. McNamaraLISA Pathfinder: First steps to observing gravitational waves from spaceM. HewitsonIn-flight Performance of the Optical Metrology System on LISA PathfinderW. WeberPhysical model of the LISA Pathfinder differential acceleration measurement and its application to LISAK. DanzmannThe Status of LISAChair: O. JennrichJ. MartinoOn-flight characterization of Coldgas micro-Newton thrusters for Lisa PathfinderM. NofrariasMagnetic force noise in LISA PathfinderL. FerraioliThe LISA Pathfinder GRS Front-End ElectronicsD. VetrugnoThe Δg workflow: from measured displacements to the differential external acceleration.A. WittchenCoupling of relative intensity noise and pathlength noise to the length measurement in the optical metrology system of LISA PathfinderS. PaczkowskiLaser frequency stabilisation and interferometer path length differences on LISA PathfinderR. GiusteriThe free-fall mode experiment on LISA Pathfinder: first resultsP. WassElectrostatic test-mass force-noise disturbances as measured by LISA PathfinderR. DolesiThe contribution of Brownian noise from viscous gas damping to the differential acceleration noise measured in LISA Pathfinder between two nominally free falling test massesC. TrenkelThe engineering of LISA Pathfinder – the quietest laboratory ever flown in spaceW. KlipsteinLISA-derived Flight Phasemeter on the GRACE Follow-On MissionP. LauferMEMS Ion Thruster Chips to Significantly Enhance Cold Gas Thruster Lifetime for LISAM. TintoEnhanced Gravitational Wave Science with LISA and gLISATuesday, 6th of September 2016Chair: P. McNamaraF. RicciAdvanced VIRGO: State of the ArtC. BelczynskiEvolutionary predictions in the advanced LIGO/Virgo eraA. SesanaThe promise of multi-band gravitational wave astronomyB. SathyaprakashExploring the Universe with third generation interferometersS. SatoThe status of DECIGOG. HeinzelSatellite interferometry from LTP and GRACE Follow-On to LISAP. BinetruyCosmology with LISAChair: S. VitaleA. Giménez CañeteBeyond LISA PathfinderP. HertzNASA Astrophysics Program: Present and FutureF. SafaESA activities towards the Gravitation Waves Space ObservatoryH. WardLPF Interferometry and route to LISAJ. CampDevelopment of a US Laser System for the Gravitational Wave Mission LISAT. SchwarzePerformance of an optical three-signal test for the LISA metrologyM. LaporteStatus of the eLISA on table (LOT) electro-optical simulator for space based gravitational waves observatoriesS. AppleUF Torsion Pendulum and GRS Technology DevelopmentJ. LivaseLISA Telescope In-field Pointing and Scattered Light StudyK. IsleifThe LISA backlink – comparing optical phase reference systemsWednesday, 7th of September 2016Chair: C. SopuertaT. AlexanderEMRIs and the relativistic loss coneR. SchoedelThe stellar cusp around the Milky Way’s central black holeJ. GairImpact of eLISA design on EMRI ScienceM. van de MeentModelling spinning EMRIs with Self-ForceA. GianninasA Progress Report on the Search for the Most Extreme Binary White DwarfsI. ThorpeInitial Results from ST7-Disturbance Reduction System on LISA PathfinderG. JinOngoing development of detection of gravitational waves in space in ChinaThursday, 8th of September 2016Chair: P. BinetruyR. BlandfordThe Future of Black Hole Astrophysics in the LISA-VIRGO-LPF EraC. MooreObserving black hole merger kicks directly with gravitational wavesN. TamaniniLate time cosmology with eLISAI. DvorkinA synthetic model of the gravitational wave background from evolving binary compact objectsA. PetiteauLISA science performance in the context of LISAPathfinder first results and simulation for LISAN. CornishFast, fully precessing frequency domain waveforms for analyzing black hole mergers with LISAA. KleinSupermassive Black Hole Observations with eLISAS. HughesMeasuring EMRIs: A reality checkChair: Ch. CapriniL. MayerMassive black hole mergers and their timescales: connecting galaxy formation with gravitational wave scienceS. BabakEnchilada: analysis of simulated eLISA data setA. RicciardonePrimordial Gravitational Waves and eLISAS. SanidasCan eLISA save the day? Hunting for cosmic strings in the SKA era.G. ServantProbing cosmological phase transitions with eLISAD. WeirAcoustic waves and the detectability of first-order phase transitions by eLISAM. BonettiPost-Newtonian Dynamics of Massive Black Holes TripletsJ. Garcia-BellidoGravitational waves from primordial black holes as dark matterT. RegimbauSearching for the stochastic gravitational-wave background with Advanced LIGO and Advanced VirgoM. PieroniPrimordial GW from universality classes of pseudo-scalar inflationFriday, 9th of September 2016Chair: G. MuellerK. Holley-BockelmannThe Known Unknowns: predicting the landscape of LISA black hole sourcesE. RossiSupermassive black hole seeds: updates on the quasi star modelC. MingarelliThe Gravitational-Wave Universe seen by Pulsar Timing ArraysS. SmarttSearching for the electromagnetic counterparts to gravitational wave sourcesJ. BergéMICROSCOPE: the first few months in orbitO. JennrichThe preparation for L3 – building on LISA Pathfinder

Cosmological phase transitions can be a source of Stochastic Gravitational Wave (SGW) background. Apart from the dynamics of the phase transition, the characteristic frequency and the fractional energy density Ωgw of the SGW depends upon the temperature of the transition. In this article, we compute the SGW spectrum in the light of QCD equation of state provided by the lattice results. We find that the inclusion of trace anomaly from lattice QCD, enhances the SGW signal generated during QCD phase transition by ∼ 50% and the peak frequency of the QCD era SGW are shifted higher by ∼ 25% as compared to the earlier estimates without trace anomaly. This result is extremely significant for testing the phase transition dynamics near QCD epoch.

We study the possible occurrence of the hadron-quark phase transition (PT) during the merging of neutron star binaries by hydrodynamical simulations employing a set of temperature-dependent hybrid equations of state (EOSs). Following previous work, we describe an unambiguous and measurable signature of deconfined quark matter in the gravitational-wave (GW) signal of neutron star binary mergers including equal-mass and unequal-mass systems of different total binary mass. The softening of the EOS by the PT at higher densities, i.e., after merging, leads to a characteristic increase of the dominant postmerger GW frequency ${f}_{\mathrm{peak}}$ relative to the tidal deformability $\mathrm{\ensuremath{\Lambda}}$ inferred during the premerger inspiral phase. Hence, measuring such an increase of the postmerger frequency provides evidence for the presence of a strong PT. If the postmerger frequency and the tidal deformability are compatible with results from purely baryonic EOS models yielding very tight relations between ${f}_{\mathrm{peak}}$ and $\mathrm{\ensuremath{\Lambda}}$, a strong PT can be excluded up to a certain density. We find tight correlations of ${f}_{\mathrm{peak}}$ and $\mathrm{\ensuremath{\Lambda}}$ with the maximum density during the early postmerger remnant evolution. These GW observables thus inform about the density regime which is probed by the remnant and its GW emission. Exploiting such relations, we devise a directly applicable, concrete procedure to constrain the onset density of the QCD PT from future GW measurements. We point out two interesting scenarios: if no indications for a PT are inferred from a GW detection, our procedure yields a lower limit on the onset density of the hadron-quark PT. On the contrary, if a merger event reveals evidence for the occurrence of deconfined quark matter, the inferred GW parameters set an upper limit on the PT onset density. Both scenarios would thus have strong implications for high-density matter physics, e.g., determining the range of validity of nuclear physics and constraining the properties for quark deconfinement. These prospects demonstrate the importance of simultaneously measuring pre- and postmerger GW signals to exploit the complementarity of the information encoded in both phases. Hence, our work stresses the value added by dedicated high-frequency GW instruments.

The proposed TianQin gravitational wave observatory is aiming to detect gravitational wave signals in the millihertz frequency band, through the method of space-borne laser interferometry. In total, three satellites will be launched, each following a geocentric orbit, with an orbital altitude of about one hundred thousand kilometers. They form into an equilateral triangle formation, with an orbital period of <sc>3.6 d.</sc> The orbital plane of TianQin is fixed almost constant, towards one specific gravitational wave source, RXJ0806.3+1527, so that TianQins response to this source is maximized, and this source can be used to calibrate and assess the facilities performance. It is widely anticipated that in the millihertz frequency band, there lurks a wide variety of gravitational wave sources, ranging from massive black hole binary mergers, extreme mass ratio inspirals, Galactic binary white dwarves, stellar mass binary compact objects inspirals, as well as stochastic gravitational wave background. Meanwhile, the expected source number in such frequency band would also be huge. The successful implementation of the TianQin project would pave the way towards exciting prospects of future gravitational wave research. By successfully performing gravitational wave observation, the TianQin gravitational wave observatory can open a new window for the study of gravitational wave astronomy, gravitational wave cosmology as well as gravitational wave physics. The science prospect of TianQin gravitational wave observation can be further enhanced through a combination with multi-band gravitational wave detection and multi-messenger astronomical observations, by collaboration with gravitational wave detectors operating in different frequency bands as well as with other probes focusing on different messengers like electro-magnetic signals, neutrinos or cosmic rays. The TianQin project will also greatly promote the construction of a high-precision space-time reference system, ultra-long-range laser interferometry, high-precision satellite platform, etc. The development of cutting-edge space technologies has important applications in the national economy as well as the national strategic needs. Currently, the TianQin project has made important progress in the precision gravity measurement facility, the payload research base, the laser ranging station, the simulation facility for space-borne gravitation wave detection on ground, and the series test satellite for the TianQin project. Based on the long-term accumulation of relevant technology, the TianQin project team proposed the goal of achieving gravitational wave detection in the 2030s, and a 0123 plan roadmap is formulated, aiming to perform, step by step, lunar or relay satellite laser ranging, testing key technology like space-borne laser interferometry and drag-free control, verifying high precision space-borne laser interferometry technology, and ultimately detecting gravitational wave. By the 2030s, the scientific cooperation between scientists from all over the world and the use of various means to jointly conduct exploration and research on the Universe will face great development. So far, the TianQin project has held many international seminars and received extensive international attention and active participation. Currently, the TianQin Collaboration Group has been formally established, with a collaboration group advisory committee also established, consisting of scientists with significant influence in the field of gravitational wave detection all over the world. The TianQin project will establish a collaborative research or comprehensive cooperation agreement with foreign universities or research organizations, and vigorously promote the China-led space-borne gravitational wave detection business. Through extensive international cooperation, the TianQin project will unite domestic and foreign strengths and strive to take the lead in realizing the gravitational wave detection in the window of millihertz band.

The stochastic gravitational wave (GW) background provides a fascinating window to the physics of the very early universe. Beyond the nearly scale-invariant primordial GW spectrum produced during inflation, a spectrum with a much richer structure is typically generated during the preheating phase after inflation (or after some other phase transition at lower energies). This raises the question of what one can learn from a future observation of the stochastic gravitational wave background spectrum about the underlying physics during preheating. Recently, it has been shown that during preheating non-perturbative quasi-stable objects like oscillons can act as strong sources for GW, leading to characteristic features such as distinct peaks in the spectrum. In this paper, we study the GW production from oscillons using semi-analytical techniques. In particular, we discuss how the GW spectrum is affected by the parameters that characterise a given oscillon system, e.g. by the background cosmology, the asymmetry of the oscillons and the evolution of the number density of the oscillons. We compare our semi-analytic results with numerical lattice simulations for a hilltop inflation model and a KKLT scenario, which differ strongly in some of these characteristics, and find very good agreement.

Applications to space technology of High‐Frequency Gravitational Waves, (HFGWs), defined as having frequencies in excess of 100 kHz, are discussed. The applications to be specifically addressed include: providing (1) multi‐channel communications (both point to point and point to multipoint through all normal material things — the ultimate wireless system); (2) a remote means for causing perturbations to the motion of objects such as missiles (bullets to ICBMs), spacecraft, land or water vehicles or craft; (3) remote coalescing of clouds of hazardous vapors, radioactive dust, etc. by changing the gravitational field in their vicinity; (4) the potential for through‐earth or through‐water “X‐rays” in order to observe subterranean structures, geological formations, create a transparent ocean, view three‐dimensional building interiors, buried devices, etc.; and (5) the potential for remotely disrupting the gravitational field in a specific region of space. The utilization of a possible HFGW telescope as a navigational aid by viewing the anisotropic or patterned HFGW relic cosmic background above, on, or under the ground without reliance on GPS satellite signals is also noted. Many of the applications are discussed in the context of space technology and several approaches to the generation and possible focusing of HFGWs are referenced. A derivation of the “jerk” formulation of the quadrupole approximation for HFGW power is included in an appendix.

Gravitational waves (GWs) have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting proper definitions of GWs in flat space-time and in a cosmological setting (section ). Following, we discuss the reasons why early universe GW backgrounds are of a stochastic nature, and describe the general properties of a stochastic background (section ). We recap current observational constraints on stochastic backgrounds, and discuss the basic characteristics of present and future GW detectors, including advanced LIGO, advanced Virgo, the Einstein telescope, KAGRA, and LISA (section ). We then review in detail early universe GW generation mechanisms, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation (section ), GWs from processes that operate within extensions of the standard inflationary paradigm (section ), GWs from post-inflationary preheating and related non-perturbative phenomena (section ), GWs from first order phase transitions related or not to the electroweak symmetry breaking (section ), and GWs from general topological defects, and from cosmic strings in particular (section ). The phenomenology of these early universe processes is extremely rich, and some of the GW backgrounds they generate can be within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators.

The cosmological QCD phase transitions may have taken place between 10-5 s and 10-4 s in the early universe offers us one of the most intriguing and fascinating questions in cosmology. In bag models, the phase transition is described by the first-order phase transition and the role played by the latent heat or energy released in the transition is highly nontrivial and is being classified as the first-order phase transition. In this presentation, we assume, first of all, that the cosmological QCD phase transition, which happened at a time between 10-5 s and 10-4 s or at the temperature of about 150 MeV and accounts for confinement of quarks and gluons to within hadrons, would be of first-order. Of course, we may assume that the cosmological QCD phase transition may not be of the first-order. To get the essence out of the first-order scenario, it is sufficient to approximate the true QCD vacuum as one of possibly degenerate vacua and when necessary we try to model it effectively via a complex scalar field with spontaneous symmetry breaking. On the other hand, we may use a real scalar field in describing the non-first-order QCD phase transition. In the first-order QCD phase transition, we could examine how and when pasted or patched domain walls are formed, how long such walls evolve in the long run, and we believe that the significant portion of dark matter could be accounted for in terms of such domain-wall structure and its remnants. Of course, the cosmological QCD phase transition happened in the way such that the false vacua associated with baryons and many other color-singlet objects did not disappear (that is, using the bag-model language, there are bags of radius 1.0 fermi for the baryons) — but the amount of the energy remained in the false vacua is negligible by comparison. The latent energy released due to the conversion of the false vacua to the true vacua, in the form of pasted or patched domain walls in the short run and their numerous evolved objects, should make the concept of the radiation-dominated epoch, or of the matter-dominated epoch to be reexamined.

Gravitational-wave (GW) astronomy is transforming our understanding of the Universe by probing phenomena invisible to electromagnetic observatories. A comprehensive exploration of the GW frequency spectrum is essential to fully harness this potential. Remarkably, current methods have left the μHz frequency band almost untouched. Here, we show that this μHz gap can be filled by searching for deviations in the orbits of binary systems caused by their resonant interaction with GWs. In particular, we show that laser ranging of the Moon and artificial satellites around the Earth, as well as timing of binary pulsars, may discover the first GW signals in this band, or otherwise set stringent new constraints. To illustrate the discovery potential of these binary resonance searches, we consider the GW signal from a cosmological first-order phase transition, showing that our methods will probe models of the early Universe that are inaccessible to any other near-future GW mission. We also discuss how our methods can shed light on the possible GW signal detected by NANOGrav, either constraining its spectral properties or even giving an independent confirmation.

We present results from large-scale numerical simulations of a first order thermal phase transition in the early Universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted k−3 behavior, where k is the wave number, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-k decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wave number behavior of the velocity power spectrum is consistent with a causal k3, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about 0.05c, produced from bubbles with a mean separation of about 10−2 of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.

We present results from large-scale numerical simulations of a first order thermal phase transition in the early universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted $k^{-3}$ behaviour, where $k$ is the wavenumber, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-$k$ decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wavenumber behaviour of the velocity power spectrum is consistent with a causal $k^{3}$, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about $0.05c$, produced from bubbles with a mean separation of about $10^{-2}$ of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.