Tag Archives: #gravitationalwaves

How Many Types Of Singularities Exist In The Gravitational Waves? (Cosmology)

Yu-Zhu Chen and colleagues discussed gravitational waves with the exact cylindrical gravitational wave solutions. They showed that, there are two kinds of singularities in gravitational waves: source singularity and resonance singularity. Their study recently appeared in the Journal Symmetry.

In the weak field or say, linear approximation, gravitational waves are regarded as linear waves, which ignores the spacetime singularities. Most results about gravitational waves are deduced in this approximation, such as the gravitational quadrupole radiation, the resonance between the gravitational wave and the detector, and the linear superposition of two gravitational waves. But, there’s one another interesting theory called nonlinear theory—exact wave solutions of the Einstein equation. When you consider this theory, some new properties of gravitational waves come into sight.

Now, Yu-Zhu Chen and colleagues discussed gravitational waves with the exact cylindrical gravitational wave solutions rather than gravitational wave solutions in the linear approximation.

“Our paper is motivated by problems such as, the behavior of singularities in gravitational wave solutions and the new physical effects of gravitational wave solutions in addition to, e.g., the reflexion and the transmission.”

— they wrote.

Based on the exact solution, they analyzed singularities in gravitational waves. They showed that there are two kinds of singularities in gravitational waves.

The first kind of singularities lies at a fixed spatial position which corresponds to a source. They called it the “source singularity”.

While, by considering a cylindrical gravitational wave as a complete solution, they showed that singularities in cylindrical gravitational waves carry the information about the source. The second kind of singularities arise as time proceeds to infinity. They recognized this singularity as a resonance and called it the “resonance singularity”.

Unlike other researchers, who considered a resonance between gravitational radiation and the matter (especially the gravitational radiation detectors), Yu-Zhu Chen and colleagues suggested that a gravitational wave resonates with other gravitational waves. They mentioned that the resonance singularity only emerges when a gravitational wave with a source singularity and a gravitational wave without a source singularity possess the same frequency. Two gravitational waves with source singularities or two gravitational waves without source singularities do not resonate. The resonance also indicates that the gravitational wave with sources and the gravitational wave without sources are two of different kinds.

“We suppose that the resonance between gravitational waves is irrelevant to the symmetry of the system. In recent years, gravitational wave detection has produced rapid progress. We expect that the resonance between gravitational waves will be found in the future.”

— they wrote.

Moreover, they investigated the interference of two gravitational waves. They showed, how the interference terms of two cylindrical gravitational waves behave. Interference appears in both the metric and the energy-momentum tensor. Specifically, they showed that the interference term in the source vanishes in the sense of time-averaging.

“A gravitational wave with a source should be regarded as a gravitational radiation. Gravitational radiations will result in the energy loss of the source. With the conservation law of the energy, we may define the energy of the cylindrical gravitational radiation in our framework. We can also consider the resonance between matter waves and gravitational waves based on our previous works on scattering.”

— they concluded.

Featured image credit: Getty Images


Reference: Chen, Y.-Z.; Li, S.-L.; Chen, Y.-J.; Dai, W.-S. Cylindrical Gravitational Wave: Source and Resonance. Symmetry 2021, 13, 1425. https://doi.org/10.3390/sym13081425


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Scientists Use Artificial Intelligence To Detect Gravitational Waves (Astronomy)

Scientists can now process months’ worth of gravitational wave data in minutes

When gravitational waves were first detected in 2015 by the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), they sent a ripple through the scientific community, as they confirmed another of Einstein’s theories and marked the birth of gravitational wave astronomy. Five years later, numerous gravitational wave sources have been detected, including the first observation of two colliding neutron stars in gravitational and electromagnetic waves.

As LIGO and its international partners continue to upgrade their detectors’ sensitivity to gravitational waves, they will be able to probe a larger volume of the universe, thereby making the detection of gravitational wave sources a daily occurrence. This discovery deluge will launch the era of precision astronomy that takes into consideration extrasolar messenger phenomena, including electromagnetic radiation, gravitational waves, neutrinos and cosmic rays. Realizing this goal, however, will require a radical re-thinking of existing methods used to search for and find gravitational waves.

Recently, computational scientist and lead for translational artificial intelligence (AI), Eliu Huerta of the U.S. Department of Energy’s (DOE) Argonne National Laboratory, in conjunction with collaborators from Argonne, the University of Chicago, the University of Illinois at Urbana-Champaign, NVIDIA and IBM, has developed a new production-scale AI framework that allows for accelerated, scalable and reproducible detection of gravitational waves.

This new framework indicates that AI models could be as sensitive as traditional template matching algorithms, but orders of magnitude faster. Furthermore, these AI algorithms would only require an inexpensive graphics processing unit (GPU), like those found in video gaming systems, to process advanced LIGO data faster than real time.

The AI ensemble used for this study processed an entire month — August 2017 — of advanced LIGO data in less than seven minutes, distributing the dataset over 64 NVIDIA V100 GPUs. The AI ensemble used by the team for this analysis identified all four binary black hole mergers previously identified in that dataset, and reported no misclassifications.

“As a computer scientist, what’s exciting to me about this project,” said Ian Foster, director of Argonne’s Data Science and Learning (DSL) division, ​“is that it shows how, with the right tools, AI methods can be integrated naturally into the workflows of scientists — allowing them to do their work faster and better — augmenting, not replacing, human intelligence.”

Bringing disparate resources to bear, this interdisciplinary and multi-institutional team of collaborators has published a paper in Nature Astronomyshowcasing a data-driven approach that combines the team’s collective supercomputing resources to enable reproducible, accelerated, AI-driven gravitational wave detection.

“In this study, we’ve used the combined power of AI and supercomputing to help solve timely and relevant big-data experiments. We are now making AI studies fully reproducible, not merely ascertaining whether AI may provide a novel solution to grand challenges,” Huerta said.

Building upon the interdisciplinary nature of this project, the team looks forward to new applications of this data-driven framework beyond big-data challenges in physics.

“This work highlights the significant value of data infrastructure to the scientific community,” said Ben Blaiszik, a research scientist at Argonne and the University of Chicago. ​“The long-term investments that have been made by DOE, the National Science Foundation (NSF), the National Institutes of Standards and Technology and others have created a set of building blocks. It is possible for us to bring these building blocks together in new and exciting ways to scale this analysis and to help deliver these capabilities to others in the future.”

Huerta and his research team developed their new framework through the support of the NSF, Argonne’s Laboratory Directed Research and Development (LDRD) program and DOE’s Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program.

“These NSF investments contain original, innovative ideas that hold significant promise of transforming the way scientific data arriving in fast streams are processed. The planned activities are bringing accelerated and heterogeneous computing technology to many scientific communities of practice,” said Manish Parashar, director of the Office of Advanced Cyberinfrastructure at NSF.

The new framework builds off of a framework originally proposed by Huerta and his colleagues in 2017. The team further advanced their use of AI for astrophysics research by leveraging Argonne supercomputing resources through a two-year award from the Argonne Leadership Computing Facility’s (ALCF) Data Science Program. This led to the team’s current INCITE project on the Summit supercomputer at the Oak Ridge Leadership Computing Facility (OLCF). The ALCF and OLCF are DOE Office of Science User Facilities.

Featured image: Scientific visualization of a numerical relativity simulation that describes the collision of two black holes consistent with the binary black hole merger GW170814. The simulation was done on the Theta supercomputer using the open source, numerical relativity, community software Einstein Toolkit (https://einsteintoolkit.org/). (Image by Argonne Leadership Computing Facility, Visualization and Data Analytics Group [Janet Knowles, Joseph Insley, Victor Mateevitsi, Silvio Rizzi].)


Provided by Argonne National Laboratory

Accelerators Meet Gravitational Waves (Physics)

Physicists discuss the possibility of using particle accelerators to detect or even generate gravitational waves

In particle accelerators like the Large Hadron Collider (LHC), charged particles bob and weave in magnetic and electric fields, following tightly corralled trajectories. Their paths are computed assuming a flat Euclidean space-time, but gravitational waves ­– first observed by the LIGO and Virgo detectors in 2015 – crease and stretch this underlying geometry as they ripple out across the universe. For the past 50 years, there has been intermittent interest in the possibility of detecting observable resonant effects as a result of this extra curvature of the fabric of space-time, as the particles whizz around the accelerators repeatedly at close to the speed of light.

Advances in accelerator technology could now usher in an era of gravitational-wave astronomy in which particle accelerators play a major role. To explore this tantalising possibility, over 100 accelerator experts, particle physicists and members of the gravitational physics community participated in a virtual workshop entitled “Storage Rings and Gravitational Waves” (SRGW2021), organised as part of the European Union’s Horizon 2020 ARIES project. During this meeting, they explored the role that particle accelerators could play in the detection of cosmological backgrounds of gravitational waves. This would provide us with a picture of the early universe and give us hints about high-energy phenomena, such as high-temperature phase transitions, the nature of inflation and new heavy particles that cannot be directly produced in the laboratory.

Lively discussions at the SRGW2021 workshop – the first, apart from an informal discussion at CERN in the 1990s, to link accelerators and gravitational waves and bring together the scientific communities involved – attest to the prospective role that accelerators could play in detecting or even generating gravitational waves. The great excitement and interest prompted by this meeting, and the exciting preliminary findings from this workshop, call for further, more thorough investigations into harnessing future storage rings and accelerator technologies for gravitational-wave physics.

This text was extracted from the full meeting report in CERN Courier, where you can learn more about gravitational-wave research using particle accelerators.


Provided by CERN

Gravitational Wave Search No Hum Drum Hunt (Astronomy)

Scientists refine the search for enigmatic continuous grav waves

The hunt for the never before heard “hum” of gravitational waves caused by mysterious neutron stars has just got a lot easier, thanks to an international team of researchers.

Gravitational waves have only been detected from black holes and neutron stars colliding, major cosmic events that cause huge bursts that ripple through space and time.

The research team, involving scientists from the LIGO Scientific Collaboration (LSC), Virgo Collaboration and the Centre for Gravitational Astrophysics (CGA) at The Australian National University (ANU), are now turning their eagle eye to spinning neutron stars to detect the waves.

Unlike the massive bursts caused by black holes or neutron stars colliding, the researchers say single spinning neutron stars have a bulge or “mountain” only a few millimetres high, which may produce a steady constant stream or “hum” of gravitational waves.

The researchers are using their methods that detected gravitational waves for the first time in 2015 to capture this steady soundtrack of the stars over the thunderous noise of massive black holes and dense neutron stars colliding.

They say it’s like trying to capture the squeak of a mouse in the middle of a stampeding herd of elephants.

If successful, it would be the first detection of a gravitational wave event that didn’t involve the collision of massive objects like black holes or neutron stars.

ANU Distinguished Professor, Susan Scott from the ANU Research School of Physics, said the collision of dense neutron stars sent a “burst” of gravitational waves rippling through the Universe.

“Neutron stars are mystery objects,” Professor Scott, also a Chief Investigator with the ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav), said.

“We don’t really understand what they are made up of, or how many types of them exist. But what we do know is that when they collide, they send incredible bursts of gravitational waves across the Universe.

“In contrast, the gentle hum of a spinning neutron star is very faint and almost impossible to detect.”

Three new papers have just been published by the LSC and Virgo collaborations detailing the most sensitive searches to date for the faint hum of gravitational waves from spinning neutron stars.

Their work offers a “map to the potential El Dorado of gravitational waves.”

“One of our searches targets young supernova remnants. These neutron stars, recently born, are more deformed, and should emit a stronger stream of gravitational waves,” Dr Lilli Sun, from CGA and an Associate Investigator with OzGrav, said.

As these searches become more and more sensitive they are providing more detail than ever of the possible shape and make-up of neutron stars.

“If we can manage to detect this hum, we’ll be able to look deep into the heart of a neutron star and unlock its secrets,” Dr Karl Wette, a postdoctoral researcher with OzGrav and the CGA, said.

Professor Scott, who is also the leader of the General Relativity Theory and Data Analysis Group at ANU, added: “Neutron stars represent the densest form of matter in the Universe before a black hole will form.”

“Searching for their gravitational waves allows us to probe nuclear matter states that simply can’t be produced in laboratories on Earth.”

Featured image: An image of continuous gravitational waves. © Mark Myers, OzGrav/ Swinburne University


Provided by Australian National University

Scientists Hunt For Evidence Of ‘Lensed’ Gravitational Waves (Astronomy)

Scientists searching for evidence of lensed gravitational waves have published new research outlining the most recent findings on their quest for the first detection of these elusive signals.

Gravitational lensing has been predicted by Einstein himself, and observed by scientists for decades: light emitted by distant objects in the Universe is bent by the gravitational pull of very massive galaxies, as they cross the line-of-sight of the light source. Sometimes the pull is so strong that two copies of the same source can appear in the sky.

It has been known since the late 1970s the same would happen for gravitational waves. If a lensed gravitational wave were to be detected it would open up avenues for exploring new physics, by unlocking precision cosmology and offering new ways of testing Einstein’s general relativity. 

However, these effects are extremely hard to detect: if gravitationally lensed light is a 4-leaf clover, a lensed gravitational wave is a needle in a thousand haystacks. Last year, the team in the University’s School of Physics and Astronomy and the Institute for Gravitational Wave Astronomy had predicted that these elusive signals were unlikely to be observed by instruments currently operated by the LIGO and Virgo Collaborations. A paper was published in Physical Review Letters , soon followed by a follow-up study in Physical Reviews D.

The methodology developed at the University of Birmingham for quantifying how frequently gravitational wave lensing occurs has now  been extensively vetted by the LIGO/Virgo/KAGRA collaboration, and included in a flagship study using most recent detections, published this week on arXiv.

“Here we are, on the second episode of the hunt for lensed gravitational waves, and we are hooked for the finale.” says Riccardo Buscicchio, PhD student at the University of Birmingham and a member of the LIGO-Virgo-KAGRA collaboration. “The new collaboration results are in agreement with our previous expectations. The more sensitive the instruments become, the deeper we can look in the distant Universe, the sooner we will find the needle. The constant humming background of faint distant sources already give us some hints of when it could happen.”

The study, looking for additional signatures of lensing, includes detailed analyses of other possible effects like microlensing or double images. Riccardo adds: “While no compelling evidence has been found so far, with multiple detectors coming up online in the next decade or so, the prospects are exciting.”

Featured image: Artistic impression of lensed gravitational waves, Riccardo Buscicchio (University of Birmingham)


Notes to editor:


Provided by University of Birmingham

Can We Able To Distinguish Neutron Star & Black Hole In Compact Binary Mergers Using Just Gravitational Waves? (Astronomy)

According to Capano and colleagues, you cant distinguish between neutron stars and black holes in compact binary mergers with the help of current LIGO/ Virgo detectors and the one which were claimed by A+ and Voyager is dubious. Their study recently appeared in Arxiv.

In August 2017, the first detection of a binary neutron star merger, GW170817, made it possible to study neutron stars in compact binary systems using gravitational waves. Despite being the loudest (in terms of signal-to-noise ratio) gravitational wave detected to date, it was not possible to unequivocally determine that GW170817 was caused by the merger of two neutron stars instead of two black holes from the gravitationalwave data alone. That distinction was largely due to the accompanying electromagnetic counterpart. This raises the question: under what circumstances can gravitational-wave data alone, in the absence of an electromagnetic signal, be used to distinguish between different types of mergers?

Now, Capano and colleagues studied whether a neutron-star– black-hole binary merger can be distinguished from a binary black hole merger using gravitational-wave data alone. They build on earlier results using chiral effective field theory to explore whether the data from LIGO and Virgo, LIGO A+, LIGO Voyager, or Cosmic Explorer could lead to such a distinction.

The results suggested that the present LIGO-Virgo detector network will most likely be unable to distinguish between these systems even with the planned near-term upgrades. They also mentioned that, the success of A+ and Voyager is “dubious”.

Figure 1. loge B for each detector with MBH = 5M. The vertical line spans the range of Bayes factors for a given detector with the purple line on the left indicates a variable equation of state run and the blue line on the right indicates a constant equation of state. The horizontal black line corresponds to the loge B = 10 cut-off. Since the Cosmic Explorer 1 and 2 runs have a significantly high Bayes factors, the plots are split with different y-axis for current and third-generation detectors. © Capano et al.

They also look at the ln Bayes factor (loge B) between two models and found that, for decisive evidence, loge B ≥ 10 is required. In addition, they noted that the cases with the highest ln Bayes factor always occur with the stiff equation of state, the 5M black hole companion, and at 40Mpc.

“The highest ln Bayes factor occurs for black hole mass of 5M, even though systems with mass of black holes 10, 15, 20M have higher signal-to-noise ratios. The tidal effects decrease as mass increases and this effect is clearly of greater importance than the increase in signal strength.”

Moreover, it has been shown that, when the companion mass increases to even 10M, the Bayes factor drops rapidly regardless of distance or equation of state for the current detectors. If the equation of state is as soft as the analysis of GW170817 suggests, then LIGO Voyager will certainly be unable to distinguish neutron-star–black-hole systems from binary black holes no matter how close or loud the signal is.

Figure 2. loge B for each detector with MBH = 10M. The vertical line spans the range of Bayes factors for a given detector with the purple line on the left indicating a variable equation of state run and the blue line on the right indicating a constant equation of state. The horizontal black line corresponds to the loge B = 10 cut-off. © Capano et al.

Finally, they concluded that in order to obtain decisive evidence of neutron star-black hole from Gravitational wave data, third-generation instruments such as Cosmic Explorer will be required.


Reference: Stephanie M. Brown, Collin D. Capano, Badri Krishnan, “Using gravitational waves to distinguish between neutron stars and black holes in compact binary mergers”, Arxiv, pp. 1-9, 2021. https://arxiv.org/abs/2105.03485


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Gravitational Waves: Where Will Research Go in the Next 20 Years? (Astronomy)

 review  dedicated to the near future of gravitational wave research has been published in the scientific journal Nature, a topic that has fascinated many in recent years. Among the authors of the roadmap also Marica Branchesi, teacher at GSSI, associated with INFN.

Gravitational waves are one of the areas of research that is giving great emotions and is marked by epochal discoveries, such as their first observation announced by the LIGO-Virgo collaborations in 2016, and the observation of the merger of two neutron stars revealed for the first time, both with gravitational waves from LIGO and VIRGO interferometers, and with electromagnetic radiation from telescopes on the ground and in space, in 2017.

The work focuses on the next twenty years discussing the most important projects for gravitational physics and astronomy in the opinion of the Gravitational Wave International Committee  (GWIC), an organization created in 1997 to facilitate international collaboration and cooperation in the construction and operation of the main infrastructures dedicated to the research of gravitational waves.

Link to the article:  https://www.nature.com/articles/s42254-021-00303-8


According to Nature, the new observation window of gravitational astronomy will provide data that will transform our current knowledge in the fields of fundamental physics, astrophysics and cosmology.

 Thanks to the future generation of terrestrial observatories planned for 2030, the Einstein Telescope (in Europe) and the Cosmic Explorer (in the USA) and the LISA space mission it will be possible to observe mergers of black holes and neutron stars going back to the beginning of our Universe. Along with interferometric and electromagnetic detectors, Pulsar Timing Arrays (PTAs) telescopes will continue to evolve with new antenna networks, more sensitive and broadband receivers providing unique information on the dynamics of the largest galaxies in the Universe. 

In particular, among the leading projects for the near future: the LISA (Laser Interferometer Space Antenna) space detector, which is expected to be launched into orbit around the mid-1930s, and the European observatory Einstein Telescope (ET), which see an important involvement of Italy and the GSSI, also due to the recent appointment of Prof. Fernando Ferroni as project manager. 


 Gravitational-wave physics and astronomy in the 2020s and 2030s: Nature review presents the roadmap.

The near future of gravitational wave research has been published in the scientific journal Nature review. GWs have fascinated many in recent years with many discoveries and related research projects. Among the authors of this roadmap also Marica Branchesi, associate professor at GSSI, and INFN researcher. 

The 100 years since the publication of Albert Einstein’s theory of general relativity saw significant development of the understanding of the theory, the identification of potential astrophysical sources of sufficiently strong gravitational waves and development of key technologies for gravitational-wave detectors. In 2015, the first gravitational-wave signals were detected by the two US Advanced LIGO instruments. In 2017, Advanced LIGO and the European Advanced Virgo detectors pinpointed a binary neutron star coalescence that was also seen across the electromagnetic spectrum. The field of gravitational-wave astronomy is just starting, and this Roadmap of future developments surveys the potential for growth in bandwidth and sensitivity of future gravitational-wave detectors,

In particular, among the leading projects for the GW research in the near future: the LISA space detector (Laser Interferometer Space Antenna) whose launch into orbit is foreseen in the middle years of 2030s, and the Einstein Telescope (ET), which see an important involvement of Italy and the GSSI, also due to the recent appointment of Prof. Fernando Ferroni in the scientific directorate of the project.

Link to the article:   https://www.nature.com/articles/s42254-021-00303-8


Reference: Bailes, M., Berger, B.K., Brady, P.R. et al. Gravitational-wave physics and astronomy in the 2020s and 2030s. Nat Rev Phys (2021). https://doi.org/10.1038/s42254-021-00303-8


Provided by GSSI

6000 Hours of Research To Hear Gravitational Waves (Astronomy)

Remember the days before working from home? It’s Monday morning, you’re running late to beat the traffic, and you can’t find your car keys. What do you do? You might try moving from room to room, casting your eye over every flat surface, in the hope of spotting the missing keys. Of course, this assumes they are somewhere in plain sight; if they’re hidden under a newspaper, or fallen behind the sofa, you’ll never spot them.

Or you might be convinced you last saw the keys in the kitchen and search for them there: inside every cupboard, the microwave, dishwasher, back of the fridge, etc. Of course, if you left them on your bedside table, upending the kitchen is doomed to failure. So, which is the best strategy?

Scientists face a similar conundrum in the hunt for gravitational waves-ripples in the fabric of space and time-from rapidly spinning neutron stars. These stars are the densest objects in the Universe and, provided they’re not perfectly spherical, emit a very faint “hum” of continuous gravitational waves. Hearing this “hum” would allow scientists to peer deep inside a neutron star and discover its secrets, yielding new insights into the most extreme states of matter. However, our very sensitive “ears”-4-kilometre-sized detectors using powerful lasers-haven’t heard anything yet.

Part of the challenge is that, like the missing keys, scientists aren’t sure of the best search strategy. Most previous studies have taken the “room-to-room” approach, trying to find continuous gravitational waves in as many different places as possible. But this means you can only spend a limited amount of time listening for the tell-tale “hum” in any one location-in the same way that you can only spend so long staring at your coffee table, trying to discern a key-shaped object. And since the “hum” is very quiet, there’s a good chance you won’t even hear it.

In a recently published study, a team of scientists, led by Dr Karl Wette from the ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav) at The Australian National University, tried the “where else could they be but the kitchen?” approach.

Dr Wette explains: “We took an educated guess at a specific location where continuous gravitational waves might be, based in part on what we already know about pulsars-they’re like neutron stars but send out radio waves instead of continuous gravitational waves. We hypothesised that there would be continuous gravitational waves detected near pulsar radio waves.” Just like guessing that your missing keys will probably be close to your handbag or wallet.

Using existing observational data, the team spent a lot of time searching in this location (nearly 6000 days of computer time!) listening carefully for that faint “hum”. They also used graphic processing units-specialist electronics normally used for computer games-making their algorithms run super-fast.

“Our search was significantly more sensitive than any previous search for this location,” Dr Wette said.

“Unfortunately, we didn’t hear anything, so our guess was wrong this time. It’s back to the drawing board for now, but we’ll keep listening.”

Featured image: Continuous Gravitational waves from neutron stars © Wette


Reference: Karl Wette, Liam Dunn, Patrick Clearwater, and Andrew Melatos, “Deep exploration for continuous gravitational waves at 171–172 Hz in LIGO second observing run data”, Phys. Rev. D 103, 083020 – Published 22 April 2021. DOI: https://doi.org/10.1103/PhysRevD.103.083020


Provided by Australian National University

How Thermal Radiation Affects Gravitational Waves and Space-time Singularities? (Quantum / Cosmology)

The recent observations of gravitational waves and supermassive black holes can be considered as the main probes of General Relativity (GR) in its fundamental aspects which are: 1) the propagation of space-time perturbations, 2) the existence of singularities. Despite of these undeniable successes, several shortcomings affect GR because the whole phenomenology cannot be addressed in the framework of the Einstein picture. The theory is missing at ultraviolet scales because of the lack of a self-consistent theory of Quantum Gravity, and at infrared scales because it is not capable of encompassing clustering phenomena related to large-scale structure and the observed accelerated expansion of the cosmic fluid. These are generically dubbed as dark matter and dark energy but, up to now, no particle counterpart has been discovered to address them at fundamental level.

In this perspective, extensions and modifications of GR are considered as a reliable way out of the above problems assuming that gravitational field has not been completely explored.

These extensions come from effective theories on curved spacetimes or as alternative formulations like teleparallel gravity and its related models.

A main role to test theories is played by cosmology because phenomena connected to the so called dark side can substantially affect structure formation and cosmic dynamics. Their equivalent geometric explanations could be a major step towards a comprehensive theory of gravity at all scales.

In general, dynamical characteristics of gravitational waves can be the features probing a given theory of gravity. Specifically, speed, damping, dispersion, and oscillations of gravitational waves could be used to fix and reconstruct interactions into gravitational Lagrangian and then be a sort of roadmap inside the wide forest of competing theories of gravity. For example, further gravitational polarization modes, besides the two standard ones of GR, emerge when further degrees of freedom are considered into the theory. In general, as soon as modifications or extensions of GR are taken into account, scalar modes are present into dynamics.

Motivated by these considerations, it is possible to investigate the propagation of gravitational waves in various gravitational models. For example, in F(T) extended teleparallel gravity, in domain wall models, in scalar tensor and F(R) gravity theories, in Chern-Simons Axion Einstein gravity and in several media as in strong magnetic fields or in viscous fluids.

Furthermore, the behavior of gravitational waves can be used to test past and future singularities and then contributes in their classification. Another important issue is connected to thermal effects emerging during the cosmic evolution.

“We point out that the contribution of thermal radiation can heavily affect the dynamics of gravitational waves giving enhancement or dissipation effects both at quantum and classical level. These effects are considered both in General Relativity and in modified theories like F(R) gravity.”

— told Odintsov, lead author of the study

Now, Odintsov and colleagues investigated how thermal effects on various cosmological backgrounds affect the propagation of gravitational waves. In particular, they want to take into account such effects in GR, in modified theories of gravity and in presence of future singularities. Lets have a closer look on their findings:

(A) Thermal effects in Cosmology

At first, they considered thermal effects in cosmology and showed that, when hubble parameter (H) is large, the temperature of the universe becomes large and they may expect the generation of thermal radiation as in the case of the Hawking radiation. The Hawking temperature T is proportional to the inverse of the radius rH of the apparent horizon and the radius rH is proportional to the inverse of the Hubble rate H. Therefore, the temperature T is proportional to the Hubble rate H. In simple terms, at cosmological scales, thermal effects emerge with respect to the Hubble radius and then they can strongly affect the cosmic evolution, in particular, at early epochs or nearby singularities. In other words, thermal effects can dynamically affect the cosmological background and then the evolution of phenomena on it.

(B) Thermal effects in future cosmological singularities

It is well known that in the cosmic future several kinds of space-time singularity can happen. Such singularities have been classified as follows:

  • Type I, which is also called as “Big rip”, in this type of singularity, scale factor a(t), the total effective pressure peff and the total effective energy density ρeff diverges strongly.
  • Type II, which is also called as “sudden/pressure singularity” and it is milder than the Big Rip scenario. Here, only the total effective pressure diverges, and the total effective energy density & the scale factor remain finite.
  • Type III, in which both the total effective pressure and the total effective energy density diverges, but the scale factor remains finite. So, this type of singularity is milder than Type I (Big Rip) but stronger than Type II (sudden).
  • Type IV, which is the mildest from a phenomenological point of view.

According to authors, the thermal radiation usually makes the singularities less singular, that is, the Big Rip (Type I) singularity or the Type III singularity transit to the Type II singularity.

(C) Thermal effects in Scalar-field cosmologies

In this sub-section, they showed that the thermal radiation assumes a key role in determining the evolution of the scalar field and then of the universe.

Gravitational waves in a dynamical background

In this section, they considered the propagation of gravitational waves in a dynamical cosmological background where thermal contributions are present. They showed mathematically, how these terms affect the evolution of gravitational waves. First, they reviewed the propagation of gravitational waves in a general medium. Gravitational waves are derived as perturbations of Einstein field equations. In the Einstein equations, not only the curvature but also the energy-momentum tensor depends on the metric and therefore the variation of the energy-momentum tensor gives a non-trivial contribution to the propagation of gravitational waves.

“We showed thermal radiation contribution play a key role in the evolution of the Gravitational waves”

(D) Thermal corrections in quantum matter

In this sub-section, they considered a real scalar field φ as the source of matter. They deal with the scalar field as a quantum field at finite temperature. In the case of high temperature or in the massless case, the scalar field plays the role of radiation. On the other hand, in the limit where the temperature is vanishing but the density is finite, they obtained the dust, which can be considered as cold dark matter.

Enhancement and dissipation of gravitational waves with thermal effects

In this section, they investigated the propagation of gravitational massless spin-two modes, and showed that thermal contribution affects the evolution of the gravitational wave amplitude.

(A) The behavior of gravitational waves near the singularities

In this sub-section, they studied the behavior of gravitational waves near the Type II singularity and the Big Rip (the Type I) singularity. They showed that the enhancement of the gravitational wave occurs near the Type II singularity but it could not occur near the Big Rip (Type I) singularity.

(B) Gravitational waves in the early universe

In this subsection, they showed that if there is no thermal effect, that is α = 0, there is no enhancement or dissipation of the gravitational wave, but if we include the thermal effect, enhancement or dissipation occur.

The propagation of scalar modes with thermal effects

In this section, they developed similar discussion in a generalized context where scalar modes are included. In case of the Type II singularity, just before the singularity, the scalar field oscillates very rapidly. In the case of Big Rip (the Type I) singularity, the amplitude of scalar field increases or decreases very rapidly. While, in the case of bouncing universe, they found that, scalar field (ω(η)) vanishes at t = ±t0 and therefore mass, m² diverges. If m² >, which may depend on the parameters near t = ±t0, the scalar field oscillates very rapidly and if m² < 0, the amplitude of the scalar field increases or decreases very rapidly.

They also mentioned that expanding universe can be realized by the perfect fluid. The perfect fluid also generates scalar waves, whose propagating velocity is known as the sound speed Cs, which is given by:

Therefore if we find the equation of state (EoS), we can find the speed. Thus, in case of the Type II singularity, they found,

Therefore C²s diverges to negative infinity. Because c²s is negative, the amplitude of the perfect fluid wave rapidly decreases or increases without oscillation. But, this behavior is much different from that in the scalar field, where the scalar field oscillates very rapidly.

In case of the Big Rip (the Type I) singularity, they found

which is finite but because C²s is negative, the amplitude of the perfect fluid wave decreases or increases exponentially without oscillation. Even in case of the scalar field, the amplitude of the scalar field increases or decreases very rapidly but m² diverges in the case of scalar field, the increase or decrease is much more rapid.

In case of the bouncing universe, the sound speed is given by,

Which diverges at t=t0 as the m² of the scalar field. Then, the propagation of the perfect fluid wave might be similar to that in the scalar field.

In case of the inflation, H ∼ H0, they found

which is finite but could be negative as long as ηH is small enough. Therefore the perfect scalar wave does not propagate although the scalar wave can propagate.

All the results given above, tell us that the propagation of scalar modes depends on the mechanism which generates the expansion of the universe and, since thermal effects affect the effective mass, they have to be considered in the evolution. And last,

(A) Scalar waves in modified gravity vs compressional waves of cosmic fluid

In this sub-section they showed how we can distinguish scalar modes with respect to the compressional waves of a perfect fluid? They showed that a perfect fluid, where the EoS parameter is w < 0, does not generate a compressional wave. Therefore if we find massive scalar waves, it could be an evidence for modified gravity. However, even in modified gravity, there are various models. In the case of F(R) gravity, however, the coupling of massive scalar with matter is universal, that is, it does not depend on the kind of matter because the coupling appears by the rescaling of metric. This structure is rather characteristic of F(R) gravity and it may give some clue to observationally discriminate F(R) gravity with respect to other modified gravity models.

“In the case of F(R) gravity, the effects of scalar modes or compressional fluids strictly depend on the “representation” of the theory in the Einstein or the Jordan frames. This could constitute an important feature in order to distinguish the true physical frame by the observations”

— wrote authors of the study

Finally, they concluded that dynamics related to the above discussion could be observationally tested by interferometers. In fact, at suitable sensitivities, it seems realistic to disentangle GR contributions with respect to other contributions in the stochastic background of gravitational waves. In a future study, they will develop this topic in detail.


Reference: Salvatore Capozziello, Shin’ichi Nojiri, Sergei D. Odintsov, “Thermal effects and scalar modes in cosmological gravitational waves”, pp. 1-20, Arxiv, 2021. https://arxiv.org/abs/2104.10936


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