vendredi 26 février 2016

Ears wide open...

... to catch loud and clear the Einstein's symphony in full spectrum

Frequency Classification of Gravitational Waves

The Gravitation-Wave (GW) Spectrum Classification

Characteristic strain hc vs. frequency for various GW detectors and sources. [QA: Quasar Astrometry; QAG: Quasar Astrometry Goal; LVC: LIGOVirgo Constraints; CSDT: Cassini Spacecraft Doppler Tracking; SMBH-GWB: Supermassive Black Hole-GW Background.]

We have presented a complete frequency classification of GWs according to their detection methods. ... several bands are amenable to direct detection... Although the prospect of a launch of space GW is only expected in about 20 years, the detection in the low frequency band may have the largest signal to noise ratios. This will enable the detailed study of black hole co-evolution with galaxies and with the dark energy issue. Foreground separation and correlation detection method need to be investigated to achieve the sensitivities 10-16 -10-17 or beyond in Ωgw to study the primordial GW background for exploring very early universe and possibly quantum gravity regimes. When we look back at the theoretical and experimental development of GW physics and astronomy over the last 100 years, there are many challenges, some pitfalls, and during last 50 years close interactions among theorists and experimentalists. The subject and community have become clearly multidisciplinary. One example is the interaction of the GW community and the Quantum Optics community in the last 40 years to identify standard quantum uncertainties in measurement, to realize that this is not an obstacle of measurement in principle, and to find ways to overcome it. Another example is the interaction of the physics community and the astronomy community to understand and to identify detectable and potentially detectable GW sources. With current technology development and astrophysical understanding, we are in a position using GWs to study more thoroughly galaxies, supermassive black holes and clusters together with cosmology, and to explore deeper into the origin of gravitation and our universe. Next 100 years will be the golden age of GW astronomy and GW physics. The current and coming generations are holding such promises.
(Submitted on 1 Nov 2015)
In the same vein, the interested reader is invited to learn about the multi-band gravitational wave astronomy concepts and its obstacles here.

... and get the pitch of the dark note
With obvious short-comings in our understanding of fundamental principles of nature dangling, e.g. the lack of a dark matter candidate or the observed matter/antimatter asymmetry, and in absence of evidence for new physics at collider experiments, so-called dark sectors become increasingly attractive as add-on to the Standard Model. If uncharged under the Standard Model gauge group, dark sectors could even have a rich particle spectrum without leaving an observable imprint in measurements at particle colliders. Hence, this could leave us in the strenuous situation where we might have to rely exclusively on very feeble possibly only gravitational interactions to infer their existence. 
For dark sectors to address the matter/anti-matter asymmetry via electroweak baryogenesis, usually a strong first-order phase transition is required. It is well known that a first-order phase transition is accompanied by three mechanisms that can give rise to gravitational waves in the early universe [6–13]: collisions of expanding vacuum bubbles, sounds waves, and magnetohydrodynamic turbulence of bubbles in the hot plasma. However, for previously studied models, e.g. (N)MSSM [14], strongly coupled dark sectors [15], or the electroweak phase transition with the Higgs potential modified by a sextic term [16], the resulting GW frequencies after red-shifting are expected to have frequencies of some two or more orders of magnitude below the reach of aLIGO. On the other hand, if electroweak symmetry breaking is triggered in the dark sector at temperatures significantly above the electroweak scale, e.g. by radiatively generating a vev using the Coleman-Weinberg mechanism, GW with frequencies are within the aLIGO reach, i.e. 1-100 Hz. However, we will explain that the overall amplitude of the signal is too small for aLIGO at present sensitivity, but it can be probed by the next generation of interferometers [These future experiments also include the advanced LIGO/VIRGO detectors operating in years 2020+ at the projected final sensitivity]. 
At the same time, already now, aLIGO can probe beyond the standard model physics. We will investigate the consequences of topological defects, such as a domain wall passing through the interferometer. We will model this by introducing a non-vanishing effective photon mass localised on the domain wall, while vanishing elsewhere [this is not a gravitational effect, but effectively it looks like local ripples affecting propagation of photons]. The signatures of passing domain walls can be well separated from black-hole mergers and motivates and extension of ongoing search strategies.

(Submitted on 11 Feb 2016 (v1), last revised 16 Feb 2016 (this version, v2))

mercredi 10 février 2016

Celebrating the possible unification of Gravity and Gauge interactions the day after Mardi Gras

... and the day before the expected announcement of detection of gravitational waves, is it reasonable?
In General Relativity the Lorentz group is realized as a local symmetry of the tangent manifold. There exists no spinor representations of the diffeomorphisms and this dictates the use of this local symmetry in curved space-time. Usually the dimension of the tangent space is taken to be equal to the dimension of the curved manifold and the Lorentz symmetry is then simply a manifestation of the equivalence principle for spaces without torsion. Considering the group of local Lorentz transformations in tangent space, we can reformulate General Relativity as a gauge theory where the gauge fields are the spin-connections. If the dimensions of space time and tangent space are the same, the gauge fields (spin-connections) simply encode the same amount of information about dynamics of the gravitational field as the affine connections and nothing more. However, the dimension of the tangent group must not necessarily be the same as the dimension of the manifold [1] 
... one can unify gauge interactions with gravity by considering higher dimensional tangent spaces in a four dimensional space-time. The gauged tangent space Lorentz group describes simultaneously the symmetry groups of gravity and gauge interactions, provided a metricity condition is satisfied. The spin-connections of the higher dimensional tangent space fully incorporate information on the affine connection of space-time as well as the gauge fields. Those connections which are responsible for gravity are “composite” because they satisfy extra constraints which allow to express them in terms of the derivatives of the vielbeins. On the other hand the spin-connections responsible for gauge interactions do not obey any constraints and hence are independent. The complete geometric unification of gravity and gauge interactions is realized by writing the action of the theory just in terms of curvature invariants of the tangent group which contains the Yang-Mills action for gauge fields. The realistic group which unifies the gravity with gauge interactions and contains the Standard Model is SO (1, 13) in a fourteen dimensional tangent space. It corresponds to SO(10) grand unified theory concerning the gauge fields content, however, it has double the number of fermions, half of which can be made very massive via Brout-Englert-Higgs mechanism. The SO(1,13) is broken first {to SO(1,3)×SO(4)×SO(10) then} to SO(1,3)×U(1)×SU(2)×SU(3) and then to SO(1,3)×U(1)em×SU(3) by using Brout-Englert-Higgs mechanism. Since the Dirac operator plays a fundamental role in this setting, it is natural to look for connections between this construction and that of noncommutative geometry. In addition, the need to add Higgs scalar fields suggests that a total unification of gravity, gauge and Higgs fields within one geometrical setting, should be possible by replacing the continuous four dimensional manifold by a noncommutative space which has both discrete and continuous structures [5]. This possibility and others will be the subject of future investigations.
Notes added: ... Michel Dubois-Violette, communicated to us the following. In 1970, R. Greene has proved that a 4-dimensional Lorentzian manifold admits locally an isometric smooth free embedding in Minkowski space M(1, 13) [9]. There is a similar result proved the same year for the Euclidean signature in M.L. Gromov and V.A. Rokhlin [10]. This means that one can include an arbitrary deformation of the four-manifold in the same flat space and eventually expect to quantize space-time in the fixed Minkowski space M(1, 13)

(Submitted on 6 Feb 2016 (v1), last revised 14 Feb 2016 (this version, v2))

dimanche 7 février 2016

Waiting for the most wanted wave in the physics world ... and then

A quantitative forecast for the advanced LIGO detector
Tonight at the hour I types these lines the wind blows strongly behind the window and I know there is a storm warning on the Atlantic French coast. I wish all the best to mariners and people by the sea. The wave I have in mind in this post is quite different; nevertheless it has already started to make some fuss but I want to keep my heads on straight looking for sound estimations when one could watch it for real. Here is the most specific piece of information I could find:
Recent advances in gravitational-wave astronomy make the direct detection of gravitational waves from the merger of two stellar-mass compact objects a realistic prospect. Evolutionary scenarios towards mergers of double compact objects generally invoke common envelope evolution which is poorly understood, leading to large uncertainties in merger rates. We explore the alternative scenario of massive overcontact binary (MOB) evolution, which involves two very massive stars in a very tight binary which remain fully mixed due to their tidally induced high spin. We use the public stellar-evolution code MESA to systematically study this channel by means of detailed simulations. We find that, at low metallicity, MOBs produce double-black-hole (BH+BH) systems that will merge within a Hubble time with mass ratios close to one, in two mass ranges, ∼ 25 . . . 60 M and  130 M , with pair instability supernovae (PISNe) being produced in-between. Our models are also able to reproduce counterparts of various stages in the MOB scenario in the local Universe, providing direct support for it. We map the initial parameter space that produces BH+BH mergers, determine the expected chirp mass distribution, merger times, Kerr parameters and predict event rates. We typically find that for [metallicity] Z<Z/10, there is one BH+BH merger for ∼1,000 core-collapse supernovae. The advanced LIGO (aLIGO) detection rate is more uncertain and depends on the metallicity evolution. Deriving upper and lower limits from a local and a global approximation for the metallicity distribution of massive stars, we estimate aLIGO detection rates (at design limit) of ∼ 19 − 550 yr-1 for BH+BH mergers below the PISN gap and of ∼ 2.1 − 370 yr-1 above the PISN gap [the first quoted number of the ranges corresponds to a local approximation, the second one to a global approximation to the metallicity distribution]. Even with conservative assumptions, we find that aLIGO should soon detect BH+BH mergers from the MOB scenario and that these could be the dominant source for aLIGO detections.

The standard formation scenario of BH+BH binaries involves a number of highly uncertain aspects of binary interactions (Figure B.1). The main uncertainties include, in particular, the treatment of common-envelope (CE) evolution (Ivanova et al. 2013) and the efficiency of accretion and spin-up from mass transfer. These lead to uncertainties in the expected merger rates of several orders of magnitude (Abadie et al. 2010). In contrast, the MOB scenario presented here relies mostly on reasonably well understood physics of the evolution of massive stars [Figure 2], although there are still significant uncertainties in the treatment of, e.g., stellar winds (Langer 2012), rotational mixing (Maeder & Meynet 2012) and the BH formation itself (Heger et al. 2003; Ugliano et al. 2012; Pejcha & Thompson 2015).

Even for the ongoing first science run (O1) of aLIGO the prospects for detection should be promising. Given that the sensitivity of aLIGO is currently about 1/3 of the design sensitivity, the expected detection rate is ∼4 % of our calculated values.


In fact, the most massive mergers, which probe a large fraction of the whole Universe, could well be the dominant source for aLIGO detections (Abadie et al. 2010). Another factor that helps the detection of BH+BH mergers from low-metallicity populations, that is not taken into account in the above estimates, is that, because of the possibly long merger delay times (see Figure 4), even systems which were formed at rather high redshift may merge at low redshift (cf., Mandel & de Mink 2016). 

A remaining caveat of concern for our estimated detection rates is related to the relatively low gravitational-wave frequencies of the more massive BH+BH binaries. The emitted frequencies during in-spiral are expected to peak approximately at the innermost stable circular orbit (ISCO) before the plunge-in phase and the actual merging. However, even determining the ISCO for a merging binary system it is non-trivial and depends, for example, on the spins of the BHs (Balmelli & Damour 2015), which requires numerical or sophisticated (semi-)analytical calculations within general relativity and cannot simply be estimated using a test particle in a Kerr field. For the BH+BH mergers above the PISN gap, the emitted frequencies are most likely ≤ 100 Hz, and with redshift corrections the frequencies to be detected are easily smaller by a factor of two or more. Such a low frequency is close to the (seismic noise) edge of the detection window of aLIGO. However, the waveform amplitudes of the more massive BH+BH binaries are larger (for a given distance) and are also enlarged further by a factor of (1+z). Finally, it may be possible that higher frequency signals from the ringdown of the single, rapidly spinning BH produced could be detectable, despite their expected smaller wave amplitudes. An important question to address is whether the first generation of LIGO should have detected such massive BH+BH merger events. Given that the sensitivity of the first generation of LIGO was about 10 times lower, the number of detections should have been 1000 times lower. Therefore even for our upper limits, it is not surprising that there have been no detections during the previous science runs of the first generation LIGO detectors (Abadie et al. 2012).
(Submitted on 14 Jan 2016)

A Gargantua's mouthful of quanta
Time will tell if the former estimations were correct... Now assuming that the direct detection of gravitational waves is achieved sooner or later then comes the next natural question that fits better the editorial line of this blog : is a quantum of gravitational wave detectable? 
In the LIGO experiment, if it is successful, we shall detect a classical gravitational wave, not an individual quantum of gravity. A classical wave may be considered to be a coherent superposition of a large number of gravitons. LIGO is supposed to detect a wave with a strain amplitude f of the order of 10-21. According to [Landau and Lifshitz, 1975], page 370, the energy density of this wave is 
E = (c2/32πG)ω22,            (2)
where G is Newton’s constant of gravitation and ω is the angular frequency. For a wave with angular frequency 1 Kilohertz and amplitude 10-21, Eq. (2) gives an energy density of roughly 10-10 ergs per cubic centimeter. A single graviton of a given angular frequency ω cannot be confined within a region with linear dimension smaller than the reduced wavelength (c/ω). Therefore the energy density of a single graviton of this frequency is at most equal to the energy of the graviton divided by the cube of its reduced wave-length, namely 
Es = (ω4/c3).                 (3) 
For an angular frequency of 1 Kilohertz, the single graviton energy density is at most 3.10-47 ergs per cubic centimeter. So any gravitational wave detectable by LIGO must contain at least 3.1037 gravitons...
Poincare Prize Lecture International Congress of Mathematical Physics Aalborg, Denmark, August 6, 2012
Freeman Dyson, Institute for Advanced Study, Princeton, New Jersey

Undetected gravitons have you a mass?
NonCommutative Geometry (NCG) is a natural extension to our familiar notions of Riemannian geometry, that has the additional benefit of producing the action of all the Standard Model fields in addition to gravity terms, purely through geometrical considerations. Thus NCG treats both gravity and matter on an equal footing and provides us with concrete relationships between matter and gravitational couplings. The gravitational sector of (the asymptotic expansion of) this theory produces modifications to General Relativity and in this paper we explore the ramifications of these modifications on the formation and evolution of gravitational waves. 
We have shown that the theory contains both massive and massless gravitons and that the requirement that the mass of these gravitons be positive fixes the sign of one of the couplings in the theory (for a given choice of sign conventions). We also show that both these modes are sourced by the quadrupole moment of a system (just as in standard GR) and that the retarded Green’s function is not restricted to the past light cone of the observer (unlike GR), as one would expect for a system with massive modes. We have explicitly calculated the energy loss for a circular binary system and compared the results to those of standard GR. We have demonstrated that the amplitude of these NCG modifications is suppressed by the distance between the observer and the source of the gravitational waves and hence will typically be small 
Despite the extremely small amplitude of deviations from standard results, we have shown that NCG produces several distinctive features. Firstly, the amplitude of the energy lost by a binary pair can be higher or lower than the expected value, depending on the orbital period of the pair and the distance to the observer. This opens up the possibility that the observed energy loss from such a pair would be seen to oscillate as the binary moves with respect to the Earth. Whilst such effects are likely to be beyond current observational resolution, they allow for an unexpected beat phenomenon, which would be a concrete signature of NCG.  
One can immediately use the results of this paper to examine circular binary systems, in order to constrain the value of β [10]. Similarly, one can include eccentricity which may result in more restrictive constraints on the theory. An alternative avenue would be to use the gravitational wave-forms given here to deduce the consequences for direct gravity wave searches (LIGO, VIRGO, LISA, etc). In particular, to extend these result to the large field regime and look for modifications to the chirp that develops at the end of in-spiral events.
(Submitted on 24 May 2010)

One can find in the literature several binary pulsars for which the rate of change of the orbital frequency is well-known and the predictions of GR agree with the data to a high accuracy. Since the magnitude of the [NCG] deviations from GR must be less than the allowed uncertainty in the data, we are able to constrain [8] β, namely β>7.5×10-13m-1. (24) This constraint is not too strong but since it is obtained from systems with high orbital frequencies, future observations of rapidly orbiting binaries, relatively close to the Earth, could improve it by many orders of magnitude.
It is particularly encouraging that by studying graviational waves propagation we were able to constrain one of the free parameters of the theory, namely the one related to the coupling constants at unification.
(Submitted on 20 Jan 2013 (v1), last revised 22 Jan 2013 (this version, v2))

Update (on the upper limit of graviton mass :-)
Warning: This is not a blind-injection

 ... assuming a modified dispersion relation for gravitational waves [97], our observations constrain the Compton wavelength of the graviton to be λg>1013 km, which could be interpreted as a bound on the graviton mass mg<1.2×10-22 eV/c2. This improves on Solar System and binary pulsar bounds [9899] by factors of a few and a thousand, respectively, but does not improve on the model dependent bounds derived from the dynamics of Galaxy clusters [100] and weak lensing observations [101]. 
B. P. Abbott et al.*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 21 January 2016; published 11 February 2016)

Cumulative posterior probability distribution for λg (black curve) and exclusion regions for the graviton Compton wavelength λg from GW150914. The shaded areas show exclusion regions from the double pulsar observations (turquoise), the static Solar System bound (orange) and the 90% (crimson) region from GW150914

The observation of GW150914 has given us the opportunity to perform quantitative tests of the genuinely strong-field dynamics of GR. We investigated the nature of GW150914 by performing a series of tests devised to detect inconsistencies in the predictions of GR. With the exception of the graviton Compton wavelength and the test for the presence of a non-GR polarization, we did not perform any study aimed at constraining parameters that might arise from specific alternative theories to GR [13, 14, 85], such as Einstein- æther theory [97] and dynamical Chern–Simons [98], or from compact-object binaries composed of exotic objects such as boson stars [99] or gravastars [100]. Studies of this kind are not possible yet, since we lack predictions for what the inspiral-merger-ringdown GW signal should look like in those cases. We hope that the observation of GW150914 will boost the development of such models in the near future.  
We will attempt to measure more than one damped sinusoid from the data after GW150914’s peak, thus extracting the quasi-normal-modes and inferring the final black-hole’s mass and spin. We will, thus, be able to test the no-hair theorem [65, 66] and the second law of black-hole dynamics [70, 71]. However, signals louder than GW150914 might be needed to achieve these goals. GR predicts the existence of only two transverse polarizations for GWs. In the future, we plan to investigate whether an extended detector network will allow the measurement of non-transverse components [13] in further GW signals.
The detection of GW150914 ushers in a new era in the field of experimental tests of GR: within the limits set by our sensitivity, all the tests we have performed provided no evidence against the predictions of GR.
(LIGO Scientific Collaboration and Virgo Collaboration)

//last edit 13 Feb
The hypertext link to the blind injection has been changed to a more relevant one.