Different windows to the Universe.

Fundamental Physics using Gravitational Waves

Speed of gravitational interactions: In general relativity, GWs propagate at the speed of light. Unique identification of a GW event with an electromagnetic (EM) source would allow us to measure the propagation velocity of gravity with unprecedented accuracies. The best sources for this measurement are extra-galactic GRBs which will be observed as a GW burst. For instance, a delay of one day in the arrival time from a source at a distance of one giga light-year would determine the relative speeds to better than 10^-11. If the propagation speed of GWs is less than c, this would indicate that the graviton has an effective non-zero mass which would have other observable effects. By observing GWs from coalescing compact binaries, one can put stringent bounds on the Compton wavelength of the massive graviton¹. Recent studies have shown that the best bounds on the mass of graviton (< 1.6 × 10^-23 eV) expected from second-generation ground-based interferometers would be significantly better (by an order of magnitude) than the currently available bounds².

Number of GW polarization states: GR predicts two states of GW polarizations. But there are competing theories, such as scalar-tensor theories, which predict more than two polarizations. Using a network of GW detectors, it would be possible to constrain the strength of various polarization states in different theories. Both to measure the propagation velocity of GWs and the number of polarizations, it is crucial to have good timing accuracy of the GW signal which can only be achieved through a worldwide network of GW interferometers.

Black-hole spectroscopy and testing 'No Hair' theorem: Black-hole (BH) perturbation theory studies the stability of a BH under perturbation. It is known that an excited Kerr BH relaxes to its axisymmetric state by partially emitting the energy in the distortion as GW. The GWs consist of a superposition of quasi-normal modes (QNMs), whose frequency and damping time depend uniquely on the mass and spin angular momentum of the parent BH (the "No-Hair" theorem) and not on the nature of the external perturbation. Observation of QNMs would enable tests of No Hair theorem.

Testing deviations from GR: While all the above refer to verifying or measuring some of the fundamental properties of gravity as predicted by GR, GWs would also allow one to test small deviations from GR. This would be possible by precisely measuring various PN coefficients in the GW phasing formula by the advanced GW detectors³.

Astrophysics with Gravitational Waves

Here we touch up on what new astrophysics can be learnt by observing GWs. Using matched filtering technique it will be possible to extract the individual masses of the BHs or NSs in a binary very accurately. This mass measurement will be the first direct determination of BH mass and is free from degeneracies such as mass-inclination angle degeneracy. If the BHs have nonzero spin, GW observations will give us the valuable information about the spins too.

At least a fraction of short GRBs (sGRBs) are hypothesized to be powered by binary-NS or NS-BH mergers. The observational evidences for this hypothesis are all indirect. The most unambiguous confirmation could be from a GW signal which is uniquely associated with a sGRB. If many such signals are observed by advanced detectors, the statistics may give important clues about the sGRBs and their progenitors. Parameter estimation of GW signals from binaries containing at least one NS could give valuable information about the equation of state of the NS interior which, in turn, could give us vital information about the composition of the NS core and the physics of such a highly dense state.

Ground-based GW interferometers will be sensitive to the signals from intermediate mass (with masses between 50 - 400 M_sun) BH (IMBH) binary coalescences. These binaries are observable up to distances of the order of a few Gpcs. Though there are indirect evidences of the existence of IMBHs (through Ultra Luminous X-ray sources), estimation of the mass of the BH from GW observations could prove their existence beyond doubt. GW observations of these binaries could give valuable insights about BH formation scenarios. Low frequency space-based GW missions such as LISA would observe supermassive BH mergers. Since signals last for months in the LISA data stream, one would hope to localize the merger source accurately in the sky so that multi-wavelength EM follow up, looking for an EM afterglow or precursor, is possible. Such multi-messenger observations carry key inputs for understanding the nature of galaxy mergers and the merger history of supermassive BHs.

Supernova explosions are expected to emit bursts of GWs. Advanced GW detectors would be sensitive to SN events inside and near our galaxy. Due to the complex physics and astrophysics involved, the strength of GW emission from SN explosions will depend up on various parameters and is uncertain. If detected, GWs could give us access to the internal processes which take place (such as core bounce) during the explosion and help us constrain various astrophysical models. Observations of continuous-wave signals from NSs could enhance our knowledge about various mechanisms driving instabilities in NSs such as accretion, spin misalignment etc.

The future of Astronomy lies in coordinated observations in completely different windows such as EM, GWs and Neutrinos. Electromagnetically triggered GW search significantly reduces the computational burden and parameter space of search. With advanced GW telescopes, GW observations would act as triggers for EM follow ups. Neutrino observations associated with a SN event would carry complementary information to those from GWs. Already, EM triggered searches for continuous wave GW signals from known pulsars in our galaxy have been undertaken and with improved sensitivity these would become more powerful tools of astronomy.

Cosmology using gravitational waves

GW observations will have tremendous impact on our understanding of cosmology. GW observations of compact binary mergers would allow direct measurement of luminosity distance to the source. If a GW observation is coincident with an EM event (these are called 'Standard Sirens') which gives information about redshift of the source, together they play an important role in determining various cosmological parameters⁴ by probing the luminosity distance � redshift relation. A good example of a 'standard siren' is sGRBs observed in GWs as compact binary mergers. With advanced LIGO, these sources could be capable of measuring Hubble constant to less than 5% accuracy depending up on th number of such sources seen by LIGO⁵. For measuring luminosity distance with ground based GW detectors, one needs geographically separated network of these interferometers, emphasizing the important role the GW detector network would play for cosmological studies. Since many of the supermassive binary BH mergers are likely to have EM counterparts, using the distance-redshift relation from many such sources, LISA will be able to put interesting constraints on the equation of state of dark energy (of the order of a few percent), thus shedding light on one of the outstanding issues of present-day cosmology⁶. Advanced ground-based detectors, such as third generation Einstein Telescope, could have the capability to observe the first generation of BHs ("seed BHs") in the Universe up to very high red shifts (z = 10), and thus to constrain structure formation models⁷.

The cosmological GW background is expected to be produced by processes in the very early Universe. The observation of this stochastic background can provide a picture of the Universe very shortly (~10 ²¹ s) after the big bang, while the cosmic-microwave background observation can only provide a picture of the Universe after ~10⁵ years after the big bang. Unfortunately, the expected strength of this background is too low for the current ground-based detectors (and the planned space-borne detector LISA) to detect. But these detectors can put interesting upper-limits on the strength of this background, thus test a number of current speculations about the very early Universe. The proposed big-bang observer mission will make a direct observation of this background possible.

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