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It is known that cosmic magnetic field, if present, can generate anisotropicstress in the plasma and hence, can act as a source of gravitational waves.These cosmic magnetic fields can be generated at very high temperature, muchabove electroweak scale, due to the gravitational anomaly in presence of thechiral asymmetry. The chiral asymmetry leads to instability in the plasma whichultimately leads to the generation of magnetic fields. In this article, wediscuss the generation of gravitational waves, during the period ofinstability, in the chiral plasma sourced by the magnetic field created due tothe gravitational anomaly. We have shown that such gravitational wave will havea unique spectrum. Moreover, depending on the temperature of the universe atthe time of its generation, such gravitational waves can have a wide range offrequencies. We also estimate the amplitude and frequency of the gravitationalwaves and delineate the possibility of its detection by future experiments likeeLISA.

Chiral plasma instability and primordial Gravitational wave