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n ationary models can correlate small-scale density perturbations with the long-wavelength gravitational waves (GW) in the form of the Tensor-Scalar-Scalar (TSS) bispectrum. This correlation a ects the mass-distribution in the Universe and leads to the odiagonal correlations of the densityeld modes in the form of the quadrupole anisotropy. Interestingly, this eect survives even after
the tensor mode decays when it re-enters the horizon, known as the fossil eect. As a result, the o-diagonal correlation function between dierent Fourier modes of the density uctuations can be
thought as a way to probe the large-scale GW and the mechanism of in ation behind the fossil eect. Models of single eld slow roll in ation generically predict a very small quadrupole anisotropy in TSS while in models of multiple elds in ation this e
ect can be observable. Therefore this large scale quadrupole anisotropy can be thought as a spectroscopy for dierent in ationary models. In addition,in models of anisotropic in ation there exists quadrupole anisotropy in curvature perturbation power spectrum. Here we consider TSS in models of anisotropic in ation and show that the shape of quadrupole anisotropy is di
erent than in single eld models. In addition in these models the
quadrupole anisotropy is projected into the preferred direction and its amplitude is proportional to gNewhereNe is the number of e-folds and g is the amplitude of quadrupole anisotropy in
curvature perturbation power spectrum. We use this correlation function to estimate the large scale GW as well as the preferred direction and discuss the detectability of the signal in the galaxy surveys like Euclid and 21 cm surveys
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