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Lorentz invariant dark-spinor and inflation

We investigate the possibility of the inflation driven by a Lorentz invariant non-standard spinor field. As these spinors are having dominant interaction via gravitational field only, they are considered as \emph{Dark Spinors}. We study how these dark-spinors can drive the inflation and investigate the cosmological (scalar) perturbations generated by them. Though the dark-spinors obey a Klein-Gordon like equation, the underlying theory of the cosmological perturbations is far more complex than the theories which are using a canonical scalar field. For example the sound speed of the perturbations is not a constant but varies with time. We find that in order to explain the observed value of the spectral-index $n_s$ one must have upper bound on the values of the background NSS-field. The tensor to scalar ratio remains as small as that in the case of canonical scalar field driven inflation because the correction to tensor spectrum due to NSS is required to be very small. In addition we discuss the relationship of results with previous results obtained by using the Lorentz invariance violating theories.