Abstract:
Inflationary scenario has been very successful in solving various problems associated with the standard Big Bang cosmology. But the nature of the field that drives accelerated expansion (inflaton) is still unknown to us. The inflationary models with scalar fields, under the slow-roll approximations, are well studied. In contrast, inflationary scenario with spinor fields have not attracted much attention. In earlier works the `classical' Dirac spinor field was studied as a candidate of inflaton. However, there were some issues with inflationary scenario driven by the Dirac spinor. One of the most important problem with Dirac spinor is that it produces highly scale dependent power-spectrum (with spectral index ns 4), which is inconsistent with the CMB observations.
Recently, one special type of spinor was proposed by Ahluwalia (2005, 2013) which is an eigenspinor of charge conjugation operator, also known as Elko. This spinor is called the Non-Standard Spinor (NSS) as it has an unusual property: (CPT)2 = I. NSS field is a spin-1/2 field with mass dimension one, whereas the `classical' Dirac spinor is a spin-1/2 fermion with mass dimension 3/2 . This new spinor field obeys the Klein-Gordon equation instead of Dirac equation. NSS can interact only through Higgs and with gravity, therefore it is dark by nature. Thus it is worth investigating the role of NSS in the unknown dark sector of the universe like: Dark matter, dark energy and inflation etc. In this thesis our focus is on the NSS driven accelerated expansion of the universe.
In the earlier NSS theories there was one major inconsistency -- the equation of motion of NSS obtained from the energy-momentum tensor did not match with the equation of motion calculated using the Euler-Lagrange equation. Recently a consistent theory of NSS was developed which removed this inconsistency. In this thesis we use a consistent NSS theory to study the first order cosmological perturbation theory for NSS. The NSS Lagrangian and the energy-momentum tensor can be expressed as follows:
where and : is the NSS and its dual. The covariant derivatives are defined as: : r @ : + : and r @ where, is the spin connection. In the expression of energy-momentum tensor the F term, which was absent in the earlier works, appears because of the variation of with respect to the metric (Bohmer et al., 2010). Using a simple ansatz of the perturbed NSS and its dual, = ' , : = ': where ' is a scalar and is a constant spinor with the property : = 1, we have calculated omponents of the perturbed energymomentum tensor. The perturbation theory for NSS becomes like a scalar field theory. However, calculation of the energy-momentum tensor shows the presence of additional terms in comparison with the standard canonical scalar field. We construct the modified Mukhanov-Sasaki equation for the NSS. Unlike scalar field case, the sound speed square is shown to be c2 s 6= 1 in general. The spectral index for the scalar perturbation is shown to give a nearly scale invariant powerspectrum which is consistent with the observation provided that ~ F '2 8M2 pl < 104. With this upper bound c2 s 1. Thus in case of first order perturbation theory, NSS becomes indistinguishable with the canonical scalar field theories.
In this thesis we have also studied the attractor behavior of NSS cosmology. In inflationary and dark energy theories it is difficult to find exact initial conditions. Therefore it is important that these theories show the attractor behavior, which will allow a wide class of solutions with different initial conditions to have similar asymptotic behaviour. The search for an attractor in case of NSS was attempted before also (see Wei, 2011). But no stable fixed points were found in the earlier attempts. In this thesis it is shown that the NSS equations can give inflationary-attractor which corresponds to 60 e-foldings. We have also demonstrated, with a new definitions of variables, that in the presence of barotropic perfect fluid the dynamical equations of the NSS can have stable fixed points. The stable fixed points can give us late-time attractor for NSS which can be useful in alleviating the cosmic coincidence problem. The stable fixed points are achieved by redefining the kinetic and potential part of NSS.