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We study the dynamics of a timelike vector field which violates Lorentz invariance when the background spacetime is in an accelerating phase in the early universe. It is shown that a timelike vector field is difficult to realize an inflationary phase, so we investigate the evolution of a vector field within a scalar field driven inflation model. And we calculate the power spectrum of the vector field without considering the metric perturbations. While the time component of the vector field perturbations provides a scale invariant spectrum when $xi = 0$, where $xi$ is a nonminimal coupling parameter, both the longitudinal and transverse perturbations give a scale invariant spectrum when $xi = 1/6$.
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Assuming that superstring theory is the fundamental theory which unifies all forces of Nature at the quantum level, I argue that there are key limitations on the applicability of effective field theory techniques in describing early universe cosmology.
We have investigated if the vector field can give rise to an accelerating phase in the early universe. We consider a timelike vector field with a general quadratic kinetic term in order to preserve an isotropic background spacetime. The vector field potential is required to satisfy the three minimal conditions for successful inflation: i) $rho>0$, ii) $rho+3P < 0$ and iii) the slow-roll conditions. As an example, we consider the massive vector potential and small field type potential as like in scalar driven inflation.
I review the Trans-Planckian Censorship Conjecture (TCC) and its implications for cosmology, in particular for the inflationary universe scenario. Whereas the inflationary scenario is tightly constrained by the TCC, alternative early universe scenarios are not restricted.
We assume that the early universe is homogeneous, anisotropic, and is dominated by the mutually BPS 2255 intersecting branes of M theory. The spatial directions are all taken to be toroidal. Using analytical and numerical methods, we study the evolution of such an universe. We find that, asymptotically, three spatial directions expand to infinity and the remaining spatial directions reach stabilised values. Any stabilised values can be obtained by a fine tuning of initial brane densities. We give a physical description of the stabilisation mechanism. Also, from the perspective of four dimensional spacetime, the effective four dimensional Newtons constant G_4 is now time varying. Its time dependence will follow from explicit solutions. We find in the present case that, asymptotically, G_4 exhibits characteristic log periodic oscillations.
We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature.
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