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8. AN OSCILLATORY UNIVERSE WITH CONFORMAL INVARIANCE AND CIRCULAR TIME AXIS SYMMETRY

It is argued that the standard model of the universe based on the General Theory of Relativity(GTR) is neither conformally invariant nor time- symmetric over large time scales. This leads to various problems such as global non-conservation of energy in GTR and singularity. It is shown that in an alternative theory of gravitation such as quasi-steady state model with inflationary inputs, the first problem goes away. The second issue is settled by circular time axis with oscillations embedded on it such that the small arc behaviour is like the quasi-steady state exponential expansion, earlier proposed by Hoyle, Burbidge and Narlikar .

The Interacting and Non-constant Cosmological Constant

We propose a time-varying cosmological constant with a fixed equation of state which evolves mainly through its interaction with the background during most of the long history of the universe. However, such interaction does not exist in the very early and the late time universe and produces the acceleration during these epochs when it becomes very nearly a constant. It is found that after the initial inflationary phase , the cosmological constant, that we call as lambda parameter, rolls down from a large constant value to another but very small constant value and further during dominates the present epoch showing up in form of the dark energy driving the acceleration.

AVOIDANCE OF SINGULARITY AND GLOBAL NON-CONSERVATION OF ENERGY IN GENERAL RELATIVITY

We show that the singularity in the General Theory of Relativity (GTR) is the expression of a non-Machian feature. It can be avoided with a scale-invariant dynamical theory, a property lacking in GTR. It is further argued that the global non-conservation of energy in GTR also results from the lack of scale-invariance and the field formulation presented by several authors can only resolve the problem in part. Assuming the global energy conservation, we propose a negative energy density component with a positive equation of state that can drive the late-time inflation while the positive energy component confines to the smaller scales.

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