Generalisation from the local 4-dimensional spacetime form for a proper time interval provides an alternative basis for a unified theory contrasting with the more familiar approach of appending extra dimensions of space. In both cases the main goal is to derive a structure of matter that accounts for empirical observations from the properties of the additional components. Previous work has focussed upon the direct and significant connections that this new approach makes with the Standard Model of particle physics while also providing a link with dark matter models. In this paper we elaborate on how a further sector of generalised proper time, incorporating the key component of negative pressure, can account for the apparent dark energy fuelling the accelerating large-scale expansion of the universe. Through comparison with existing dark energy models we elucidate the elementary composition of this sector, its potential relation to an effective cosmological constant term, and the nature of possible interaction with the visible and dark matter sectors.

Unification based upon the generalisation of proper time is proposed as a comprehensive framework to account for the fundamental structure of matter, in a manner contrasting with the more familiar approach based on extra dimensions of space. The elementary properties of matter to be incorporated include the Standard Model of particle physics together with a source for the dark sector and a coherent formalism for quantum gravity. We elaborate upon the manner in which all such material phenomena and empirical properties as distributed in an extended 4-dimensional spacetime can be encompassed within, and derived from, the continuous flow of time alone via a generalised arithmetic form for infinitesimal intervals of proper time. This approach will also be compared and contrasted with the basic structure of causal set theory as a means of demonstrating how it is possible to construct a full physical theory essentially from elements of time alone, as explicitly developed from the most elementary level. The conception of time as utilised and elucidated in this theory, with emphasis upon the causal continuum properties and as the basis for unification, will be clarified.

Many models with structures of matter associated with a structure of extra spatial dimensions have been proposed in recent decades. On employing a further generalisation from the local 4-dimensional spacetime form to a general form for proper time, we describe how matter fields resembling the Standard Model of particle physics can be accommodated far more directly than with a higher-dimensional spacetime theory. The successful identification of key features of visible matter in this non-spatial sector of extra dimensions in turn motivates seeking a candidate for dark matter residing in the original extra spatial dimension sector, and provides a close guide for the explicit form this invisible matter might take. We describe how such Standard Model and dark matter sectors in different extra-dimensional branches of generalised proper time are gravitationally connected through their common root in the local 4-dimensional spacetime and consider further possible mutual interactions and implications in comparison with existing dark matter models. A yet further possible branch of generalised proper time can be connected with dark energy models, hence in principle accounting for all three major components of cosmological structure within this framework.