Temporal No-Linearity: An Alternative to Dark Energy

Abstract

Mathematical compatibilities and constraints of a hypothetical 5D space-time with time referenced by two coordinates (3-2) have been revisited in detail in several recent papers. It has been prescribed from the GR the compatibility constraints of the FLRW metric in each temporal brane, to be restricted to Closed Universes, Smooth Initial Singularities, and “Open CTC”. In a first view, this leads to leaving these works considering mathematical games discarded by the Standard Candles data. However, if time would be referred by two coordinates, they would not be linearly related, and it will be mathematically stated that space-time may not be flat in any case because time-like branes geometry will never be. If so, the time scale “lived” over a two-time dimension geodesic necessarily is not constant over its linear projection on one of both coordinates. Consequently, the correlations between Redshift and Distance Modulus—Distance Ladder—may be corrected by a synchronization function (if a no-linear two-time geodesic trajectory over a “warped temporal geometry” is linearly divided into constant segments, then their projections are not linear in any case). We apply an example of time-trajectory over the time slices, matching the Standard Candle data for a Closed Universe dominated by matter (>90%) in a bulk 3-2 configuration, with open temporal branes and smooth singularity. If time can be referred by two coordinates, then there is no need of Darkness to explain astrophysical data and Universe can be closed.