# w=1/3 to w=-1 evolution in a Robertson-Walker space-time with constant scalar curvature

## TL;DR

This paper explores a specific Robertson-Walker space-time with constant scalar curvature and zero spatial curvature, showing how the cosmological fluid transitions from radiation to dark energy-like behavior, predicting universe age and evolution.

## Contribution

It introduces a model with fixed scalar curvature and flat space that naturally explains the transition of the cosmological fluid's equation of state without additional hypotheses.

## Key findings

- Transition from w=1/3 to w=-1 in the cosmological fluid.
- Predicted universe age range of 7.3 to 13.7 billion years.
- Model aligns with observed Hubble parameter and temperature.

## Abstract

The Ricci tensor of a Robertson-Walker space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein's equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, the RW geometry with constant scalar curvature and flat space, fixes the limit values w=1/3 and w=-1, without any hypothesis on the cosmological fluid. The value of the scalar curvature fixes the time-scale for the transition. For this reason, we investigate the 'toy-universe' with Hubble parameter h = 0.673 and temperature Tcmb = 2.72K. The model predicts an age of the universe in the range 7.3-13.7 Gyr.