# Unification of DE-DM from Diffusive Cosmology

## TL;DR

This paper develops a unified framework for dark energy and dark matter using dynamical space-time theories with diffusive energy transfer, showing that the standard cosmological model is a fixed point of these theories.

## Contribution

It introduces a novel dynamical space-time approach that models diffusive interactions between dark energy and dark matter, extending previous non-Lagrangian formulations.

## Key findings

- Analytical solutions obtained for the theories.
- The $ ext{Lambda}$CDM model is a large-time fixed point.
- Asymptotic behavior matches previous diffusive models.

## Abstract

Generalized ideas of unified dark matter and dark energy in the context of dynamical space time theories with a diffusive transfer of energy are studied. The dynamical space-time theories are introduced a vector field whose equation of motion guarantees a conservation of a certain Energy Momentum tensor, which may be related, but in general is not the same as the gravitational Energy Momentum tensor. This particular energy momentum tensor is built from a general combination of scalar fields derivatives as the kinetic terms, and possibly potentials for the scalar field. By demanding that the dynamical space vector field be the gradient of a scalar the dynamical space time theory becomes a theory for diffusive interacting dark energy and dark matter. These generalizations produce non-conserved energy momentum tensors instead of conserved energy momentum tensors which leads at the end to a formulation for interacting DE-DM. We solved analytically the theories and we show that the $\Lambda$CDM is a fixed point of these theories at large times. A particular case has asymptotic correspondence to previously studied non-Lagrangian formulations of diffusive exchange between dark energy dark matter.