# $\Lambda(t)$CDM and the present accelerating expansion of the universe from 5D scalar vacuum

## TL;DR

This paper explores a 5D scalar vacuum model where our 4D universe's accelerated expansion is explained through geometrically induced effects, eliminating the need for dark energy.

## Contribution

It introduces a 5D scalar vacuum framework that naturally produces a dynamical cosmological constant explaining acceleration without dark energy.

## Key findings

- Derived a cosmological model with only a cosmological constant.
- Obtained a universe model with matter, radiation, and a dynamical cosmological constant.
- Aligned the model with observational data.

## Abstract

In this letter we investigate some consequences of considering our 4D observable universe as locally and isometrically embeded into a 5D spacetime, where gravity is described by a Brans-Dicke theory in vacuum. Once we impose the embeding conditions we obtain that gravity on the 4D spacetime is governed by the Einstein field equations modified by an extra term that can play the role of a dynamical cosmological constant. Two examples were studied. In the first we derive a cosmological model of a universe filled only with a cosmological constant. In the second we obtain a cosmological solution describing a universe filled with matter, radiation and a dynamical cosmological constant, in agree with observational data. Due to the 5D geometrical origin for the dynamical cosmological constant we interpret that the acceleration in the expansion is explained without the introduction of a dark energy component. Moreover, all 4D matter sources are geometrically induced in the same manner as it is usually done in the Wesson's induced matter theory.