TITLE:
A Geometric Scalar Field as a Unified Model of Dark Energy and Dark Matter
AUTHORS:
Gaël Ronsyn
KEYWORDS:
Scalar-Tensor Theories, Dark Matter, Dark Energy, Rotation Curves, Effective Field Theory
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.3,
July
31,
2026
ABSTRACT: We present a minimal effective framework in which a single geometric scalar field, written as
Z(
x
)=t(
x
)−iτ(
x
)
, accounts for both dark-energy-like behaviour in homogeneous cosmology and dark-matter-like phenomenology in galaxies. The real component
t(
x
)
is fixed by the cosmological slicing, while all dynamics reside in the internal scalar
τ(
x
)
, which enters the action through a canonical kinetic term and a small nonminimal coupling
ξR
τ
2
. In FLRW backgrounds, the slow evolution of
τ(
t
)
generates an effective energy density and pressure that reproduce dark-energy-like behaviour. Allowing for spatial inhomogeneities, gradients of the same field produce an effective density
ρ
eff
≃
1
2
(
∇τ
)
2
, modifying the Newtonian potential. In static disk geometries, the harmonic solution
τ(
r
)=Aln(
r/
r
0
)
yields an
r
−2
effective density and asymptotically flat rotation curves. The relation
v
flat
2
=πG
A
2
matches SPARC data, while numerical solutions show that the same scalar field reproduces late-time acceleration and galactic dynamics within a controlled effective description.