TITLE:
A 5D Scalar Field Integrated with General Relativity and Photonic Contributions: A Dark Matter-Free Explanation for Gravitational Lensing and Cosmological Observations
AUTHORS:
Bahman Masarratbakhsh
KEYWORDS:
Scalar Field, Dark Matter Alternative, Gravitational Lensing, Galaxy Rotation Curves, 5D Gravity, Compactification, Cosmology, General Relativity, Time Delay, FLRW Perturbations
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.2,
March
30,
2026
ABSTRACT: We propose and extend a 5-dimensional (5D) scalar field model integrated with General Relativity (GR) to explain gravitational lensing and cosmological observations without invoking dark matter. The scalar field
τ
˜
(
x
μ
,χ
)
, with
χ∈
S
1
as a compactified extra dimension, generates a 4D time-delay potential
τ
0
(
x
)
that contributes to spacetime curvature alongside baryonic matter. We further incorporate an explicit photonic term,
τ
γ
, to the time-delay field
τ(
x,t
)
, accounting for the energy-momentum carried by photons, which produces an additional observable delay component. By combining real (baryonic), relativistic (scalar field), and photonic mass contributions, we derive a deflection angle
α=
4GM
c
2
b
, consistent with GR, using Fermat’s principle. The model reproduces the angular power spectrum
C
ℓ
(
τ
)
, matching DES Y3 weak lensing data within
<0.01σ
for
30<ℓ<3000
. Preliminary tests against strong lensing (CLASH), galaxy rotation curves (SPARC), CMB anisotropies (Planck), and large-scale structure (SDSS) suggest compatibility, with the photonic term reducing free parameters and improving fits. This integrated framework offers a promising, dark matter-free alternative, warranting further numerical validation.