Quantum Vacuum: A New
Perspective on Dark Matter and Dark
Energy in Cosmology
Riddhiman Bhattacharya FRSA
Independent Researcher and Fellow of Royal Society of Arts, FRSA
riddhiman.butai2005@gmail.com

1. AimIn our view of the universe as a superfluid, dark energy,
and dark matter are intrinsic to the quantum vacuum. We
link dark energy to the energy density within the superfluid and associate dark matter with fluctuations in thesuperfluid [1]. These phenomena reflect contrasting aspects of the dynamic vacuum, influenced by opposing gravitational and pressure forces. Dark matter becomes noticeable under gravitational dominance, while dark energy
takes precedence when pressure forces come into play.
2. Motivation and Mathematical Considerations
We’ll describe Matter through the relativistic equation of
perfect fluid, as it’s cosmologically considered a fluid. weconsider Perfect fluid [there is no dissipative current, thus
making simple], and constructing a simple cosmologicalmodel using the variables energy/mass rest density (ρ),
pressure (p), and velocity vector of matter flow (u), electromagnetic wave [EMW] speed (c), metric tensor (gµν ) describing the dynamic matter’s spacetime structural form toget (1)matter = (ρc2 + p)u u + pg
Tµν(1)µ ν(µν)and according to Matter Tensor (Tµν ), (2):equal to minus of energy density pvacuum = ρvacuum.
This mathematical equivalence positions vacuum energy
as a cosmological constant (Λ) with w = −1, addressing
the cosmological constant problem [5, 6]. In conventional
quintessence models of dark energy, the accelerated expansion results from the ratio between the kinetic andpotential energy of a scalar field. This variation allows
the equation of state parameter (w) to range from −1 to
1, introducing a new fundamental force without experimental confirmation. When we examine vacuum in regions far removed from the gravitational influence of large
cosmic structures, it manifests as dark energy using thevariables energy/mass rest density of vacuum(ρ), pressure
vacuum(p) and velocity vector of vacuum’s energy flow (u),cosmological constant (Λ):
Energy of Dynamic Complex Scalar Vacuum=ρΛ+ρbosonic disintegration matterρlost by quantum fluctuations that produce matter

where ηαβ is the metric tensor of Minkowski describing vacuum’s flat space-time geometry as we considered gravity
very minute (≈ 0) and deducing the vacuum tensor from(4).
Energy of dynamic complex scalar vacuum according
to observations ≈ Λ → ρ ≈ 0w = −1 → −pvacuum = −(pvacuumuvacuumuvacuumTαβαβmatter = T vacuum + T bosonic matter + T fermionic matter (2)Tµν(µν)(µν)(µν)

In course of our work, we’ll use the cosmological equationof statepw=
ρ
where w is our state parameter. Now, we’ll again use thesimplification of considering the viscous fluid of the quantum vacuum as a perfect fluid through the relativistic equation of perfect fluid using the variables energy/mass rest
density of vacuum(ρ), pressure vacuum(p) and velocity
vector of vacuum’s energy flow (u), EMW speed (c), metric tensor (gµν ) describing the geometry of vacuum’svacuum
space-time, and we get vacuum tensor Tµνvacuum = (ρvacuumc2 + pvacuum)uvacuumuvacuum
Tµνµν
vacuum+ pvacuumg(µν)

(3)

− (4)

vacuum)+pvacuumηαβ(5)4.2 Dark MatterIn our study, we suggest that vacuum dark fluid’s geometry influenced by gravity within fermionic matterstructures shows curvature. Near the Sun in our solarsystem, there’s maximum curvature, deflecting electromagnetic waves by 0.875 arcseconds. On a larger scale likegalaxies, vacuum curvature takes a closed spheroidal
shape due to gravitational forces, causing rotation andperipheral density concentration. This leads to observed
dark matter concentration and pressure reduction. The
spheroidal shape matches dwarf spheroidals, maximizing
vacuum energy as dark matter. In this scenario of complete
vacuum entrapment by fermionic matter, a dust matter cosmological model fits, where gravitational fields depend only
on mass, momentum, and stress density of a perfect fluidwith positive mass density and negligible pressure. [2]3. Introduction
galaxy cluster(GC)The vacuum’s most evident connection lies with dark energy. Independent groups, including the High-Z Supernova Search Team (led by Brian Schmidt and AdamRiess in 1998) and the Supernova Cosmology Project(led by Saul Perlmutter in 1999), experimentally discovered the accelerating expansion of the universe. This discovery strongly indicates the existence of vacuum energy
as a constant force, equivalent to a positive cosmologicalconstant in General Relativity or dark energy, driving theacceleration [5].
To account for this expansion, the concept of dark energy
has been proposed in two primary forms:• A constant energy density uniformly filling the vacuum,known as the cosmological constant.
• A scalar field, such as quintessence, with an energy density changing extremely slowly over time and space, leading to minimal inhomogeneity in the vacuum—difficult todistinguish from a cosmological constant.
The Vacuum Dark Fluid theory posits that dark fluid, in thepresence of matter, slows down and coagulates around it,
attracting more dark fluid and amplifying the gravitational
force near large masses, like galaxies [8]. This effect is consistently present but becomes noticeable only in the presence of substantial mass. In the Newtonian limit, the scalar
field’s contribution to the galaxy’s mass involves an effective
density that diminishes, leading to a fading effective pressure. In this context, the scalar field mimics the behavior ofpressureless matter [7].
4. Dark Energy and Dark Matter as form of Vaccum
EnergyTµν

fermionic matter of galaxy cluster(GC)= Tµνvacuum trapped by galaxy cluster (GC)
+Tµν

(6)
galaxy cluster(GC)Tµν
is 3 dimensional spheroid immersed
in a 4D Euclidean space-time of the existent vacuum
beyond galaxy cluster. So, in other words, no vacuumis trapped, so with metric:
ds2 = ev(r)dt2 − eλ(r)dr2 − r2dθ2 − r2 sin2 θdϕ2(7)to Einstein Clusters [Special Anisotropic fluid distribution[6] when radial stress = 0 (producing an ideal model) ]should satisfy Einstein Field Equations [3, 4]
1 νν
Rµ − r∆µ = −8πTµν(8)2So, when p = 0 according to observations and equations(6) and (7), we getgalaxy cluster (GC)Tµν

dust matter
= Tµν

(9)

On the basis of ρ:
fermionic matter of GC = ρfermionic matter of GCc2u u ρ (10)Tµν
µ νvacuum trapped by GCTµν= ρvacuum trapped of GCc2uµuν

(11)

Therefore, from (6)(9)(10),(11), we getdust matter = T GCTµνµν= ρfermionic matter of GCc2uµuν +ρvacuum trapped of GCc2uµuν
(12)

4.1 Dark Energy
Vacuum dark fluid emerges as the most plausible origin of dark energy, as the vacuum exhibits a pressure

KASHIWA DARK MATTER SYMPOSIUM 2023, Poster Presentation

Thus, Vacuum dark fluid acts like dark matter.

5. Conclusion
Dark matter and dark energy can be understood through aconcept involving the vacuum as a dark fluid, which is influenced by two opposing forces: gravity and pressure. In
its usual state as a perfect fluid, this dark vacuum behavesin two ways: it acts as matter, gravitating and attracting,and as energy, repelling and exerting pressure. This leads
to two extreme states for the dark vacuum when external
factors come into play:• In regions where the dark vacuum is confined within vast
cosmic structures dominated by matter, such as galaxyclusters, the pressure within the vacuum diminishes. In
this scenario, the dark vacuum predominantly exerts
its influence through the quantum force of gravity.
• In regions where the dark vacuum exists free from thedominance of matter, its self-gravity approaches zero. In
this case, the dark vacuum primarily manifests as a forceof pressure, with its attractive gravitational effects beingminimal.
The important results that we got from our studies are:
• The two key opposing forces that play a crucial role in thedynamic matter are:– Vacuum energy is influenced by the breakdown offermionic matter into bosonic matter.
– Quantum vacuum fluctuations give rise to the creationof fermionic matter.
• Whether fermionic matter is present or not is important,as it has a profound impact on the geometric shape of thevacuum:– The presence of fermionic matter influences theshape of empty space, causing it to curve and takeon shapes like spheroids. This results in a kind offorce without any pressure.
– When the empty space is devoid of fermionic matter,it maintains a flat geometry similar to Euclidean spaceand doesn’t exhibit any gravitational effects.
In summary, our findings align with the alternative theory of
Vacuum Dark Fluid, suggesting that dark matter and darkenergy are distinct manifestations of this quantum vacuum substance. On galactic scales, the dark fluid exhibits
behavior similar to dark matter, and then transitioning todark energy characteristics on larger scales. The vacuum
fluid undergoes feedback from the bosonic disintegration offermionic matter, leading to a non-constant energy state.
Observations indicate that as the energy increases,
gravitational self-interaction diminishes (tends to 0),
resulting in a flat Minkowskian geometry on larger
scales. In contrast, strong gravitational interaction withgalaxies causes the fluid’s geometry to assume spheroidal
curve.
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