Effect of Cosmological
Gravity Waves on Expansion
of the Universe
Munawar Karim†, Kris Green*
†Department of Physics, *Dept. of Mathematics
St. John Fisher College, Rochester, NY
[email protected]
11th East Coast Gravity Meeting
Outline of presentation
• Explain deviations from Hubble line
• Dimming of distant supernovae
• Cosmological gravity waves affect supernova
data
• Light travels through a sea of gravity waves
• New experiment
• Red: 71% of cosmological attributed to dark
energy
Ω M = 0.29, Ω Λ = 0.71
• Blue: assumes no cosmological constant
• Black: empty universe with no cosmological
constant
Observations
• Deviation from Hubble line
• Data indicate:
• (i) Early universe was decelerating
• (ii) Current universe is accelerating
Interpretations
• Universe expansion not uniform
• Cosmological constant? Does not fit data
• Dark matter?
• Dark energy?
Cosmic
gravity
waves
Light
from
supernova
Supernova
Earth
Simpler explanation
• Cosmological gravity waves
• All pervasive from Planck era to present
•
Gravity decouples: Planck era: 10-43 to 10-35 secs
• Cosmological gravity waves emerge
• Gravity waves expand with Universe
Effect on measurements
• Excessive redshift
• Light travel time increased
Properties of graviton gas
• Early universe: High density: force of gravity
exceeds gas pressure: deceleration
• Transition phase: force of gravity equals gas
pressure: steady expansion
• Current universe: Low density: force of gravity
less than gas (radiation) pressure: acceleration
Solve Einstein equation for
gas of gravitons
• Van der Waals type gas, except gravity
gravitates, interaction is long range
• Calculate altered expansion rate
• Compare with supernova data
• Deduce energy content of Universe
Cosmological Gravity Waves
• Pressure vs density of gravity waves as perfect
fluid
1 2 4π G 2 2
p = ρc −
ρ R
3
9
(
)
d
3
2
ρ R = −3pR
dR
• Equation of state
•
⎡ 2π G 2
4⎤
ρ = ⎢ 2 R + FR ⎥
⎣ 3c
⎦
−1
Stress Tensor
• Isotropic fluid: traceless stress tensor
•
T µν
⎡ 2 4π G 2 2
ρ
c
−
ρ
R
⎢
3
⎢
0
=⎢
⎢
0
⎢
0
⎣
⎤
0
0
0 ⎥
⎥
−p 0
0 ⎥
0 −p 0 ⎥
⎥
0
0 − p⎦
Einstein equation
• Perfect fluid
2
8
π
GR
4
π
G
⎛
2
2
2 2⎞

R +k=
ρ R ⎟ ; k = −1, 0, +1
⎜⎝ ρc −
⎠
3
3
2

R
k
8π G ⎛ 2 4π G 2 2 ⎞
+ 2 =
ρ R0 ⎟ ;
⎜⎝ ρc −
2
⎠
R0 R0
3
3
k
8π G T
2
H0 + 2 =
ρ0
R0
3
•
ρ
k
ρ
− 2 2 ≡ Ω R + Ω k = 1; Ω k = 1−
ρC H 0 R0
ρC
T
0
T
0
Compare with data
• Total energy density content defined as
•
"b"
2π G
3H
R
2
R0 = R ( t 0 ); R = 2 ; ρC =
; b =
3c F
8π G
R
2
F
2
0
2
F
2
0
Luminosity distance d L vs z
dL =
c (1+ z )
ρ
H0
−1
ρC
T
0
1/2
⎧
⎪
⎪ T
1/2 z1
dz
⎪ ρ0
× sinh ⎨
−1 ∫
1+ z )
0 (
⎪ ρC
⎪
⎪
⎩
1
b (1 − b )
ρ
= 0.3625
2
2
ρC
(1 + b )
T
0
2
(
)
2
⎡⎛ 1+ b 2 (1+ z )2 ⎞ 2
2
1− b (1+ z )
ρ ⎢
⎜
⎟
ρC ⎢⎝ b 2 (1+ z )2 + 1 ⎠ 1− b 2 (1+ z )2
⎣
T
0
2
(
)
⎫
⎪
⎪
⎪
⎬ Mpc
⎤ ⎪
− 1⎥ + 1 ⎪
⎥ ⎪
⎦ ⎭
µ P = m − M = 5 log d L + 25
Supernova data (Riess 2006)
•
Curve fit to data
•
Distance modulus vs
redshift spread over 13
orders
Curve fit to all data
•
Distance modulus vs
redshift data; (minus
expansion of empty
Universe)
Blue: fit with b=0.335
1.5
1
Delta (m-M) (mag)
•
Theory & Residual data
0.5
0
-0.5
-1
•
Red:
-1.5
0
0.5
1
1.5
Red-shift
• Ω M = 0.29, Ω Λ = 0.71
"Riess2006 - Empty Space" ChiSq:448
Data - Empty Space
Corrected Integral,5/1
2
Aggregate data
Binned Gold Data 2006
1
Red:
Ω M = 0.29, Ω Λ = 0.71
•
Blue: exact solution,
purely gravity waves
0.5
Delta (m-M) mag
•
0
-0.5
-1
0
0.5
1
1.5
Average red-shift
Binned Gold Data 2006
Riess 2006, ChiSq=12
Corredted Integ b=.25
2
Evolution of Universe
•
Pressure & density
vs radius: equation
of state
•
From Planck
moment to present
•
Deceleration coasting acceleration
•
zt=0.5
Results
• 5 x 1054 kg of cosmological gravity waves in
Universe
• At z=0.5 Universe transitions from deceleration
to acceleration
•
ρ0
Current density is
= 0.0725 of critical density
ρC
•
k
Ω k ≡ − 2 2 = −0.9275 (Universe is open)
R0 H 0
Conclusion
• Non-uniform expansion of Universe driven by
gravitational radiation
• Source of outward pressure is gravitational
radiation
• Source of inward pressure is gravitation
• Both properties attributed to “Dark Energy”
• Interpretation of mass and cosmological constant
Open question
• Light from supernovae is redshifted
• Is it possible to distinguish between
gravitational redshift and Doppler redshift?
• Source stationary or receding?
• Both are independent of wavelength
• Is the redshift due to either or both?
Suggested measurements
56
56
Ni, Co
•
Sample spectral lines
•
Width of light scattered
from gravity waves: Q ∝ ω 0
•
Redshift independent
of frequency
•
Graph Q ∝ ω 0
δω 0
ω0
Deductions
• From
Q ∝ ω 0 (constant z) graph and intercept,
identify Doppler vs gravity redshift
• Slope: (σ x , σ y ) correlation lengths
•
Q ∝ z constant ω 0 :time correlation length
THANK YOU