STRESS ENERGY OF ISOTROPIC AND HOMOGENOUS PHOTON GAS
DAMIAN SOWINSKI
The Electromagnetic stress energy tensor reads
T = F F
(1)
1
F F
4
In component form this breaks up into the electromagnetic energy density (2), the Poynting ux (3) and the Maxwell
st
STRESS ENERGY OF A GAS OF PARTICLES
DAMIAN SOWINSKI
Consider the stress energy tensor of a collection of N particles with 4-momenta p and mass m:
n
N
T =
d p u
n n
n=0
4 (x x ( )
n
|g|
N
n dt vn vn
=m
(1)
n=0
(t tn ) 3 (x xn (t)
|g|
We can get a better
SCALAR-MASSIVE VECTOR MODEL WITH GRAVITY
DAMIAN SOWINSKI
Lets begin with the following action:
(1)
S=
d4 x
|g|
R 2
1
1
1
+ V () F F m2 ()A A
16G
2
4
2
The rst term is the Einstein-Hilbert Lagrangian with a cosmological constant. This term will lead to the
Model of Inflation with Scalar Fields
and Radiation
Setting the Initial Conditions
Clear , H, , ti, tf, , a, T
ti
tf
1;
Exp 9
2;
Off NIntegrate:inumr
0 7;
t0
.4678;
0 1.1 10 ^ 4;
.01;
T t_ : t
1 2
t ^2
' t ^2
. Solutions;
Integrating the Equations of Mo
Distances in Cosmology
One of the most basic measurements that can be performed is that of distance. How tall
am I? How about that building? How far is it to my school or travel destination? In fact,
throughout the history of astronomy, distance measureme
SCALAR-MASSIVE VECTOR MODEL WITH GRAVITY
DAMIAN SOWINSKI
Lets begin with the following action:
(1)
S=
d4 x
|g|
R 2
1
1
1
V () F F m2 ()A A
16G
2
4
2
The rst term is the Einstein-Hilbert Lagrangian with a cosmological constant. This term will lead to the
EVOLUTION OF SCALE FACTOR FOR DIFFERENT EOS
DAMIAN SOWINSKI
Consider an FRW spacetime lled with a uid satisfying the equation of state
(1)
P =
Lets examine the Friedmann equations for the scale factor when we plug in (1):
(2)
(3)
a
a
2
8G
3
a
4G
=
( + P
6
General Relativistic Perturbation Theory
6.1
Concept Questions
1. Why do general relativistic perturbation theory using the tetrad formalism as opposed
to the coordinate approach?
2. Why is the tetrad metric mn assumed xed in the presence of perturbatio
Cosmological Consequences of a Quantum Field Theory of Gravity with a Dynamical
Critical Exponent
The classical cosmological behavior of Horavas candidate quantum theory of gravity with a dynamical critical exponent [arXiv:0901.3775] is explored. In the i