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N. Pandey Department of Mathematics and Computer Science The Papua New Guinea University of Technology, Lae, PNG,uZ i*Gravitational waves or Geometry propagates++ * Einstein s equation: In vacuum Under harmonic coordinate condition it yields FT;T  +Non-conformal Nature of Gravitational waves,,+ Weak interaction Gravitation wave equation can be reduced to In the background of Friedmann universe taken in conformally flat form R-JHW        g+Non-conformal Nature of Gravitational waves,,+ Where is scale factor of Friedmann universe and n is the wave number such that the physical wave length is given by . Two Special Cases nn9B:  Y  )Field Equations in Modified Field Theory **) G derivable by Lagrangian R Modify Lagrangian ? Choose Lagrangian Or, equivalently, ?POPPPPEP/PPPPJC< J - k(Field Equations in Modified Field Theory)) ( dThis choice of f(R) should not be disturbing because it is an observational fact that our universe is not asymptotically flat. There is enough matter on our past light cone to cause it to refocus. The total energy of the universe is exactly zero, the positive energy of gravitation and the matter particle being exactly compensated by the negative gravitational potential energy. That is why the universe is expanding. Also unitarity is not well defined except in scattering calculations in asymptotically flat spaces. An application of variational principle to this action yields the following field equations:exe,   r For n = 2 Comparable with 6  " d  'Gravitational Waves in Modified Theory (&$(' All physical fields can be regarded as embedded, or given 4~9E  Effect of Potential   Cosmological Aspects /Consider homogeneous isotropic closed universe &/ZZ0/ Cosmological Aspects( This equation is the differential equation that describes the closed Friedmann model in this f(R) theory. However, for an open Friedmann model similar calculations will follow and we get terms like ( ) instead of ( ) and M in this case can not be interpreted as a total mass. For Radiation Dominant Era In the condition of very early universe  << 1. we get {" (  E  ,    7 Spherically Symmetric field$ iwe consider spherically symmetric static field given by In vacuum It can easily be seen that 8ZZ ZZZZZZ7272 ySpherically Symmetric field$ Here it should be noted that is the total mass of the system. A simple calculation after expanding in powers of r as leads to Hence the metric becomes JOyQ0  8 Motion of Particles or Planets i We consider equations of motion of a particle or planet in this gravitational field. They are, ZZZaZZe( ` }Motion of Particles or Planets Assuming that orbit is in plane we get from the above third equation that showing that the orbit remains in this plane and also where A and B are constants A simple calculation leads to which can be reduced to xBNa ^Motion of Particles or Planets where This is the Equation of Motion in Modified Field Theory Corresponding equation in Newton s Theory Corresponding equation in Einstein theory ZZZZ + 9 Remarks Further this metric is nearly flat if . The effect of mass term M dominates for the values of r below this range and the effect of dominates for the values of r above this range. However, in this situation the Newtonian potential gets modified to . The second term is due to correction in Hilbert Lagrangian, R. However, in case of motion, the equation differs from Newtonian theory by . VxxqG L  Approximation(  We consider as a solution to Newtonian Equation. Like wise it can be seen that is a solution of Modified Field Theory Equation which represents a precessing elliptical orbit. If changes by the arguments of cosine changes by 2;. This shows that angular distance between one perihelion and the next is larger than 2; by . SPP9T  r  T  M  References  <Ellis G F R and Hawking S. Large Scale Structure of Space time, 1975, Oxford Univ. Press. Wald R 1984. General Relativity 1984, Chicago Univ. Press. Grishchuk L P Gravitational waves in the Cosmos and the Laboratory, Soviet Phys. Uspekhi, 20 (1977), 319. Pandey S N, Conformally invariant gravitational waves in a modified Gravitational Theory, Inter. J. Theor. Phys. 22 (1983), 209. Pandey S N, Higher Order Theory of Gravitation, Inter. J. Theor. Phys. 27 (1988), 695 Pandey S N, On Cosmological Solutions of a higher-order theory of gravitation, Nuovo Cimento 116 B (2001), 327. Pandey S N, Gravitation 1999, Phoenix Publishing House, New Delhi Landau L D and Lifshitz E M. 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L 0] TY,$D  0 Then modified field equations It can be seen that holds for these field equations as it is in case of Einstein general relativity. 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