FLRWFriedmann-Lemaître-Robertson-Walker Metric (an exact solution of Einstein's field theory of relativity)
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In the following, according to Randall model type II [12,13] in the teleparallel gravity theory, Friedmann equations for the brane in the FLRW background metric for effective gravity F(T) are determined as follows:
The latter is an attempt to explain the special FLRW condition of standard big bang cosmology, even without a period of inflation.
As the curvature invariants of FLRW metric are proportional to H and [??] the phase space boundaries [absolute value of H] [right arrow] [infinity], [absolute value of [rho]] [right arrow] [infinity], and [absolute value of [??]] [right arrow] [infinity] generically entail a space-time singularity.
To be compatible with the modification of the FLRW metric, we reduce a number of degrees of freedom of the field [phi](t, r) and preserve the rotational symmetries just as what we did before.
Combining with the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric of 4D spacetime, the field equation given in GR derives the Friedmann equation (FE) that governs the dynamic and development of the universe.
The closed Universe Friedmann - Lemaitre - Robertson Walker (FLRW) spacetime metric is given by [4-10]:
The Milne metric is a special case of a Friedmann-Lemaitre-Robertson-Walker (FLRW) model in the limit of zero energy density (empty universe).
Here there is no contradiction with (1) nor with the FLRW universe; but the concept appears to imply that dark matter is pressure and that mass is compression work.
Throughout the work, we assume flat, homogeneous, isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) metric,
The spacetime metric for k = 1 according to Friedmann-Lemaitre-Robertson-Walker (FLRW) is [1,3]
In fact, this is easy to do on a Friedmann-Lemaitre-Robertson-Walker (FLRW) setting, with a metric of the form: