Photon size in higher dimensional phantom cosmology

Abstract

We study a higher dimensional cosmology with phantom field associated with a negative kinetic term. Assuming that the universe possesses the phantom field defined in $D$ dimensional spacetime, we investigate in detail the solutions involved in the higher dimensional phantom cosmology, to explicitly predict photon size and phantom field strength at present in nature. To be specific, we find that the photon size decreases drastically at the early stage of the universe after the Big Bang. Next we explicitly demonstrate the dependences of the photon size, universe size and phantom field strength on the spacetime dimensionality $D$. We observe that the size of the universe undergoes stiff explosion with different types of slope depending on $D$. Moreover the scale factor of the universe at present is shown to approach to a saturated value, which is independent of $D$ and is the same as that in the $D=4$ Friedmann-Robertson-Walker cosmology. The photon size and phantom field strength in the greater dimensionality are also shown to be larger and lower than those in the smaller one, respectively. Next the photon size at present $b_{*}$ in $D=5$ is numerically shown to be extremely small, namely $b_{*}=6.08\times 10^{-216}$ cm, comparing to $b_{*}=1.56\times 10^{-63}$ cm in $D=10$. In contrast, the phantom field strength at present $\sigma_{*}$ is shown to be relatively large $\sigma_{*}=4.72\times 10^{24}$ (dyne$)^{1/2}$ in $D=5$, comparing to $\sigma_{*}=1.39\times 10^{22}$ (dyne$)^{1/2}$ in $D=10$.