1206.6164 (Antonio Enea Romano)

Conditions for low-redshift positive apparent acceleration in smooth
inhomogeneous models    [PDF]

Antonio Enea Romano

It is known that a smooth LTB model cannot have a positive apparent central acceleration. Using a local Taylor expansion method we study the low-redshift conditions to obtain an apparent negative deceleration parameter $q^{app}(z)$ derived from the luminosity distance $D_L(z)$ for a central observer in a LTB space, confirming that central smoothness implies a positive central deceleration. We then consider red-shifts greater than zero and find the critical values of the parameters defining a centrally smooth LTB model which give a negative apparent acceleration at that point, providing a graphical representation of the conditions in the $q_0^{app},q_1^{app}$, which are respectively the zero and first order terms of the central Taylor expansion of $q^{app}(z)$. We calculate $q^{app}(z)$ with two different methods to solve the null geodesic equations, one based on a local central expansion of the solution in terms of cosmic time and the other one using the exact analytical solution in terms of generalized conformal time. The expansion of the solution in terms of cosmic time is quite useful also for other applications requiring foliation of space-time in space-like hyper-surfaces, such as spatial averaging, which is much more difficult to study using conformal time.

View original: http://arxiv.org/abs/1206.6164