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- Title
Conditions for low-redshift positive apparent acceleration in smooth inhomogeneous models.
- Authors
Romano, Antonio
- Abstract
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. Since observational data is only available at redshift greater than zero we find the critical values of the parameters defining a centrally smooth LTB model which give a positive apparent acceleration at $$z>0$$, providing a graphical representation of the conditions in the $$q_0^{app},q_1^{app}$$ plane, which are respectively the zero and first order terms of the central Taylor expansion of $$q^{app}(z)$$. We finally derive a coordinate independent expression for the apparent deceleration parameter based on the expansion of the relevant functions in red-shift rather than in the radial coordinate. 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.
- Subjects
REDSHIFT; ACCELERATION (Mechanics); TAYLOR'S series; HUBBLE'S law; LUMINOSITY; SMOOTHNESS of functions; GEODESIC equation
- Publication
General Relativity & Gravitation, 2013, Vol 45, Issue 8, p1515
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-013-1541-x