Cosmography and Large Scale Structure by 𝑓(𝑅)-Gravity: New Results

Table 2

Column 1: Cluster name. Column 2: first derivative coefficient, 𝑎₁, of 𝑓(𝑅) series. Column 3: 1𝜎 confidence interval for 𝑎₁. Column 4: second derivative coefficient, 𝑎₂, of 𝑓(𝑅) series. Column 5: 1𝜎 confidence interval for 𝑎₂. Column 6: characteristic length, 𝐿, of the modified gravitational potential, derived from 𝑎₁ and 𝑎₂. Column 7: 1𝜎 confidence interval for 𝐿.

Name	𝑎1	[𝑎1−1𝜎, 𝑎1+1𝜎]	𝑎2	[𝑎2−1𝜎, 𝑎2+1𝜎]	𝐿	[𝐿−1𝜎, 𝐿+1𝜎]
			(kpc^2)	(kpc^2)	(kpc)	(kpc)
A133	0.085	[0.078, 0.091]	−4.98⋅10^3	[−2.38⋅10^4, −1.38⋅10^3]	591.78	[323.34, 1259.50]
A262	0.065	[0.061, 0.071]	−10.63	[−57.65, −3.17]	31.40	[17.28, 71.10]
A383	0.099	[0.093, 0.108]	−9.01⋅10^2	[−4.10⋅10^3, −3.14⋅10^2]	234.13	[142.10, 478.06]
A478	0.117	[0.114, 0.122]	−4.61⋅10^3	[−1.01⋅10^4, −2.51⋅10^3]	484.83	[363.29, 707.73]
A907	0.129	[0.125, 0.136]	−5.77⋅10^3	[−1.54⋅10^4, −2.83⋅10^3]	517.30	[368.84, 825.00]
A1413	0.115	[0.110, 0.119]	−9.45⋅10^4	[−4.26⋅10^5, −3.46⋅10^4]	2224.57	[1365.40, 4681.21]
A1795	0.093	[0.084, 0.103]	−1.54⋅10^3	[−1.01⋅10^4, −2.49⋅10^2]	315.44	[133.31, 769.17]
A1991	0.074	[0.072, 0.081]	−50.69	[−3.42⋅10^2, −13]	64.00	[32.63, 159.40]
A2029	0.129	[0.123, 0.134]	−2.10⋅10^4	[−7.95⋅10^4, −8.44⋅10^3]	988.85	[637.71, 1890.07]
A2390	0.149	[0.146, 0.152]	−1.40⋅10^6	[−5.71⋅10^6, −4.46⋅10^5]	7490.80	[4245.74, 15715.60]
MKW4	0.054	[0.049, 0.060]	−23.63	[−1.15⋅10^2, −8.13]	51.31	[30.44, 110.68]
RXJ1159	0.048	[0.047, 0.052]	−18.33	[−1.35⋅10^2, −4.18]	47.72	[22.86, 125.96]