Diego Saez-Gomez

More documents

Recommendations

Info

cosmological evolution, e of the Solar system, the force of the coupling between Sun and a body of mass m aracterized by the Newtonian law, F N = G mM ⊙ F F N = G mM r 2 . (5.2) cosm r 3 = The ⊙ H0 2 Little Rip where r 2 . (5.2) M⊙ =1.9 F N 10 30 GM kg is Sun the mass of the Sun, and r is the distance between the Sun and the body m. Here, in both cases it is assumed that F ⊙ =1.9 10 30 i = | F i |, as both forces have radial directions, kg is thebut mass opposite of thesign. Sun, Hence, and r we is may the distance between the Sun ody m. Here, in both cases it is assumed that F Little Rip in viable f(R) gravity i = | F compare both quantities along the cosmological For the case of the Earth-Sun system, i |, as r both = forces 149.6 have × 10 radial 9 evolution, , but opposite sign. Hence, we mayF compare cosm both quantities along the cosmological , = r3 F N F cosm = r3 GM⊙ H2 0 h(z) 2 − (1 + z)h(z) h (z) , (5.3) of the previous sections, h(0) = 1 and a) h F N GM⊙ H2 0 h(z) 2 − (1 + z)h(z) h (z) (0) = 3 2 Ω(0) of both where forces recall athat z =0is we defined given H(z) by=H 0 h(z) in , section 3, whereH(5.3) 0 = 100 hkms −1 Mpc −1 with h = 0.71 ± 0.03. Let’s compare both forces for the Earth-Sun system, where r = all that we defined 149.6 × H(z) 10 9 m=H is the 0 h(z) Earth-Sun in section distance, 3, whereH at the 0 = present 100 hkms time, −1 z Mpc = 0, −1 0.71 ± Earth-Sun 0.03. Let’ssystem (i) F cosm ∼ 0.82 × 10 −22 , (ii) F cosm compareF N both forces for the Earth-Sun system, where r = 0 9 m is the Earth-Sun distance, At z=0 at theF cosm present =1.4 time, × 10 z −22 = 0, h(0) 2 − h(0)h (0) , (5.4) F N F cosm h(z) 2 − (1 + z)h(z) h (z) , (31) where recall that H(z) =H 0 h(z), where H 0 =100hkms −1 Mpc −1 with h =0.71±0.03. m, the ratio (31) yields F cosm /F N =1.4×10 −22 [h(0) 2 − h(0)h (0)] and by considering the same initial conditions m ,andb) h (0) = −0.1, theratio F N ∼ 1.95 × 10 −22 . (32) =1.4 × 10 −22 h(0) 2 − h(0)h (0) , (5.4) Then, Fby N assuming the initial conditions from section 3, h(0) = 1 and a) h (0) = 3 2 Ω(0) m , and b) h (0) = −0.1, assuming the initial conditions from section 3, h(0) = 1 and a) h (0) = 3 2 Ω(0) m , and −0.1, (i) F HS NOcosm ∼ 0.82 × 10 −22 , (ii) F cosm ∼ 1.95 × 10 −22 . (5.5) F N F N 1.10 22 1.10 22 (i) F cosm ∼ 0.82 × 10 −22 , (ii) F cosm Hence, F N both values are too small ∼ 1.95 × 10 −22 . (5.5) F N to produce any kind of instability on the orbits of the 1.510 22 z 1.210 22 z 8.10 23 oth values are too small to produce any kind of instability on 5.10 the 23 orbits of the 6.10 23 4.10 23 – 14 – – 14 – 1.0 0.5 0.0 0.5 1.0 1.0 0.5 0.0 0.5 1.0 0 HS NO DSG, Class.Quant.Grav. 30 095008 (2013)
Testing F(R) gravity with Sne Ia data A simple model f(R) =a R R 0 n R + b R 0 Viability conditions To ensure the occurrence of a matter dominated epoch at high redshifts: 0.75 −bn b>0 and n>1 or b0.75 n−1 R R 0 Fixed point: matter dominated epoch a = n [2n(1 + q 0 +2δ 1 ) − 3(1 + δ 1 )] (n − 1) [3 + n(8n − 13)] (q 0 − 1)(1 + δ 2 ) b = k(1 − q 0) −n 2n 2 (q 0 − 1) − 3(1 + δ 1 )+4n(1 + δ 1 ) (n − 1) [3 + n(8n − 13)] (1 + δ 2 ) A. Cruz-Dombriz, P. Dunsby, DSG, in preparation
Page 1 and 2: Cosmological constraints on modifie
Page 3 and 4: Brief Article The Author April 6, 2
Page 5 and 6: FLRW cosmologies 12 3 No Big Bang (
Page 7 and 8: FLRW cosmologies Future singulariti
Page 9 and 10: Viable f(r) gravity Viability condi
Page 11 and 12: 3 Cosmological evolution in viable
Page 13 and 14: Cosmological evolution in viable f(
Page 15 and 16: Cosmological evolution in viable f(
Page 17 and 18: 8 − 3H 2 − 2Ḣ = 1 κ 2 p m +
Page 19 and 20: (z = 0) = H 0 = 100 hkms −1 Mpc
Page 21 and 22: (z = 0) = H 0 = 100 hkms −1 Mpc
Page 23: effective repulsive force 12h R ∼
Page 27 and 28: Testing F(R) gravity with Sne Ia da
Page 29 and 30: ere right lethand us remind side (r
Page 31 and 32: e previous section, we study two pa
Page 33 and 34: en at redshift z = 1000 where δ is

Diego Saez-Gomez

Create successful ePaper yourself

Delete template?

Save as template?