Diego Saez-Gomez

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1 aside from the gravity part, also contains I. FORMULAE a matter contribution, namely F(R) gravity aside from the gravity part, also contains a matter contribution, namely S = d 4 x √ −g f(R)+2κ 2 L m . (2.1) c 1 (R/R HS ) n f(R) =R − R HS c Action, 2 (R/R HS ) n +1 , =R + Rn (aR n − b) S = d 4 x √ −g f(R)+2κ 2 L m . 1+cR n . (2.1) (1) Here the coupling constant is given by κ 2 = 8πG, while L m stands for the Lagrangian I. FORMULAE corresponding to the matter that fills the Here the coupling constant S EH = d 4 x √ is −g given by κ R +2κ 2 2 particular system to be studied. Note that the = 8πG, while L L m → S = d 4 x √ m stands −g for the f(R)+2κ 2 Lagrangian Hilbert-Einstein action is recovered for f(R) =R in (2.1), The field equations corresponding corresponding to the matter that fills the particular system to be studied. LNote m . that the (2) to action (2.1) are obtained by the variation of this action with respect to the metric tensor Hilbert-Einstein action is recovered for f(R) =R in (2.1), The field equations corresponding g c 1 (R/R HS ) n f(R) =R − R to action (2.1) are obtained by the variation of this action with HS respect c 2 (R/R to HS the ) n metric +1 , f(R) tensor =R + Rn (aR n − b) µν , what yields 1+cR n . g Field µν , what equations, yields R µν f R (R) − 1 R µν f R (R) − 1 2 g S µνf(R)+g µν f R (R) EH = d −∇ 4 x √ −g 2 g µνf(R)+g µν f R (R) −∇ µ ∇ ν f R (R) =κ 2 T µν (m) . (2.2) R +2κ µ ∇ ν f R (R) =κ 2 2 L T µν (m) m → S = d . (2.2) 4 x √ −g f(R)+2κ 2 L m . Here the subscript R denotes derivatives with respect to R. We assume a flat FLRW metric, Here the subscript R denotes derivatives with respect to 3 R. We assume a flat FLRW metric, where as usual the energy-momentum tensor is defined as: T µν (m) = −√ 2 δ ( √ −gL m ) ds 2 = −dt 2 + a(t) 2 dx i2 . −g δg 3 µν (2.3) ds 2 = −dt 2 + a(t) 2 i=1 dx i2 . (2.3) Spatially Then, for flat this FLRW metric, equations, modified FLRW equations i=1 are obtained through the 00 and ij components of the field equations (2.2), Then, for this metric, modified FLRW equations are obtained through the 00 and ij components of the field equations (2.2), H 2 = 1 κ H 2 = 1 2 ρ m + Rf R − f − 3f R κ 2 ρ m + Rf 2 3HṘf RR , R − f − 3f R 2 3HṘf RR , −3H 2 − 2Ḣ = 1 κ −3H 2 − 2Ḣ = 1 2 p m + f Ṙ2 f RRR +2HṘf RR + ¨Rf RR + 1 R κ 2 p m + f Ṙ2 f RRR +2HṘf RR + ¨Rf RR + 1 2 (f − Rf R) , (2.4) R 2 (f − Rf R) , (2.4) where dots denote derivatives with respect the time, Hubble parameter is defined as usual H(t) =ȧ/a, and Ricci scalar for the metric (2.3) isR =6(2H2 +Ḣ). Here, we are interested where dots denote derivatives with respect the time, Hubble parameter is defined as usual in studying a subclass of modified gravities, the so-called H(t) =ȧ/a, and Ricci scalar for the metric (2.3) isR =6(2H2 viable f(R) gravities, as they +Ḣ). Here, we are interested accomplish some indispensable conditions to be considered realistic candidates to describe
Viable f(r) gravity Viability conditions for F(R) gravity 1. f RR > 0 for hight curvature, which ensures the existence of stable high curvature regimes, as the matter dominated epoch. 2. 1 + f R > 0, which avoids the appearance of a negative effective gravitational coupling G eff = G/(1 + f R ), and the anti-gravity regime, implying also the avoidance of the graviton to turn into a ghost. 3. f R → 0 as R →∞. GR has to be recovered at early times. Together with f RR > 0, implies f R < 0, and consequently −1
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: FLRW cosmologies Future singulariti
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 and 24: effective repulsive force 12h R ∼
Page 25 and 26: Testing F(R) gravity with Sne Ia da
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

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