2012 International Workshop on String Theory and Cosmology Evolution of Universe In Eddington-inspired Born-Infeld Gravity Inyong Cho Seoul National University of Science & Technology 2012 International Workshop on String Theory and Cosmology Pusan, Korea, Jun 14-16, 2012 - In preparation with Hyeong-Chan Kim (CNU) & Taeyoon Moon (CQUeST)

Outline 1. Introduction to EiBI Gravity A. Formalism B. Field Equations C. Some Physical Solutions 2. Evolution of Universe filled with Perfect Fluid A. Isotropic case B. Anisotropic case 3. Conclusions

Eddington-inspired Born-Infeld Gravity Formalism Einstein Gravity Field:

Eddington Gravity (1924) Field: Varying S, Integrating by parts, Eliminating a vanishing trace, we get

Therefore, Eddington’s action :- viable and alternative starting point to GR :- :- dual to GR However, incomplete : NOT including MATTER Later attempts to couple matter with :- start with Palatini gravitational action coupled to matter -- no derivatives in g :- EOM for g   back into  can eliminate g :- : complicated, but Dynamics is fully equivalent to the original metric theory

Eddington-inspired Born-Infeld Gravity One parameter (k) theory :- coupling matter insisting neither on Affine action, nor on Einstein action (Vollick 2004) :- : independent :- Matter is in usual way (Not in sqrt) :- For large -limit  Eddington limit :- For small -limit  Einstein limit In vacuum  Equivalent to Einstein Gravity

Field Equations : Energy-Momentum Conservation  Matter plays in the background metric

Some Physical Solutions (Banados-Ferreira 2010) Corrections to Poisson Equation By expanding Field Equations to 2nd order in k : Metric : with and : Poisson Equation

Black Hole Solutions In vacuum  Equivalent to Einstein Gravity Therefore, EiBI in vacuum or with only CC is the same with EH

Schwartzchild-de Sitter BH SAME with Einstein Solution Charged BH : non vacuum : electric field

Perfect Fluid : FRW Universe Banados & Ferreira (2010) Metric : EM tensor : For radiation,

1) Typy-I : near 2) Typy-II : near Bouncing Non Singular

Other Phenomenological Results :- star (sun) formation simulation by using Poisson Eq.  puts viable bounds on the value of k :- dark matter :- density perturbation Etc…

Evolution of Universe with Perfect Fluid Metric & Auxiliary Metric Energy-Momentum Tensor

EOM 1 From these, we get

EOM 2 From these, we get

Friedmann Equations Volume Part : Anisotropic Part : :- In r >> and r << limits, consider cases of i) w>0 ii) w=0 iii) w<0 iv) w=-1 :- Consider k>0 case only

1) w>0

2) w=0

3) -1<w<0 Isotropic Case : like Einstein Anisotropic Case: differs from Einstein for -1<w<1/3

Anisotropy w>0 case :- decays to 0 exponentially at both ends  Initial Singularity in Anisotropy is REMOVED !  Late-time anisotropy approaches a constant :- has a maximum in the intermediate period 2) w<0 case :- decays to 0 exponentially  Late-time anisotropy approaches a constant :- diverges initially like in Einstein

4) w=-1

EiBI : Palatini-type Gravity + Matter Conclusions EiBI : Palatini-type Gravity + Matter Cosmological solution : avoids initial singularity, or bouncing For perfect fluid w>0 : non-singular initial beginning w=0 : initial de Sitter -1<w<0 : similar to Einstein Gravity w=-1 : same with Einstein Gravity Late time evolution : similar to Einstein Gravity