Why Study Modified Gravity? Andrei Frolov (SFU) Unscreening - PowerPoint PPT Presentation

U NSCREENING S CALARONS arXiv:1704.04114 , arXiv:1312.4625 Andrei Frolov Jun-Qi Guo (SFU) Daoyan Wang (UBC) José Tomás Gálvez Ghersi (SFU) Alex Zucca (SFU) Gravity and Cosmology 2018 Yukawa Institute for Theoretical Physics, Kyoto, Japan 13 February 2018 Andrei Frolov (SFU) Unscreening Scalarons GC2018 1 / 33

Why Study Modified Gravity? Andrei Frolov (SFU) Unscreening Scalarons GC2018 2 / 33

T HE B EST A NSWER I F OUND S O F AR ... Andrei Frolov (SFU) Unscreening Scalarons GC2018 2 / 33

M AYBE IT ’ S G RAVITY WE D ON ’ T U NDERSTAND M ODIFY E INSTEIN -H ILBERT ACTION TO INCLUDE OTHER STUFF , E . G . � � f ( R ) �� − g d 4 x S = 16 π G + � m UV MODIFICATION : IR MODIFICATION : f ( R ) = R − µ 4 f ( R ) = R + R 2 M 2 R Capozziello et. al. [ astro-ph/0303041 ] Starobinsky (1980) Carroll et. al. [ astro-ph/0306438 ] F OR F(R) THEORY TO MAKE SENSE WE NEED : f ′ > 0 – otherwise gravity is a ghost f ′′ > 0 – otherwise gravity is a tachyon Andrei Frolov (SFU) Unscreening Scalarons GC2018 3 / 33

M AYBE IT ’ S G RAVITY WE D ON ’ T U NDERSTAND M ODIFY E INSTEIN -H ILBERT ACTION TO INCLUDE OTHER STUFF , E . G . � � f ( R ) �� − g d 4 x S = 16 π G + � m UV MODIFICATION : IR MODIFICATION : f ( R ) = R − µ 4 f ( R ) = R + R 2 M 2 R Capozziello et. al. [ astro-ph/0303041 ] Starobinsky (1980) Carroll et. al. [ astro-ph/0306438 ] F OR F(R) THEORY TO MAKE SENSE WE NEED : f ′ > 0 – otherwise gravity is a ghost f ′′ > 0 – otherwise gravity is a tachyon Andrei Frolov (SFU) Unscreening Scalarons GC2018 3 / 33

M AYBE IT ’ S G RAVITY WE D ON ’ T U NDERSTAND M ODIFY E INSTEIN -H ILBERT ACTION TO INCLUDE OTHER STUFF , E . G . � � f ( R ) �� − g d 4 x S = 16 π G + � m UV MODIFICATION : IR MODIFICATION : f ( R ) = R − µ 4 f ( R ) = R + R 2 M 2 R Capozziello et. al. [ astro-ph/0303041 ] Starobinsky (1980) Carroll et. al. [ astro-ph/0306438 ] F OR F(R) THEORY TO MAKE SENSE WE NEED : f ′ > 0 – otherwise gravity is a ghost f ′′ > 0 – otherwise gravity is a tachyon Andrei Frolov (SFU) Unscreening Scalarons GC2018 3 / 33

M AYBE IT ’ S G RAVITY WE D ON ’ T U NDERSTAND M ODIFY E INSTEIN -H ILBERT ACTION TO INCLUDE OTHER STUFF , E . G . � � f ( R ) �� − g d 4 x S = 16 π G + � m UV MODIFICATION : IR MODIFICATION : f ( R ) = R − µ 4 f ( R ) = R + R 2 M 2 R Capozziello et. al. [ astro-ph/0303041 ] Starobinsky (1980) Carroll et. al. [ astro-ph/0306438 ] F OR F(R) THEORY TO MAKE SENSE WE NEED : f ′ > 0 – otherwise gravity is a ghost f ′′ > 0 – otherwise gravity is a tachyon Andrei Frolov (SFU) Unscreening Scalarons GC2018 3 / 33

E XPECT D EVIATION FROM Λ CDM C OSMOLOGY Oyaizu, Lima & Hu ( 0807.2462 ) Andrei Frolov (SFU) Unscreening Scalarons GC2018 4 / 33

I NVOKE C HAMELEON TO S ATISFY L OCAL T ESTS 1 ρ R / κ 2 ( n =4, | f R 0 |=0.1) n =4 ρ (g cm -3 ) ρ | f R 0 | =0.001 10 -10 R /κ 2 (g cm -3 ) | f R 0 | =0.01 10 -23 | f R 0 | =0.05 | f R 0 | =0.1 10 -24 10 4 100 1000 10 -20 r / r Hu & Sawicki ( 0705.1158 ) 0.1 1 10 100 1000 r / r Andrei Frolov (SFU) Unscreening Scalarons GC2018 5 / 33

F IELD E QUATIONS IN F(R) G RAVITY Vary the action with respect to the metric: � � f ( R ) �� − g d 4 x S = 16 π G + � m Einstein equations turn into a fourth-order equation: � � � f ′ − 1 f ′ R µν − f ′ ; µν + 2 f g µν = 8 π G T µν A new scalar degree of freedom φ ≡ f ′ − 1 appears: � f ′ = 1 3 ( 2 f − f ′ R ) + 8 π G T 3 Can rewrite fourth-order field equation as two second order ones! Andrei Frolov (SFU) Unscreening Scalarons GC2018 6 / 33

A N EW S CALAR D EGREE OF F REEDOM Equation for φ ≡ f ′ − 1 is just a scalar wave equation: � φ = V ′ ( φ ) − � Matter directly drives the field φ by a force term: � = 8 π G ( ρ − 3 p ) 3 Effective potential can be found by integrating V ′ ( φ ) ≡ d V d φ = 1 3 ( 2 f − f ′ R ) In practice, easier to obtain in parametric form: d V d R ≡ d V d φ d R = 1 3 ( 2 f − f ′ R ) f ′′ d φ Andrei Frolov (SFU) Unscreening Scalarons GC2018 7 / 33

E XAMPLE I: (S AFE ) UV M ODIFICATION 2.5 f ( R ) = R + R 2 2 V/M M 2 2.0 φ = 2 R 1.5 M 2 in vacuum 1.0 M 2 = M 2 R 2 V = 1 12 φ 2 0.5 3 0 massive scalar field! φ –1 –0.5 0 0.5 1 scalar degree of freedom φ is heavy and hard to U ( φ ) = V ( φ ) + � ( φ ∗ − φ ) excite Andrei Frolov (SFU) Unscreening Scalarons GC2018 8 / 33

E XAMPLE I: (S AFE ) UV M ODIFICATION 2.5 f ( R ) = R + R 2 2 V/M in matter M 2 2.0 φ = 2 R 1.5 M 2 in vacuum 1.0 M 2 = M 2 R 2 V = 1 12 φ 2 0.5 3 0 massive scalar field! φ –1 –0.5 0 0.5 1 scalar degree of freedom φ is heavy and hard to U ( φ ) = V ( φ ) + � ( φ ∗ − φ ) excite Andrei Frolov (SFU) Unscreening Scalarons GC2018 8 / 33

E XAMPLE II: (F AILED ) IR M ODIFICATION 0.5 f ( R ) = R − µ 4 V/ µ 2 R 0.4 φ = µ 4 R 2 0.3 φ � � µ 4 R − µ 8 2 0.2 i V = n v 3 R 3 a c u u 2 3 µ 2 � � 0.1 m 1 3 2 − φ = φ 2 0 field φ is unstable! 0.2 0.4 0.6 0.8 1 Dolgov & Kawasaki U ( φ ) = V ( φ ) + � ( φ ∗ − φ ) ( astro-ph/0307285 ) Andrei Frolov (SFU) Unscreening Scalarons GC2018 9 / 33

E XAMPLE II: (F AILED ) IR M ODIFICATION 0.5 f ( R ) = R − µ 4 V/ µ 2 R 0.4 φ = µ 4 R 2 0.3 φ � � µ 4 R − µ 8 2 0.2 i V = n v 3 R 3 a c u in matter u 2 3 µ 2 � � 0.1 m 1 3 2 − φ = φ 2 0 field φ is unstable! 0.2 0.4 0.6 0.8 1 Dolgov & Kawasaki U ( φ ) = V ( φ ) + � ( φ ∗ − φ ) ( astro-ph/0307285 ) Andrei Frolov (SFU) Unscreening Scalarons GC2018 9 / 33

C AN W E C OME U P W ITH S OMETHING B ETTER ? Hu and Sawicki [ 0705.1158 ] Starobinsky [ 0706.2041 ] � � α ( R / R 0 ) n 1 f ( R ) = R − 1 + β ( R / R 0 ) n R 0 f ( R ) = R + λ ( 1 + ( R / R 0 ) 2 ) n − 1 R 0 1.0 1.0 n=1 n=1 0.9 0.9 n=2 n=2 n=4 n=4 0.8 0.8 0.7 0.7 0.6 0.6 (R-F)/R 0 (R-F)/R 0 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 10 -2 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0 10 1 10 2 R/R 0 R/R 0 ... and many other models ... Andrei Frolov (SFU) Unscreening Scalarons GC2018 10 / 33

D ISAPPEARING C OSMOLOGICAL C ONSTANT Starobinsky [ 0706.2041 ] V/R 0 1 + R 2 � − 1 − 1 G �� � 1.4 f ( R ) = R + λ 1.2 2 λ R φ = − 1.0 ( 1 + R 2 ) 2 0.8 A singularity ( R = + ∞ ) ( f ′ = 0 ) 0.6 B stable dS min C unstable dS max ( f ′ = 0 ) 0.4 ( f ′′ = 0 ) D critical point 0.2 ( f ′ = 0 ) E flat spacetime φ E 0 ( f ′′ = 0 ) F critical point B C A D F ( R = −∞ ) G singularity –1.5 –1.0 –0.5 0 0.5 1.0 1.5 Andrei Frolov (SFU) Unscreening Scalarons GC2018 11 / 33

D ISAPPEARING C OSMOLOGICAL C ONSTANT Starobinsky [ 0706.2041 ] V/R 0 1 + R 2 � − 1 − 1 G �� � 1.4 f ( R ) = R + λ 1.2 2 λ R φ = − 1.0 ( 1 + R 2 ) 2 0.8 A singularity ( R = + ∞ ) ( f ′ = 0 ) 0.6 B stable dS min C unstable dS max ( f ′ = 0 ) 0.4 ( f ′′ = 0 ) D critical point 0.2 ( f ′ = 0 ) E flat spacetime φ E 0 ( f ′′ = 0 ) F critical point B C A D F ( R = −∞ ) G singularity –1.5 –1.0 –0.5 0 0.5 1.0 1.5 Andrei Frolov (SFU) Unscreening Scalarons GC2018 11 / 33

D ISAPPEARING C OSMOLOGICAL C ONSTANT Starobinsky [ 0706.2041 ] V/R 0 1 + R 2 � − 1 − 1 G �� � 1.4 f ( R ) = R + λ 1.2 2 λ R φ = − 1.0 ( 1 + R 2 ) 2 0.8 A singularity ( R = + ∞ ) ( f ′ = 0 ) 0.6 B stable dS min C unstable dS max ( f ′ = 0 ) 0.4 ( f ′′ = 0 ) D critical point 0.2 ( f ′ = 0 ) E flat spacetime φ E 0 ( f ′′ = 0 ) F critical point B C A D F ( R = −∞ ) G singularity –1.5 –1.0 –0.5 0 0.5 1.0 1.5 Andrei Frolov (SFU) Unscreening Scalarons GC2018 11 / 33

D ISAPPEARING C OSMOLOGICAL C ONSTANT Starobinsky [ 0706.2041 ] V/R 0 1 + R 2 � − 1 − 1 G �� � 1.4 f ( R ) = R + λ 1.2 2 λ R φ = − 1.0 ( 1 + R 2 ) 2 0.8 A singularity ( R = + ∞ ) ( f ′ = 0 ) 0.6 B stable dS min C unstable dS max ( f ′ = 0 ) 0.4 ( f ′′ = 0 ) D critical point 0.2 ( f ′ = 0 ) E flat spacetime φ E 0 ( f ′′ = 0 ) F critical point B C A D F ( R = −∞ ) G singularity –1.5 –1.0 –0.5 0 0.5 1.0 1.5 Andrei Frolov (SFU) Unscreening Scalarons GC2018 11 / 33

D ISAPPEARING C OSMOLOGICAL C ONSTANT Starobinsky [ 0706.2041 ] V/R 0 1 + R 2 � − 1 − 1 G �� � 1.4 f ( R ) = R + λ 1.2 2 λ R φ = − 1.0 ( 1 + R 2 ) 2 0.8 A singularity ( R = + ∞ ) ( f ′ = 0 ) 0.6 B stable dS min C unstable dS max ( f ′ = 0 ) 0.4 ( f ′′ = 0 ) D critical point 0.2 ( f ′ = 0 ) E flat spacetime φ E 0 ( f ′′ = 0 ) F critical point B C A D F ( R = −∞ ) G singularity –1.5 –1.0 –0.5 0 0.5 1.0 1.5 Andrei Frolov (SFU) Unscreening Scalarons GC2018 11 / 33

D ISAPPEARING C OSMOLOGICAL C ONSTANT Starobinsky [ 0706.2041 ] V/R 0 1 + R 2 � − 1 − 1 G �� � 1.4 f ( R ) = R + λ 1.2 2 λ R φ = − 1.0 ( 1 + R 2 ) 2 0.8 A singularity ( R = + ∞ ) ( f ′ = 0 ) 0.6 B stable dS min C unstable dS max ( f ′ = 0 ) 0.4 ( f ′′ = 0 ) D critical point 0.2 ( f ′ = 0 ) E flat spacetime φ E 0 ( f ′′ = 0 ) F critical point B C A D F ( R = −∞ ) G singularity –1.5 –1.0 –0.5 0 0.5 1.0 1.5 Andrei Frolov (SFU) Unscreening Scalarons GC2018 11 / 33