Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Tachyon inflation in DBI and RSII context

Mini workshop “Cosmology and Strings 2016” (2-5 November 2016, Nis, Serbia)

  • Login to see the comments

  • Be the first to like this

Tachyon inflation in DBI and RSII context

  1. 1. Tachyon inflation in DBI and RSII context Based on: M. Milosevic, D.D. Dimitrijevic, G.S. Djordjevic, M.D. Stojanovic, Dynamics of tachyon fields and inflation - comparison of analytical and numerical results with observation, Serbian Astron. J. (2016). doi:10.2298/SAJ160312003M. N. Bilic, D. Dimitrijevic, G. Djordjevic, M. Milosevic, Tachyon Inflation in an AdS Braneworld With Back-reaction, (2016) 19. http://arxiv.org/abs/1607.04524 Mini Workshop „Cosmology and String 2016“ Nis, November 2-5, 2016
  2. 2. Introduction and Motivation  The inflationary universe scenario in which the early universe undergoes a rapid expansion has been generally accepted as a solution to the horizon problem and some other related problems of the standard big-bang cosmology  Recent years - a lot of evidence from WMAP and Planck observations of the CMB  Quantum cosmology: probably the best way to describe the evolution of the early universe.
  3. 3. Tachyons and Non-standard Lagrangians  Traditionally, the word tachyon was used to describe a hypothetical particle which propagates faster than light.  In modern physics this meaning has been changed  The field theory of tachyon matter proposed by A. Sen  String theory: states of quantum fields with imaginary mass (i.e. negative mass squared)  It was believed: such fields permitted propagation faster than light  However it was realized that the imaginary mass creates an instability and tachyons spontaneously decay through the process known as tachyon condensation
  4. 4. Tachyion Fields  No classical interpretation of the ”imaginary mass”  The instability: The potential of the tachyonic field is initially at a local maximum rather than a local minimum (like a ball at the top of a hill)  A small perturbation - forces the field to roll down towards the local minimum.  Quanta are not tachyon any more, but rather an ”ordinary” particle with a positive mass.  Tachyon potential:  Dirack-Born-Infeld (DBI) Lagrangian (0) , '( 0) 0, ( ) 0V V T V T ( ) 1V T g T T
  5. 5. Tachyon inflation  Consider the tachyonic field T minimally coupled to Einstein's gravity  Where R is Ricci scalar, g – determinant of the metric tensor and tachyon action  Friedman equation:  The energy-momentum conservation equation: 41 16 T S gRd x S G 4 ( , ) , ( ) 1T S g T T d x V T g T T 2 2 2 2 1/2 1 3 (1 )Pl a V H a M T 2 3 ( ) 3 0 1 H P T V HT VT 2 2 ( ) 1 ( ) 1 V T T P V T T Energy density and pressure:
  6. 6. Nondimensionalization  Rescaling field, potential and time  The equation is transformed to  The nondimensional Hubble parameter  The nondimensional energy-momentum conservation equation  The nondimensional Friedman equation 0 , T x T 0 1 ( ) ( ) . T V x U x V T 0 , t t 3 2 0 '( ) '( ) 3 3 0. ( ) ( )o U x U x x HT x x HT x U x U x 0 .H T H 2 '( ) 3 0. ( )1 x U x Hx U xx 22 2 0 2 2 2 1/22 0 1 ( ) ( ) 33 (1 )1pl XH U x U x H T M xx
  7. 7. Tachyon inflation  Parameters:  The system of dimensionless equations  In addition, the Friedman acceleration equation 2 4 0 0 2 3 wher, (2 ) e s Pl s T M X M g 2 2 0 2 2 2 3/2 0 ( ) 3 1 (1 ) ( ) 3 ( )(1 ) 0 ( ) X U x H x x dU x x X U x x x U x dx 2 0 ( ) 2 X H P 2 2 ( ) 1 ( ) 1 U T x P U x x
  8. 8. Tachyon inflation  The slow-roll parameters  Number of e-folds  In the slow-roll aproximation  Observational parameters  The scalar spectral index  The tensor-to-scalar ratio * 1 0 ln | | , 0,i i d H i dN H 1 2 12 2 1 2 1 , 2 3 , 2 2 H H H HH x H x x 1 (16 )i r x 1 2 1 2 ( ) ( )is i x xn ( ) ( ) e i t t N t H t dt 2 2 0 1 ( ) where ( ) 1( ) , | ( ) | e ix e x U x N x X dx x U x 2 2 0 2 2 2 3/2 0 2 20 2 ( ) 3 1 (1 ) ( ) 3 ( )(1 ) 0 ( ) ( ) ( ( ) 1 ) 2 1 X U x H x x dU x x X U x x x U x dx X U T H U x x x
  9. 9. Tachyon inflation  Numerical results 0 4 60 120, 1 12 1 ( ) (left) 1 ( ) (right) cosh( ) N X U x x U x x
  10. 10. Tachyon inflation in an AdS braneworld  Randall–Sundrum models imagine that the real world is a higher-dimensional universe described by warped geometry. More concretely, our universe is a five- dimensional anti-de Sitter space and the elementary particles except for the graviton are localized on a (3+1)-dimensional brane or branes.  Proposed in 1999 by Lisa Randal and Raman Sundrum  A simple cosmological model of this kind is based on the second Randall-Sundrum (RSII) model  Inflation is driven by the tachyon field originating in string theory
  11. 11. The RSI Model  The model was originally proposed as a possible mechanism for localizing gravity on the 3+1 universe embedded in a 4+1 dimensional space-time without compactification of the extra dimension.  Observer – negative tension brane; separation - such that the strength of gravity on observer’s brane is equal to the observed four- dimensional Newtonian gravity.  x 5 x z 0z  z l 5( )d x z   N. Bilic, “Space and Time in Modern Cosmology”
  12. 12. The RS II Model  Observers reside on the positive tension brane and the negative tension brane is pushed off to infinity.  The Planck mass scale is determined by the curvature of the AdS space- time rather than by the size of the fifth dimension.  Radion – massless scalar field; fluctuation of interbrane distance along extra dimension z   z  0z  N. Bilic, “Space and Time in Modern Cosmology”
  13. 13. Randal-Sundrum model and tachyon-like inflation  Cosmology on the brane is obtained by allowing the brane to move in the bulk. Equivalently, the brane is kept fixed at z=0 while making the metric in the bulk time dependent.  The fluctuation of the interbrane distance along the extra dimension implies the existence of the radion.  Radion - a massless scalar field that causes a distortion of the bulk geometry.  The bulk spacetime of the extended RSII model in Fefferman-Graham coordinates is described by the metric     2 2 2 2 (5) 22 2 2 2 1 1 1 ( ) 1 ( ) a b abds G dX dX k z x g dx dx dz k z k z x                The bulk space-time metric The spatially flat FRW metric
  14. 14. Randal-Sundrum model and tachyon-like inflation  , ,4 4 2 2 2 , , 4 4 2 2 3 1 (1 ) 1 16 2 (1 ) gR S d x g g d x g k G k k                              1/k   2 sinh 4 / 3 G   br S (0) 4 br , ,4 1S d x g g 2 , , , , 4 3 1 1 2 g g                4 k    2 2 1 k    the brane tension 2 8 2 1 3 3 a G G H a k         
  15. 15. Hamilton’s Equations  The Hamiltonian density  Hamilton’s equations  Nondimensionalization 2 2 2 8 2 4 1 1 / ( ) 2 H 3 3 H H H H H H 2 4 / , / ( ), / ( )), , / ( ) h H k k k k k
  16. 16. Randal-Sundrum model  The dimensionless Hamiltonian’s equations are obtained 4 8 2 8 2 2 8 2 10 2 5 8 2 1 / 4 3 / 3 2 1 / 4 3 / 3 1 / h h                                                    2 2 2 2 8 1 3 12 Gk a h a                2 2 2 2 2 2 2 2 3 4 2 2 4 2 3 1 , sinh , 6 2 sinh , 6 3 1 1 / , 2 1 1 2 1 / d d p                                                  A combined dimensionless coupling The Hubble expansion rate preassure energy density 2 2 ( ) 1 2 6 h p N h               Additional equations, solved in parallel
  17. 17. Randal-Sundrum model  Slow-roll parameters are  Observational parameters: the tensor-to-scalar ration (r) and scalar spectral index (ns) * 0 1ln | | , 1i i H H d i Hdt     *-Hubble rate at an arbitrarily chosen timeH 1 i 1 i 2 i 2 s 1 i 2 i 1 i 1 i 2 i 2 i 3 i 1 16 ( ) 1 ( ) ( ) 6 8 1 2 ( ) ( ) 2 ( ) 2 ( ) ( ) ( ) ( ) 3 r C n C C                                
  18. 18. Numerical solution  Initial values:  Tachyion field: inverse quartic tachyon potential  No a priori reason to restrict possible initial values of the radion field; a range of initial values based on the natural scale dictated by observations.  Conjugate momenta  After the system of equation is solved, the slow-roll parameters are calculated  Conditions: 0 0 0 1 ( ) 1 ( ) ( ) f f i N N N 6 1 4 1 0 2 1 1, 192 3 ( ) N
  19. 19. Numerical results
  20. 20. Numerical results 0 60 120 1 12 0.05 0.5 N
  21. 21. Numerical results
  22. 22. Numerical results
  23. 23. Numerical results 0 0 60 120, 1 12 and 0 0.5 (left) 115 120, 0.05, 1.25 (right) N N
  24. 24. Conclusion  We have investigated a model of inflation based on the dynamics of a D3-brane in the AdS5 bulk of the RSII model. The bulk metric is extended to include the back reaction of the radion excitations.  The slow-roll equations of the tachyon inflation are quite distinct to those of the standard tachyon inflation with the same potential.  The ns-r relation in our model is substantially different from the standard one and is closer to the best observational value.  The agreement with observations is not ideal and it is fair to say that the present model is disfavoured but not excluded.  However, the model is based on the brane dynamics which results in a definite potential with one free parameter only.  We have analysed the simplest tachyon model. In principle, the same mechanism could lead to a more general tachyon potential if the AdS5 background metric is deformed by the presence of matter in the bulk
  25. 25. References  D. Steer, F. Vernizzi, Tachyon inflation: Tests and comparison with single scalar field inflation, Phys. Rev. D. 70 (2004) 43527.  N. Bilic, G.B. Tupper, AdS braneworld with backreaction, Cent. Eur. J. Phys. 12 (2014) 147–159.  P.A.R. Ade, N. Aghanim, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, et al., Planck 2015 results: XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20.  L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)  N. Bilic, D. Dimitrijevic, G. Djordjevic, M. Milosevic, Tachyon inflation in an AdS braneworld with back-reaction, (2016) 19. http://arxiv.org/abs/1607.04524.  M. Milosevic, D.D. Dimitrijevic, G.S. Djordjevic, M.D. Sto- janovic, Serb. Astron. J. 192, 1-8 (2016).  N. Bilic, D.D. Dimitrijevic, G.S. Djordjevic, M. Milosevic, M. Stojanovic, AIP Conf. Proc. 1722, 050002 (2016);

×